我们应该更多地听取谁的意见？面向多元化对齐的福祉感知偏好获取

# Who Should We Listen to More?Welfare-Aware Preference Acquisition forPluralistic Alignment
Source: [https://arxiv.org/html/2610.19035](https://arxiv.org/html/2610.19035)
Tianwei Gao\*Affiliation:University of North Carolina at Chapel HillLianrui GengAffiliation:University of North Carolina at Chapel HillMohit BansalAffiliation:University of North Carolina at Chapel HillZhun Deng††thanks:Contact: zhundeng@cs\.unc\.eduAffiliation:University of North Carolina at Chapel Hill

###### Abstract

Pluralistic alignment needs to accommodate diverse preferences under limited human feedback\. Using AI simulators to label preference comparisons reduces annotation costs, but variation in simulation accuracy across individuals can leave some people’s preferences poorly represented in training\. We study how to allocate human feedback across people to construct training data for pluralistic alignment, and how this allocation affects the trained policy\. To make this allocation explicit and controllable, we define a social welfare objective over individual supervision utilities that measure label quality\. Each query’s marginal welfare gain depends on its expected supervision improvement, the recipient’s current utility, and application\-designated priority\. Welfare\-Aware Preference Acquisition \(WAPA\) uses auxiliary reference models to estimate query gains and individual utilities, then selects queries by estimated marginal welfare gain while updating recipient utilities\. We prove exact optimality of the acquisition algorithm for the estimated welfare objective under a fixed query budget and model predictions\. Experiments on six Roleplay collections and four OpinionQA regions demonstrate improved supervision and controllable allocation tradeoffs\. Policy training on four Roleplay collections improves preference prediction for both seen and unseen individuals\. When prioritizing a designated group and poorly represented individuals, acquiring human labels for 20% of comparisons recovers 75–86% of the average predictive utility gap between policies trained entirely on AI\-generated labels and entirely on ground\-truth labels\. Our code is released at[https://github\.com/ZDCSlab/Welfare\-Aware\-Preference\-Acquisition](https://github.com/ZDCSlab/Welfare-Aware-Preference-Acquisition)\.

## 1Introduction

Aligning language models with human preferences often requires costly human feedback\. Large language models provide preference labels at scale\[[Lee et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib42)\]\. Here, they serve as AI simulators, using individual profiles to predict preferences over response pairs\. Under a limited budget, human feedback is allocated to selected comparisons, while AI\-generated labels provide supervision for the rest\[[Miranda et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib35)\]\. For pluralistic alignment, which seeks to accommodate diverse preferences\[[Sorensen et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib9)\], differences in simulation accuracy across individuals create different needs for human feedback\. A shared budget therefore raises the question:*who should we listen to more*when selecting feedback for pluralistic alignment?

We study preference acquisition as training data collection for pluralistic alignment\. Preference\-based training uses such data to learn individual and group preferences\[[Singh et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib33);[Zhang et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib16)\]\. Allocating a limited human\-feedback budget determines whose preferences receive more accurate supervision for downstream training\. Existing acquisition methods select feedback to improve policy learning\[[Muldrew et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib23);[Lin et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib30)\], while active elicitation supports preference inference and personalized responses\[[Shenfeld et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib3);[Blair et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib40)\]\. Selecting useful feedback does not by itself specify how supervision gains should be valued across recipients: allocations with similar average gains can benefit different individuals\. We make the value of these gains to their recipients explicit in the acquisition objective and examine how the resulting allocation affects downstream policy alignment\. This raises two connected questions: ❶*how should acquisition balance supervision improvements across people*, and ❷*do these allocation choices translate into better alignment with diverse preferences after policy training?*

Following[Castricato et al\. \[2025\]](https://arxiv.org/html/2610.19035#bib.bib14), we call an individual represented by a user profile a*persona*\. We distinguish two priorities in valuing an improvement in supervision for a given persona: \(1\)*Current disadvantage in supervision quality*\. Among queries with similar expected supervision gains, acquisition should place greater weight on personas whose preferences are currently represented less accurately\. This priority is dynamic: as a persona’s estimated supervision utility improves, its disadvantage decreases\. The goal is to avoid leaving some personas poorly served even when average supervision quality is high\[[Chakraborty et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib21);[Ramesh et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib22)\]\. \(2\)*Fixed application\-designated importance*\. An application may assign higher, fixed weights to personas whose needs or preferences are especially relevant to its purpose, independent of how accurately their preferences are currently represented\. For example, drawing on the preference setting of[Mukherjee et al\. \[2026\]](https://arxiv.org/html/2610.19035#bib.bib2), an educational assistant designed for guided practice may place greater weight on users who prefer Socratic guidance over brief answers\. These two priorities need not align: a persona that is especially important to the application may already be well represented, whereas a poorly represented persona may not belong to the application\-priority group\.

We define each persona’s supervision utility as a measure of how accurately the training supervision represents their preferences\. We aggregate these utilities through a social welfare objective\[[Zhong et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib45)\]that expresses the two allocation priorities\. The marginal welfare gain of a query depends on its expected supervision improvement, the recipient’s current utility, and their application\-designated priority\. To our knowledge, we provide the first welfare\-based formulation of fair human\-feedback budget allocation for pluralistic alignment training data\.

Human preference labels are unavailable before acquisition, so query gains and persona utilities must be estimated\. We introduce Welfare\-Aware Preference Acquisition \(WAPA\), which uses auxiliary reference models to estimate both quantities from errors in AI\-generated labels\. At each step, WAPA selects the query with the largest estimated marginal welfare gain and updates the recipient’s estimated utility before the next selection\. We prove that this greedy rule exactly maximizes the estimated welfare objective under a fixed query budget, with model predictions held fixed\. Human labels on selected comparisons and AI\-generated labels on the remaining comparisons together form the preference dataset for downstream policy training\.

We evaluate WAPA for feedback budget allocation on six Roleplay collections and four OpinionQA regions, with downstream policy alignment experiments on four Roleplay collections\. At a 20% human\-feedback budget, WAPA improves supervision quality across the population, the lowest\-utility 10% of personas, and a predefined target group\. Varying welfare priorities controls the tradeoffs among these acquisition outcomes\. Training on these labels improves preference prediction for seen and unseen personas\. When prioritizing a designated group and personas with lower supervision quality, WAPA recovers 75–86% of the average predictive utility gap between policies trained entirely on AI\-generated labels and entirely on ground\-truth labels\.

Our contributions are threefold:

- •We formulate human\-feedback budget allocation for pluralistic alignment training data through a social welfare objective\. The formulation accounts for both personas whose preferences are poorly represented in training supervision and application\-designated priorities\.
- •We develop WAPA, which estimates query gains and persona utilities to select feedback by marginal welfare gain\. We prove exact optimality of the acquisition algorithm for the estimated welfare objective under a fixed query budget and model predictions\.
- •Experiments on Roleplay and OpinionQA characterize how welfare priorities shape allocation and supervision quality\. Policy training on Roleplay improves preference prediction for seen and unseen personas over Random and welfare\-matched Entropy at matched feedback budgets\.

![Refer to caption](https://arxiv.org/html/2610.19035v1/framework.png)Figure 1:Welfare\-aware preference acquisition for pluralistic alignment\.
## 2Problem Setup

We formalize the allocation of a shared human\-feedback budget across persona\-specific preference comparisons to construct supervision for downstream pluralistic alignment\.

Preference acquisition protocol\.We consider a population ofNNpersonas, each specified through a user profile as illustrated in Figure[1](https://arxiv.org/html/2610.19035#S1.F1)A, andMMcommon prompts\. Write\[n\]=\{1,…,n\}\[n\]=\\\{1,\\ldots,n\\\}and let𝒞=\[N\]×\[M\]\\mathcal\{C\}=\[N\]\\times\[M\]index the comparison pool\. For each persona–prompt pair\(i,j\)∈𝒞\(i,j\)\\in\\mathcal\{C\}, we consider two fixed candidate responsesri​j1r\_\{ij\}^\{1\}andri​j0r\_\{ij\}^\{0\}to promptjjfor personaii\. The initially unobserved labelYi​j∈\{0,1\}Y\_\{ij\}\\in\\\{0,1\\\}records that persona’s preference, withYi​j=1Y\_\{ij\}=1indicating preference forri​j1r\_\{ij\}^\{1\}overri​j0r\_\{ij\}^\{0\}\. We denote the true preference probability bypi​j∗:=Pr\(Yij=1\)p\_\{ij\}^\{\*\}:=\\ProbOp\(Y\_\{ij\}=1\)\. A fixed base modelπ0\\pi\_\{0\}estimates this probability asp^i​j\\widehat\{p\}\_\{ij\}\. A*query*reveals the true preference label of one comparison\. The query budgetBBspecifies how many labels we can acquire\. After queryingS⊆𝒞S\\subseteq\\mathcal\{C\}, we denote the resulting preference dataset by𝒟S\\mathcal\{D\}\_\{S\}\. It retains allN​MNMcomparisons with their persona profiles, prompts, and candidate responses, using observed labelsYi​jY\_\{ij\}onSSand soft pseudo\-labelsp^i​j\\widehat\{p\}\_\{ij\}elsewhere\.

Persona supervision utility\.We evaluate probabilistic preference supervision quality using a strictly proper scoring rule, whose expected loss is uniquely minimized by the true preference probability\[[Gneiting and Raftery, 2007](https://arxiv.org/html/2610.19035#bib.bib32)\]\. We adopt Brier loss as a concrete implementation choice\. Specifically, for a query setS⊆𝒞S\\subseteq\\mathcal\{C\}, we define personaii’s supervision utility in a natural and simple way as:

Ui\(S\):=1−1M∑j:\(i,j\)<SE\(p^i​j−Yi​j\)2,U\_\{i\}\(S\):=1\-\\frac\{1\}\{M\}\\sumop\\displaylimits\_\{j:\(i,j\)\\notin S\}\\mathbb\{E\}\(\\widehat\{p\}\_\{ij\}\-Y\_\{ij\}\)^\{2\},\(1\)where the expectation is over the preference labelYi​jY\_\{ij\}for each comparison\. Queried comparisons contribute zero loss because their labels are known, while unqueried comparisons retain the target model’s predictions\.

Social welfare and allocation priorities\.Following previous research on social welfare and fair resource allocation\[[Harsanyi, 1955](https://arxiv.org/html/2610.19035#bib.bib6);[Atkinson, 1970](https://arxiv.org/html/2610.19035#bib.bib8);[Mo and Walrand, 2000](https://arxiv.org/html/2610.19035#bib.bib7)\], we assign each persona a positive weightwiw\_\{i\}, normalized so that∑i=1Nwi=1\\sumop\\displaylimits\_\{i=1\}^\{N\}w\_\{i\}=1\. For a query setSS, define:

J⁡\(S\)=∑i=1Nwi​hρ​\(Ui​\(S\)\+ε\),hρ​\(u\)=\{uρ/ρ,ρ​,0,log⁡u,ρ=0,J\(S\)=\\sumop\\displaylimits\_\{i=1\}^\{N\}w\_\{i\}h\_\{\\rho\}\\\!\\left\(U\_\{i\}\(S\)\+\\varepsilon\\right\),\\qquad h\_\{\\rho\}\(u\)=\\begin\{cases\}u^\{\\rho\}/\\rho,&\\rho\\neq 0,\\\\\[2\.0pt\] \\log u,&\\rho=0,\\end\{cases\}\(2\)whereρ61\\rho\\leqslant 1andε\>0\\varepsilon\>0is a fixed positive shift\. The curvature parameterρ\\rhocontrols sensitivity to low supervision utility\. Atρ=1\\rho=1, improvements are valued linearly; forρ<1\\rho<1, concavity favors gains for personas with lower utility, holding their weights fixed\. Smallerρ\\rhostrengthens this priority\. Further, the weight parameterswiw\_\{i\}reflect the consideration on application\-specific subgroup priority\. Specifically, for a designated subgroupG⊆\[N\]G\\subseteq\[N\], called the*Target subgroup*, we use the following weight parameters to show additional attention allocated to this subgroup:

wi=1\+\(γ−1\)𝟏\{i∈G\}N\+\(γ−1\)​\|G\|,γ\>1\.w\_\{i\}=\\frac\{1\+\(\\gamma\-1\)\\mathbf\{1\}\\\{i\\in G\\\}\}\{N\+\(\\gamma\-1\)\|G\|\},\\qquad\\gamma\\geqslant 1\.\(3\)
Hereγ\>1\\gamma\>1increases Target members’ weights, reflecting the importance assigned to representing their preferences in downstream application\. The acquisition objective is

maxS⊆𝒞⁡J⁡\(S\),subject to​\|S\|=B\.\\max\_\{\\begin\{subarray\}\{c\}S\\subseteq\\mathcal\{C\}\\end\{subarray\}\}J\(S\),\\text\{ subject to \}\|S\|=B\.\(4\)Setting\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)then recovers average supervision utility maximization\. In Section[3\.3](https://arxiv.org/html/2610.19035#S3.SS3), we shall analyze the theoretical benefits of this welfare design: first, suitable weight parameters can support an allocation meeting jointly feasible group\-wise requirements atρ=1\\rho=1\. Second, we examine how negative values ofρ\\rhoshape the tradeoff between target\-subgroup priority and fairness considerations for personas with lower supervision utility\.

## 3Method

In this section, we introduce the Welfare\-Aware Preference Acquisition \(WAPA\) framework\. Our approach is guided by two principles: ❶ quantify each query’s welfare gain by estimating persona supervision utilities and social welfare without observing the true preference labels; and ❷ allocate the shared labeling budget to maximize estimated welfare\. We first introduce our cross\-model approach to utility and welfare estimation, then present our welfare\-aware acquisition algorithm\. Finally, our theoretical analysis examines how the welfare objective balances the two desiderata in query allocation and establishes the algorithm’s optimality for the estimated welfare objective\.

### 3\.1Welfare\-Aware Preference Acquisition \(WAPA\)

In this subsection, we first estimate persona supervision utilities and develop an acquisition algorithm that maximizes the resulting estimated welfare objective under the shared query budget\. For utility estimation, we adopt a cross\-model approach, using predictions fromTTreference models as an empirical proxy for the underlying distribution of the true label in Eq\. \([1](https://arxiv.org/html/2610.19035#S2.E1)\)\. Specifically, for comparison\(i,j\)\(i,j\), letq^i​j\(t\)∈\[0,1\]\\widehat\{q\}\_\{ij\}^\{\(t\)\}\\in\[0,1\]denote reference modeltt’s prediction for the eventYi​j=1Y\_\{ij\}=1\. We use their ensemble meanμ^i​j:=1T​∑t=1Tq^i​j\(t\)\\widehat\{\\mu\}\_\{ij\}:=\\frac\{1\}\{T\}\\sumop\\displaylimits\_\{t=1\}^\{T\}\\widehat\{q\}\_\{ij\}^\{\(t\)\}as an estimate ofpi​j∗p\_\{ij\}^\{\*\}and substitute this estimate into Eq\. \([1](https://arxiv.org/html/2610.19035#S2.E1)\), yielding the plug\-in estimators of persona utilityand welfare:

U^i​\(S\)\\displaystyle\\widehat\{U\}\_\{i\}\(S\)=1−1M∑j:\(i,j\)<S\[μ^i​j\(1−p^i​j\)2\+\(1−μ^i​j\)p^i​j2\],J^\(S\)=∑i=1Nwihρ\(U^i\(S\)\+ε\)\.\\displaystyle=1\-\\frac\{1\}\{M\}\\sumop\\displaylimits\_\{j:\(i,j\)\\notin S\}\\left\[\\widehat\{\\mu\}\_\{ij\}\(1\-\\widehat\{p\}\_\{ij\}\)^\{2\}\+\(1\-\\widehat\{\\mu\}\_\{ij\}\)\\widehat\{p\}\_\{ij\}^\{\\,2\}\\right\],\\quad\\widehat\{J\}\(S\)=\\sumop\\displaylimits\_\{i=1\}^\{N\}w\_\{i\}h\_\{\\rho\}\\\!\\left\(\\widehat\{U\}\_\{i\}\(S\)\+\\varepsilon\\right\)\.\(5\)We further define WAPA scoresi​j:=μ^i​j​\(1−p^i​j\)2\+\(1−μ^i​j\)​p^i​j2s\_\{ij\}:=\\widehat\{\\mu\}\_\{ij\}\(1\-\\widehat\{p\}\_\{ij\}\)^\{2\}\+\(1\-\\widehat\{\\mu\}\_\{ij\}\)\\widehat\{p\}\_\{ij\}^\{\\,2\}to be the estimated Brier loss for persona\-prompt pair\(i,j\)\(i,j\), reflecting the estimated utility gain for querying the true human label\. Building on this estimation, we quantify the welfare gain for each query and present our main algorithm \(Algorithm[1](https://arxiv.org/html/2610.19035#alg1)\) for welfare\-aware budget allocation across personas \(Figure[1](https://arxiv.org/html/2610.19035#S1.F1)B\)\.

Algorithm 1Welfare\-aware preference acquisition \(WAPA\)1:Estimated welfare

J^​\(⋅\)\\widehat\{J\}\(\\cdot\), comparison pool

𝒞\\mathcal\{C\}, budget

BB
2:

S←?S\\leftarrow\\varnothing
3:for

t=1,…,Bt=1,\\ldots,Bdo

4:

\(it,jt\)∈arg⁡max\(i,j\)∈𝒞∖S​\[J^​\(S∪\{\(i,j\)\}\)−J^​\(S\)\]\(i\_\{t\},j\_\{t\}\)\\in\\arg\\max\_\{\(i,j\)\\in\\mathcal\{C\}\\setminus S\}\\left\[\\widehat\{J\}\(S\\cup\\\{\(i,j\)\\\}\)\-\\widehat\{J\}\(S\)\\right\]
5:

S←S∪\{\(it,jt\)\}S\\leftarrow S\\cup\\\{\(i\_\{t\},j\_\{t\}\)\\\}
6:endfor

7:return

SS

We remark that the welfare gain has the following first\-order expansion, illustrating why this welfare\-based acquisition process reflects both the target subgroup priority and the fairness consideration for low supervision utility persona:

�i​j​\(S\)≈si​jM×wi×\(U^i​\(S\)\+ε\)ρ−1\.\\Delta\_\{ij\}\(S\)\\approx\{\\frac\{s\_\{ij\}\}\{M\}\}\\times\{w\_\{i\}\}\\times\{\\bigl\(\\widehat\{U\}\_\{i\}\(S\)\+\\varepsilon\\bigr\)^\{\\rho\-1\}\}\.\(6\)where first term illustrates the estimated utility gain, the second term represents the priority received by personas in target subgroup\. Forρ<1\\rho<1, the third term gives greater weight to personas with lower current estimated supervision utility\. Algorithm[1](https://arxiv.org/html/2610.19035#alg1)is simple to implement and computationally efficient: each step selects the query with the largest estimated welfare gain and updates only the recipient’s estimated utility, and uses precomputed model predictions throughout\. We shall formalize its optimality in Theorem[3\.3](https://arxiv.org/html/2610.19035#S3.Thmtheorem3)that this greedy procedure exactly maximizes the estimated welfare objectiveJ^\\widehat\{J\}under the query budget without model retraining during acquisition\. We defer its time complexity results to Appendix[C\.1](https://arxiv.org/html/2610.19035#A3.SS1)\.

### 3\.2From Preference Acquisition to Pluralistic Alignment

Alignment objective\.Following[Miranda et al\. \[2025\]](https://arxiv.org/html/2610.19035#bib.bib35), the selected human labels and remaining AI supervision jointly train the policy \(Figure[1](https://arxiv.org/html/2610.19035#S1.F1)C\)\. We implement alignment using Direct Preference Optimization \(DPO\), initializing the policy fromπ0\\pi\_\{0\}and retaining a fixed copy as its reference\. Following[Rafailov et al\. \[2023\]](https://arxiv.org/html/2610.19035#bib.bib31), letfθ​\(i,j\)f\_\{\\theta\}\(i,j\)denote the DPO\-implied preference probability of a policy with parametersθ\\theta\. LetℓCE\\ell\_\{\\mathrm\{CE\}\}denote binary cross\-entropy\. The alignment objective isdefined as

ℒalign\(θ;S\)=1N​M\[\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{align\}\}\(\\theta;S\)=\\frac\{1\}\{NM\}\\Bigg\[∑\(i,j\)∈SℓCE\(Yi​j,fθ\(i,j\)\)\+∑\(i,j\)∈𝒞∖SℓCE\(p^i​j,fθ\(i,j\)\)\],\\displaystyle\\sumop\\displaylimits\_\{\(i,j\)\\in S\}\\ell\_\{\\mathrm\{CE\}\}\\\!\\left\(Y\_\{ij\},f\_\{\\theta\}\(i,j\)\\right\)\+\\sumop\\displaylimits\_\{\(i,j\)\\in\\mathcal\{C\}\\setminus S\}\\ell\_\{\\mathrm\{CE\}\}\\\!\\left\(\\widehat\{p\}\_\{ij\},f\_\{\\theta\}\(i,j\)\\right\)\\Bigg\],\(7\)
The welfare priorities affect alignment through the selected setSS, directing observed feedback toward preferences that are poorly captured or assigned greater importance\. AI\-generated preference labels are commonly used directly as supervision\[[Suh et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib1);[Miranda et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib35)\]\. Building on prediction\-powered inference\[[Angelopoulos et al\., 2023](https://arxiv.org/html/2610.19035#bib.bib4);[Sui et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib5)\], we also introduce a theoretically motivated refinement that uses acquired human preference labels to correct bias in plug\-in pseudo\-labels\. After welfare\-aware acquisition, direct use of plug\-in pseudo\-labels yields similar downstream Mean predictive utility, while refinement improves Tail utility \(Appendix[G\.16](https://arxiv.org/html/2610.19035#A7.SS16)\)\. We provide implementation details in Appendix[D\.3](https://arxiv.org/html/2610.19035#A4.SS3)\. We further provide a conditional generalization bound under certain assumptions linking supervision utility to downstream preference prediction error \(Appendix[C\.4](https://arxiv.org/html/2610.19035#A3.SS4)\)\.

### 3\.3Theoretical Analysis

In this section, we provide theoretical analysis for our framework design\. For fixedB\>0B\>0, we denote𝒮B\\mathcal\{S\}\_\{B\}the collection of all acquisition setsSSwith size\|S\|=B\|S\|=B\. For givenρ61\\rho\\leqslant 1and positive normalized weightww,Sρ,wS\_\{\\rho,w\}will always denote a welfare optimizer for Equation \([4](https://arxiv.org/html/2610.19035#S2.E4)\), i\.e\.,

Sρ,w∈arg⁡max⁡∑iS∈𝒮B⁡wi​hρ​\(Ui​\(S\)\+ε\),S\_\{\\rho,w\}\\in\\arg\\max\_\{S\\in\\mathcal\{S\}\_\{B\}\}\\sumop\\displaylimits\_\{i\}w\_\{i\}h\_\{\\rho\}\(U\_\{i\}\(S\)\+\\varepsilon\),\(8\)andSρ,unifS\_\{\\rho,\\mathrm\{unif\}\}denotes a maximizer of the same objective with equal weights\.

Weighted welfare objective supports subgroup priority\.First, we illustrate why the welfare weight parameters introduced in Section[2](https://arxiv.org/html/2610.19035#S2)matter for pluralistic alignment under limited feedback\. We focus on subgroup priority: mean\-utility maximization can leave subgroup requirements unmet even when they are jointly feasible within the budget\. We then show that suitable welfare weights can induce an allocation that meets these needs\.

Specifically, fixKKsubgroups\{Gk\}k=1K\\\{G\_\{k\}\\\}\_\{k=1\}^\{K\}forming a partition of\[N\]\[N\], and for each nonempty subgroupGkG\_\{k\}, letu¯k∈\[0,1\]\\underline\{u\}\_\{k\}\\in\[0,1\]denote its minimum acceptable average supervision utility\. The corresponding requirements are:

1\|Gk\|​∑i∈GkUi​\(S\)\>u¯k,k∈\[K\]\.\\frac\{1\}\{\|G\_\{k\}\|\}\\sumop\\displaylimits\_\{i\\in G\_\{k\}\}U\_\{i\}\(S\)\\geqslant\\underline\{u\}\_\{k\},\\qquad k\\in\[K\]\.\(9\)These requirements are jointly feasible if some allocationS⊆𝒞S\\subseteq\\mathcal\{C\}with\|S\|=B\|S\|=Bsatisfies them all\. They provide a concrete way to examine what the welfare objective can express\.

###### Theorem 3\.1\(Informal\)\.

\(a\)\(a\)For anyδ∈\(0,1\)\\delta\\in\(0,1\), there exists a two\-subgroup instance with jointly feasible requirements andu¯1=1\\underline\{u\}\_\{1\}=1, yet every allocation maximizing unweighted mean utility under the shared budget leavesG1G\_\{1\}with average utilityδ\\delta\.

\(b\)\(b\)Suppose the groups form a partition of the population and their requirements are jointly feasible\. Then there exist positive normalized weights, constant within each subgroup, such that at least one maximizer ofJ⁡\(S\)J\(S\)withρ=1\\rho=1satisfies all requirements\.

Suitable weights can therefore support an allocation that meets feasible subgroup requirements while preserving as much average utility as those requirements permit\.

Negativeρ\\rhoshape the trade\-off between target subgroup priority and fairness considerationWe further show that choosing negativeρ\\rhoadds a trade off between target subgroup priority and fairness consideration for supervision disadvantage in the following theorem\.

###### Theorem 3\.2\(Informal\)\.

Assume there is a unique feasible allocation that maximizes the minimum persona utility\. For any fixedε\>0\\varepsilon\>0and positive normalized weights, there exists a sufficiently smallρ0<0\\rho\_\{0\}<0, such that whenρ<ρ0\\rho<\\rho\_\{0\}, both weighted and unweighted welfare have this max–min allocation as a unique maximizer\.

Together, these components connect individual preference representation to a population\-level objective\. We defer the formal statements and proofs of these theorems to Appendix[C\.2](https://arxiv.org/html/2610.19035#A3.SS2)\.

Algorithm[1](https://arxiv.org/html/2610.19035#alg1)achieves optimality for the estimated welfare objective\. For fixedρ,w\\rho,wand model estimations, we denoteS^ρ,w\\widehat\{S\}\_\{\\rho,w\}the outcome of Algorithm[1](https://arxiv.org/html/2610.19035#alg1)\. The following theorem establishes thatS^ρ,w\\widehat\{S\}\_\{\\rho,w\}is an exact maximizer of the welfare objective\. Its proof is deferred to Appendix[C\.3](https://arxiv.org/html/2610.19035#A3.SS3)\.

###### Theorem 3\.3\(Exact optimality of WAPA\)\.

LetS^ρ,w\\widehat\{S\}\_\{\\rho,w\}denote the output of Algorithm[1](https://arxiv.org/html/2610.19035#alg1)\. Then it satisfiesJ^​\(S^ρ,w\)=maxS∈𝒮B⁡J^​\(S\)\.\\widehat\{J\}\(\\widehat\{S\}\_\{\\rho,w\}\)=\\max\_\{S\\in\\mathcal\{S\}\_\{B\}\}\\widehat\{J\}\(S\)\.This conclusion allows zero scores and ties, and requires neither calibrated reference predictions nor independence among labels or reference models\.

## 4Experiments

We trace the effects of welfare\-aware acquisition from the queries selected to the policy trained on them, guided by three research questions \(RQs\)\.

- •RQ1: How effective is WAPA at preference acquisition?We test how much prediction error each method removes with the same label budget, across welfare settings \(Section[4\.1](https://arxiv.org/html/2610.19035#S4.SS1)\)\.
- •RQ2: How do welfare parameters shape acquisition tradeoffs?We examine who benefits as subgroup priorityγ\\gammaand sensitivity to supervision disadvantageρ\\rhovary \(Section[4\.2](https://arxiv.org/html/2610.19035#S4.SS2)\)\.
- •RQ3: Does WAPA improve downstream alignment?We test whether the selected queries improve preference prediction after downstream alignment \(DPO\) \(Section[4\.3](https://arxiv.org/html/2610.19035#S4.SS3)\)\.

Datasets and acquisition protocol\.Roleplay provides six persona collections with synthetic pairwise preferences\[[Singh et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib33)\]; OpinionQA provides four regional subsets with 3–5\-option questions\[[Santurkar et al\., 2023](https://arxiv.org/html/2610.19035#bib.bib12)\]\. Roleplay supports acquisition and DPO; OpinionQA evaluates acquisition only\. Main\-text Roleplay results cover Africa, Asia, North America, and Europe; the other collections appear in Appendix[G\.2](https://arxiv.org/html/2610.19035#A7.SS2)\. The base model is Qwen3\-4B\-Instruct\-2507, with Qwen3\.8\-Max, GLM\-5\.2, and DeepSeek\-V4\-Flash as references\. The main query budget covers 20% of all comparisons\. A fixed, randomly selected 10% of personas form the Target group\. We compare equal\-weight mean welfare\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)and target\-priority, inequality\-sensitive welfare\(2,−5\)\(2,\-5\), fixingε=0\.5\\varepsilon=0\.5\. Acquisition is simulated offline: methods select a complete batch from frozen predictions before revealing dataset labels, which serve as ground truth\. Only the Oracle accesses labels during selection \(Appendices[E\.1](https://arxiv.org/html/2610.19035#A5.SS1)–[G\.1](https://arxiv.org/html/2610.19035#A7.SS1)and[F\.3](https://arxiv.org/html/2610.19035#A6.SS3)\)\.

Compared methods\.Random samples uniformly; Entropy scores base\-model uncertainty; Reference Disagreement scores variance across reference predictions\. Active preference learning \(APL;[Muldrew et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib23)\) ranks implicit preference certainty\. Bayesian active learning for preference modeling \(BAL\-PM;[Melo et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib24)\) combines reference disagreement with prompt diversity\. Entropy and Reference Disagreement apply welfare weighting to their own scores under the same settings as WAPA; APL and BAL\-PM are welfare\-agnostic\. No queries retains initial predictions\. Welfare\-optimal Oracle uses all labels to maximize scalar welfare at the same query budget\. Implementation details appear in Appendix[F\.3](https://arxiv.org/html/2610.19035#A6.SS3)\.

Evaluation metrics\.For each personaii, predictive utility is one minus average normalized Brier loss:ui=1−12​Mi​∑j=1Mi‖𝐩i​jeval−𝐞yi​j‖22u\_\{i\}=1\-\\frac\{1\}\{2M\_\{i\}\}\\sumop\\displaylimits\_\{j=1\}^\{M\_\{i\}\}\\\|\\mathbf\{p\}^\{\\mathrm\{eval\}\}\_\{ij\}\-\\mathbf\{e\}\_\{y\_\{ij\}\}\\\|\_\{2\}^\{2\}\[[Gneiting and Raftery, 2007](https://arxiv.org/html/2610.19035#bib.bib32)\]\. HereMiM\_\{i\}is the number of evaluated comparisons,𝐩i​jeval\\mathbf\{p\}^\{\\mathrm\{eval\}\}\_\{ij\}is the evaluated probability vector, and𝐞yi​j\\mathbf\{e\}\_\{y\_\{ij\}\}is the observed one\-hot label\. Higher utility is better\. Acquisition utility increases as queried predictions are replaced with observed one\-hot labels, removing their prediction error\. Unqueried comparisons retain initial predictions\. Acquisition utility therefore measures the supervision quality of the resulting dataset\. Downstream utility instead uses trained\-policy probabilities on test comparisons\. Mean averages utility across all personas\. Tail averages the lowest\-utility 10% of personas, ranked separately for each method; Target averages the same designated personas across methods \(Appendix[F\.4](https://arxiv.org/html/2610.19035#A6.SS4)\)\.

Table 1:Acquisition utility \(%\) at 20% query budget with welfare\-agnostic and welfare\-weighted methods\. Bold marks the best budgeted method for each welfare setting\.MethodRoleplay\-AfricaRoleplay\-AsiaRoleplay\-North AmericaRoleplay\-EuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetNo queries81\.8777\.0580\.9681\.2577\.3782\.3181\.8177\.5781\.7281\.5077\.9180\.11Welfare\-agnostic baselines \(shared across settings\)APL82\.8678\.5081\.9482\.3679\.1683\.6882\.7378\.9982\.6482\.5078\.9481\.25BAL\-PM87\.0283\.3686\.4486\.4083\.2487\.3386\.7882\.8886\.5486\.5883\.3685\.43\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random85\.5381\.8184\.8785\.0481\.6585\.5385\.5382\.2985\.2385\.2382\.2584\.57Entropy86\.7581\.8385\.7086\.1882\.2687\.6986\.7682\.4786\.2586\.4382\.2184\.79Reference Disagreement87\.3783\.6086\.7586\.8683\.6387\.6986\.9883\.1986\.8687\.1583\.8886\.17WAPA90\.3887\.5390\.3989\.8487\.0689\.5490\.2287\.8190\.4590\.0887\.0689\.55Welfare\-optimal Oracle96\.7594\.6197\.0396\.4694\.3396\.0596\.7295\.1596\.8696\.4693\.1696\.68\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random85\.5381\.8184\.8785\.0481\.6585\.5385\.5382\.2985\.2385\.2382\.2584\.57Entropy86\.7782\.0987\.2986\.1882\.0989\.1786\.7582\.3487\.9486\.4482\.2686\.63Reference Disagreement87\.3583\.2290\.9586\.8383\.1991\.6386\.9782\.7090\.6687\.1083\.6190\.34WAPA90\.2487\.1194\.4389\.7186\.7893\.5390\.0287\.2494\.1789\.9687\.1393\.64Welfare\-optimal Oracle96\.7295\.1399\.6196\.4294\.6599\.4796\.6995\.1999\.4996\.4394\.1499\.49

Figure 2:Acquisition utility versus query budget under\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)\. All methods are evaluated at 1% budget increments\. Summaries below each subplot show the fraction of the initial\-to\-oracle utility gap recovered at 20% budget; the oracle uses full\-label access\.### 4\.1How effective is WAPA at preference acquisition under different welfare specifications?

Acquisition effectiveness at the main budget\.At a 20% query budget, WAPA achieves the highest Mean, Tail, and Target utility among budgeted methods in all four main datasets under both welfare specifications \(Table[1](https://arxiv.org/html/2610.19035#S4.T1)\)\. Across these comparisons, its gains over the strongest baseline in each metric range from 2\.86–3\.24 percentage points in Mean, 3\.18–4\.63 in Tail, and 1\.85–3\.64 in Target\. The advantage holds against baselines using the same welfare priorities as well as welfare\-agnostic methods\. At the same budget, WAPA therefore removes more base\-model prediction error on average\. WAPA also leads the methods evaluated on the two additional Roleplay datasets \(Appendix[G\.2](https://arxiv.org/html/2610.19035#A7.SS2)\)\.

Effectiveness across query budgets\.WAPA leads Random, Entropy, Reference Disagreement, APL, and BAL\-PM in Mean, Tail, and Target at every evaluated budget from 1% to 40%\. This holds across all four main datasets under both welfare specifications \(Figure[2](https://arxiv.org/html/2610.19035#S4.F2); Appendix[G\.3](https://arxiv.org/html/2610.19035#A7.SS3)\), extending the advantage beyond the main 20% budget\.

### 4\.2How do welfare parameters shape allocation and utility tradeoffs at the acquisition stage?

At a 20% budget, changing from\(1,1\)\(1,1\)to\(2,−5\)\(2,\-5\)raises WAPA’s Target utility by 3\.72–4\.09% while reducing Mean by 0\.11–0\.20%; Tail also decreases in most datasets\. We next vary one parameter at a time to separate these effects, keeping Target membership fixed \(Figure[3](https://arxiv.org/html/2610.19035#S4.F3)\)\.

Designated subgroup priority\.Atρ=1\\rho=1, raisingγ\\gammafrom 1 to 2 improves Target utility by 9\.01–10\.06 percentage points across the four main datasets while reducing Mean and Tail\. Higher subgroup priority directs more benefit toward Target members, who need not be initially worst\-off\. The selected query share confirms this shift: atρ=1\\rho=1, doublingγ\\gammaconcentrates over a third of the budget on the roughly 10% Target group\. Improving this designated group can therefore leave less feedback for poorly predicted personas outside it\.

Sensitivity to current disadvantage in supervision quality\.Changingρ\\rhofrom 1 to−5\-5improves Tail by 0\.08–0\.29 percentage points atγ=1\\gamma=1\. Atγ=2\\gamma=2, loweringρ\\rhofrom 1 to−5\-5raises Mean by 0\.41–0\.62 points and Tail by 1\.16–1\.54 points relative to\(2,1\)\(2,1\), while reducing Target utility\. Stronger sensitivity to supervision disadvantage moderates the costs of prioritizing Target\. As queries raise Target members’ estimated utilities, concavity reduces the marginal welfare gain from further queries to them\. Queries outside Target can then become more competitive\. Target membership specifies whom to prioritize;γ\\gammasets the strength of that priority, whileρ\\rhocontrols sensitivity to current disadvantage in supervision quality\. Their joint setting preserves a Target gain over\(1,1\)\(1,1\)without the full Mean and Tail costs of subgroup priority alone\. Appendix[G\.7](https://arxiv.org/html/2610.19035#A7.SS7)reports the parameter grid and an alternative Target based on initially low estimated utility\.

\(a\) Parameter effects

![Refer to caption](https://arxiv.org/html/2610.19035v1/parameter_effects.png)

\(b\) Outcome tradeoffs

![Refer to caption](https://arxiv.org/html/2610.19035v1/outcome_tradeoffs.png)

Figure 3:Parameter effects \(a\) and outcome tradeoffs \(b\) at 20% budget with a random 10% Target\. Changes from\(1,1\)\(1,1\)are in percentage points\. In \(a\), red shows Target gains and blue shows Tail losses\. In \(b\), paths holdγ\\gammafixed and follow decreasingρ\\rho; color shows Mean change\.
### 4\.3Does WAPA improve downstream alignment?

Each welfare setting specifies an acquisition objective\. We compare methods within each setting to test which selected labels most improve the trained policy at a fixed budget\. A separate parameter sweep tests how changing acquisition priorities affects downstream utility\.

Protocol\.Random, APL, BAL\-PM, Entropy, and WAPA query 20% of the training comparisons on the four main Roleplay datasets\. All use the same comparisons and DPO training protocol\. They differ in which comparisons receive human queries; the remainder retain base\-model probabilities as soft targets\. All pseudo\-labels trains entirely on base\-model probabilities; All ground\-truth labels trains entirely on dataset labels\. Figure[4](https://arxiv.org/html/2610.19035#S4.F4)and Figure[5](https://arxiv.org/html/2610.19035#S4.F5)report each utility gain over All pseudo\-labels as a percentage of the corresponding gain from All ground\-truth labels, marked at 100%\. We evaluate preference probabilities implied by each trained policy on new comparisons for training personas \(Seen\) and on new personas \(Held\-out\)\. Held\-out Target membership is fixed by persona\-description similarity to the acquisition Target\. Training and scoring details appear in Appendices[F\.5](https://arxiv.org/html/2610.19035#A6.SS5)and[F\.4](https://arxiv.org/html/2610.19035#A6.SS4)\.

Downstream gains\.With only 20% queried labels, WAPA recovers 74\.84–85\.74% of the Mean improvement from All pseudo\-labels to All ground\-truth labels under\(2,−5\)\(2,\-5\)\. BAL\-PM recovers 49\.72–59\.05% of the same reference gap, and matched Entropy recovers 40\.23–49\.38%\. These ranges cover all four datasets and both persona splits \(Figures[4](https://arxiv.org/html/2610.19035#S4.F4)and[5](https://arxiv.org/html/2610.19035#S4.F5)\)\. In absolute utility, WAPA exceeds BAL\-PM by 0\.30–0\.52 percentage points in Mean and 0\.70–1\.33 points in Tail\. Across both welfare settings, WAPA yields higher Mean and Tail utility than Random, APL, BAL\-PM, and matched Entropy \(Appendix[G\.9](https://arxiv.org/html/2610.19035#A7.SS9)\)\.

Figure 4:Seen personas: reference\-gap recovery at 20% query budget under\(2,−5\)\(2,\-5\)\. For every method and metric, 0% denotes All pseudo\-labels and 100% denotes All ground\-truth labels\.Figure 5:Held\-out personas: reference\-gap recovery at 20% query budget under\(2,−5\)\(2,\-5\)\. For every method and metric, 0% denotes All pseudo\-labels and 100% denotes All ground\-truth labels\.Tail and Target outcomes\.Under\(2,−5\)\(2,\-5\), WAPA recovers 71\.58–104\.71% of the Tail reference gap across both persona splits\. Recovery can exceed 100% because the fully labeled policy is a reference, not a performance bound\. WAPA’s Target utility exceeds matched Entropy by 0\.37–1\.00 percentage points on Seen personas and 0\.19–0\.70 points on the similarity\-defined Held\-out cohort\. The Held\-out results show that the benefit extends to personas whose labels were never available for acquisition\. The parameter sweep on North America and Africa puts these method gains in perspective\. Across four welfare settings, each Seen utility metric spans at most 0\.13 percentage points\. In the same datasets and split, WAPA’s gains over Random and matched Entropy are at least 0\.37 points under either main setting\. Appendix[G\.12](https://arxiv.org/html/2610.19035#A7.SS12)examines how the individual parameters affect Target and Tail utility\.

MethodNA \(↓\\downarrow\)Africa \(↓\\downarrow\)Overall \(↓\\downarrow\)First \(%,↑\\uparrow\)Random2\.8232\.6742\.74914\.7Entropy2\.6282\.6612\.64520\.1WAPA2\.2292\.3672\.29827\.3Full\-GT2\.3202\.2972\.30937\.9

Table 2:Human evaluation: mean rank \(1 = best\) and first\-place rate\.↓\\downarrow: lower is better;↑\\uparrow: higher is better\.Free\-response human evaluation\.We also assess whether generated responses suit the supplied personas on North America and Africa\. Random, Entropy, and WAPA acquire 20% of labels; Full\-GT uses all ground\-truth labels\. Thirteen blinded raters provided 128 rankings on an exploratory subset of 96 selected persona–prompt instances, assessing response suitability for each persona\. We average raters within instances, then instances equally\. WAPA achieves a better mean rank than Random and Entropy in both regions \(Table[2](https://arxiv.org/html/2610.19035#S4.T2)\)\. Its overall mean rank is close to Full\-GT \(2\.298 versus 2\.309\), while Full\-GT receives more first\-place rankings\. Human and judge evaluation details and qualitative cases appear in Appendices[J](https://arxiv.org/html/2610.19035#A10)and[I](https://arxiv.org/html/2610.19035#A9)\.

## 5Conclusion and Discussion

We formulated preference acquisition for pluralistic alignment as the allocation of a shared human\-feedback budget across people\. Our welfare objective values supervision gains according to recipients’ current supervision utilities and application\-designated priorities\. WAPA estimates gains and utilities using reference models and selects queries by marginal welfare gain\. Its greedy rule exactly optimizes the estimated objective under a fixed budget and fixed model predictions\.

This formulation makes the distribution of supervision improvements an explicit choice in training data collection\. Our experiments show that these priorities shape acquisition outcomes, and that training on the resulting data improves preference prediction for seen and unseen personas\. The findings connect decisions about whose feedback to acquire with how well a trained policy predicts diverse preferences\.

Future directions\.Evaluating this connection requires benchmarks that follow feedback allocation through to policy training\. We advocate developing such benchmarks with explicit acquisition priorities and measures of how benefits are distributed across people\. Evaluation with represented users would complement preference prediction with their judgments of generated responses\.

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## Appendix ARelated Work

Table[3](https://arxiv.org/html/2610.19035#A1.T3)summarizes the four research directions reviewed below\.

Table 3:Four related research directions and their relation to our work\.Research directionMain question in related workRelation to our workActive preference acquisitionWhich feedback should be collected to improve learning under a limited budget?We make the distribution of supervision gains across people an explicit part of acquisition\.Personalized / pluralistic alignmentHow can models learn or adapt to different individuals’ or groups’ preferences?Provides the alignment goal our acquisition serves\. We allocate a shared feedback budget to construct supervision for persona\-conditioned policy training\.Human–AI feedback allocationWhich queries should receive human feedback, and which can use AI feedback?Provides the labeling decision we study\. We account for persona\-level supervision quality and priorities when making that decision\.Social welfare and fair acquisitionHow should benefits and data\-collection resources be distributed across people or groups?Provides welfare formulations and allocation precedents\. We formulate and optimize welfare over preference\-supervision quality for alignment\.

### A\.1Active acquisition for preference modeling and policy alignment

Human preference feedback supplies supervision for alignment, and active acquisition decides which feedback to obtain under a limited budget\. Existing methods connect this selection to policy training\. Active Preference Learning \(APL\) uses generation entropy and implicit preference certainty to select feedback for direct preference optimization \(DPO\)\[[Muldrew et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib23)\]; ActiveDPO uses gradients of the policy’s implicit reward to guide acquisition and alternates selection with DPO updates\[[Lin et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib30)\]\.

Other methods target preference\-model estimation: Bayesian Active Learning for Preference Modeling \(BAL\-PM\) combines epistemic uncertainty with prompt diversity\[[Melo et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib24)\], Active Reward Modeling uses Fisher information and cross\-prompt comparisons\[[Shen et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib25)\], and Active Preference Optimization \(APO\) selects uncertain contexts with policy\-error guarantees under preference\-model assumptions\[[Das et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib38)\]\. Active Multi Preference Optimization \(AMPO\) selects response subsets for self\-play preference optimization\[[Gupta et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib27)\]; Joint Preference Optimization broadens the preference object to instruction–response pairs\[[Bansal et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib28)\]\.

These methods improve the use of feedback for learning\. We study how the supervision gains from a shared human\-feedback budget should be distributed across personas for pluralistic alignment\.

### A\.2Personalized and pluralistic alignment

Pluralistic alignment encompasses perspective coverage, steerability, and representation of population preferences\[[Sorensen et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib9)\]\. OpinionQA studies demographic opinions, PRISM links individual feedback to participant backgrounds, and the Community Alignment Dataset shows why diverse response candidates matter\[[Santurkar et al\., 2023](https://arxiv.org/html/2610.19035#bib.bib12);[Kirk et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib13);[Zhang et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib16)\]\.

Methods use these forms of heterogeneity in different ways: Group Preference Optimization adapts to group preferences\[[Zhao et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib11)\], PAL learns personalized reward models\[[Chen et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib10)\], CultureSPA constructs data for cultural alignment\[[Xu et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib15)\], and FSPO uses few\-shot preference optimization on synthetic data organized by user to train a personalized model\[[Singh et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib33)\]\. MaxMin\-RLHF and Group Robust Preference Optimization incorporate worst\-group priorities into policy training\[[Chakraborty et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib21);[Ramesh et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib22)\]\.

A complementary line actively elicits individual preferences: AMPLe infers multidimensional preference weights from comparisons\[[Oh et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib26)\], PReF combines active queries with reward factorization and inference\-time personalization\[[Shenfeld et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib3)\], GATE elicits task specifications through open\-ended interaction\[[Li et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib29)\], and reflective verbal reward design uses dialogue and critiques to construct individualized reward models\[[Blair et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib40)\]\. Variational Preference Learning \(VPL\) supports active latent\-preference inference; its active policy\-adaptation experiments use simulated control tasks, while its language experiments evaluate personalized reward modeling\[[Poddar et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib36)\]\.

Selection can also concern whose feedback to obtain: Annotator\-Centric Active Learning \(ACAL\) selects annotators to capture diverse judgments in subjective NLP tasks\[[van der Meer et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib44)\], and[Ding et al\. \[2026\]](https://arxiv.org/html/2610.19035#bib.bib34)jointly select respondents and questions using information gain and response propagation\.[Mahbub et al\. \[2026\]](https://arxiv.org/html/2610.19035#bib.bib37)query uncertain items for poorly represented personas, then use the feedback to constrain coherent labels for in\-context steering\. These are close precedents for selective elicitation and recipient\-aware acquisition\.

Personalized and pluralistic alignment provide the goal our acquisition serves\. Our focus is allocating a shared human\-feedback budget across personas to construct supervision for policy alignment: which personas and comparisons should receive human feedback, given explicit welfare priorities over supervision quality? Our batch is selected before its labels are observed\. This allocation constructs supervision for persona\-conditioned policy training and complements welfare objectives applied during policy optimization\.

### A\.3Human–AI feedback allocation

Hybrid preference routing \(HyPER\) directly studies which comparisons should receive human or model annotations\[[Miranda et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib35)\]\. It predicts the performance of reward models trained on candidate mixtures and selects a routing configuration using those predictions\. Its experiments evaluate reward modeling and best\-of\-NNresponse selection; transfer to DPO or reinforcement\-learning policy training is left open\. Preference\-Calibrated Active Learning allocates budget between ground\-truth labels and judgments over AI outputs to improve statistical estimation\[[Dong et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib41)\]\.

In our setting, acquisition assigns a limited human\-feedback budget to selected comparisons; the remaining comparisons receive AI supervision\. The allocation determines how accurately the training supervision represents each persona’s preferences\. We evaluate this distribution through social welfare, using reference\-based loss estimates for both query gains and persona utilities\. All comparisons contribute to alignment: acquired labels and unqueried AI probabilities jointly supervise DPO\[[Rafailov et al\., 2023](https://arxiv.org/html/2610.19035#bib.bib31)\], allowing us to test whether acquisition improvements translate into better preference prediction by the aligned policy\.

### A\.4Social welfare and fair acquisition

Social choice and welfare\-sensitive learning provide inspiration for explicitly valuing improvements across people\[[Conitzer et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib39);[Cousins, 2021](https://arxiv.org/html/2610.19035#bib.bib20)\]\.[Zhong et al\. \[2024\]](https://arxiv.org/html/2610.19035#bib.bib45)learn party\-specific rewards from offline comparisons and optimize a collective policy under Nash, Utilitarian, and Egalitarian welfare objectives\. These welfare objectives specify how a policy should serve different parties\. Our acquisition objective specifies how to allocate the human feedback used for alignment, evaluating welfare over persona\-level supervision quality\.

Fair acquisition supplies related inspiration: minimax sampling allocates observations across groups\[[Shekhar et al\., 2021](https://arxiv.org/html/2610.19035#bib.bib19)\], FAIR coordinates collaborative acquisition for mutual benefit\[[Xu et al\., 2023](https://arxiv.org/html/2610.19035#bib.bib17)\], and fair active learning combines exploration with constrained classification\[[Camilleri et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib18)\]\.[Cai et al\. \[2022\]](https://arxiv.org/html/2610.19035#bib.bib43)already optimize data\-collection budgets using group\-specific learning curves and utilities over group performance\.

Our formulation evaluates persona\-level preference supervision under human and AI labeling, with reference\-based loss estimates providing both query gains and current utilities\. Our guarantee concerns exact optimization of the estimated acquisition objective under fixed predictions; our DPO experiments evaluate the resulting policy\.

### A\.5Positioning our acquisition problem

Table[4](https://arxiv.org/html/2610.19035#A1.T4)distinguishes feedback acquisition for policy training, active elicitation for personalization, and alignment given preference data\. APL and ActiveDPO acquire feedback to train policies\[[Muldrew et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib23);[Lin et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib30)\]\. AMPLe and PReF actively query users to infer individual preferences for personalization\[[Oh et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib26);[Shenfeld et al\., 2025](https://arxiv.org/html/2610.19035#bib.bib3)\]; here, newly elicited feedback primarily updates the representation of a user’s preferences\. Personalized and pluralistic alignment also study how models should use available preference information, through training or adaptation\. These settings can overlap: personalization can involve training, and active elicitation is itself a form of feedback acquisition\.

Our setting combines feedback acquisition for policy training with explicit allocation priorities across personas\. We distribute a shared human\-feedback budget across personas and queries, using AI feedback for the remaining queries\. The acquisition objective evaluates how the resulting supervision represents different people’s preferences; downstream policy training tests the value of that supervision for alignment\.

Table 4:Feedback acquisition, personalization, and policy alignment: feedback use, decisions, and evaluation focus in representative settings and in our work\.SettingFeedback and its useDecision studiedEvaluation focusActive acquisition for policy alignmentAcquire preference labels under a limited budget to train a policyWhich queries improve learning most effectively?Aggregate policy win rate or reward, without persona\-level breakdownActive elicitation for personalizationQuery a user to infer personal preferences and guide responsesWhat should be asked next to understand this user?Individual preference inference and personalization qualityPersonalized / pluralistic alignment given preference dataUse available preferences to train or adapt models for individuals or groupsHow should the model accommodate diverse preferences?Individual\- or group\-level alignment qualityOur welfare\-aware acquisition for pluralistic alignmentCombine selected human feedback with AI feedback for persona\-conditioned policy trainingHow should a shared budget be allocated given query gains and priorities across personas?Mean, lower\-tail, and designated\-group supervision utility

## Appendix BLimitations

Evaluating pluralistic alignment in free responses\.Our main policy evaluation measures preference prediction on fixed response pairs\. Appendix[J](https://arxiv.org/html/2610.19035#A10)complements it with exploratory human rankings of generated responses on a selected sample\. Raters assess suitability for supplied persona profiles; this does not directly measure satisfaction among the people whose preferences are modeled\. Sample selection and differences between human and LLM judge rankings further limit generalization\. Broader evaluation should use representative samples and feedback from the represented users to assess preference fulfillment and the distribution of benefits across people\.

Scope of the theoretical guarantees\.WAPA’s exact optimality guarantee concerns the estimated acquisition welfare objective under fixed predictions\. Theorem[C\.6](https://arxiv.org/html/2610.19035#A3.Thmtheorem6)further relates supervision quality, training fit, and model complexity to prediction risk on fresh personas and prompts\. This result assumes independently sampled personas and prompts, conditionally independent labels, acquisition that is independent of pool labels, and bounded empirical fitting error\. It accounts for dependencies induced by shared personas and prompts, but does not establish that maximizing acquisition welfare maximizes downstream policy welfare\. Extending these guarantees to iterative acquisition that adapts to observed labels and updated policies remains open\.

## Appendix CAlgorithmic and Theoretical Details

In this section, we shall assume thatUi​\(S\)∈\[0,1\]U\_\{i\}\(S\)\\in\[0,1\]throughout for any queried setSSand personaii\.

### C\.1WAPA algorithmic details

We now present details for the WAPA Algorithm[1](https://arxiv.org/html/2610.19035#alg1)\. Algorithm[2](https://arxiv.org/html/2610.19035#alg2)presents the detailed procedure of WAPA with frozen predictions\. For personaii, letR=1M∑j:\(i,j\)<Ssi​jR=\\frac\{1\}\{M\}\\sumop\\displaylimits\_\{j:\(i,j\)\\notin S\}s\_\{ij\}denote its remaining estimated risk, so that its estimated utility is1−R1\-R\. For personaiiand an unqueried comparison with WAPA scoress, define the exact welfare gain

Gi​\(R,s\)=wi​\[hρ​\(1−R\+sM\+ε\)−hρ​\(1−R\+ε\)\],hρ​\(u\)=\{uρ/ρ,ρ​,0,log⁡u,ρ=0\.G\_\{i\}\(R,s\)=w\_\{i\}\\left\[h\_\{\\rho\}\\\!\\left\(1\-R\+\\frac\{s\}\{M\}\+\\varepsilon\\right\)\-h\_\{\\rho\}\(1\-R\+\\varepsilon\)\\right\],\\qquad h\_\{\\rho\}\(u\)=\\begin\{cases\}u^\{\\rho\}/\\rho,&\\rho\\neq 0,\\\\ \\log u,&\\rho=0\.\\end\{cases\}\(10\)For fixediiandRR, this gain is increasing inss\. Therefore, only the highest\-scoring unqueried comparison of each persona needs to be retained\. Selecting a comparison changes only its recipient’s risk, so the other personas’ retained gains remain valid\.

Algorithm 2WAPA with Exact Marginal Allocation1:Frozen predictions

p^i​j\\widehat\{p\}\_\{ij\}and

\{q^i​j\(t\)\}t=1T\\\{\\widehat\{q\}\_\{ij\}^\{\(t\)\}\\\}\_\{t=1\}^\{T\}; budget

B∈\{0,…,N​M\}B\\in\\\{0,\\ldots,NM\\\}
2:

ρ61\\rho\\leqslant 1,

ε\>0\\varepsilon\>0, and fixed weights

wi\>0w\_\{i\}\>0with

∑i=1Nwi=1\\sumop\\displaylimits\_\{i=1\}^\{N\}w\_\{i\}=1
3:Nested selections

S0,…,SBS\_\{0\},\\ldots,S\_\{B\}, computed before labels are revealed

4:

μ^i​j←T−1​∑t=1Tq^i​j\(t\)\\widehat\{\\mu\}\_\{ij\}\\leftarrow T^\{\-1\}\\sumop\\displaylimits\_\{t=1\}^\{T\}\\widehat\{q\}\_\{ij\}^\{\(t\)\}for all

\(i,j\)\(i,j\)
5:

si​j←μ^i​j​\(1−p^i​j\)2\+\(1−μ^i​j\)​p^i​j2s\_\{ij\}\\leftarrow\\widehat\{\\mu\}\_\{ij\}\(1\-\\widehat\{p\}\_\{ij\}\)^\{2\}\+\(1\-\\widehat\{\\mu\}\_\{ij\}\)\\widehat\{p\}\_\{ij\}^\{2\}for all

\(i,j\)\(i,j\)
6:Sort each persona’s comparisons into a permutation

νi\\nu\_\{i\}such that

si,νi​\(1\)\>⋯\>si,νi​\(M\)s\_\{i,\\nu\_\{i\}\(1\)\}\\geqslant\\cdots\\geqslant s\_\{i,\\nu\_\{i\}\(M\)\}
7:

S0←?S\_\{0\}\\leftarrow\\varnothing;

ki←0k\_\{i\}\\leftarrow 0;

Ri←M−1​∑j=1Msi​jR\_\{i\}\\leftarrow M^\{\-1\}\\sumop\\displaylimits\_\{j=1\}^\{M\}s\_\{ij\}for all

ii
8:

ji←νi​\(1\)j\_\{i\}\\leftarrow\\nu\_\{i\}\(1\);

gi←Gi​\(Ri,si,ji\)g\_\{i\}\\leftarrow G\_\{i\}\(R\_\{i\},s\_\{i,j\_\{i\}\}\)for all

ii
9:

𝒜←\{1,…,N\}\\mathcal\{A\}\\leftarrow\\\{1,\\ldots,N\\\}⊳\\trianglerightPersonas with unqueried comparisons

10:Use a fixed comparison order to break ties throughout\.

11:for

b=1,…,Bb=1,\\ldots,Bdo

12:Enumerate

i∈𝒜i\\in\\mathcal\{A\}and choose

i∗∈arg⁡maxi∈𝒜⁡gii^\{\*\}\\in\\arg\\max\_\{i\\in\\mathcal\{A\}\}g\_\{i\};

j∗←ji∗j^\{\*\}\\leftarrow j\_\{i^\{\*\}\}
13:

Sb←Sb−1∪\{\(i∗,j∗\)\}S\_\{b\}\\leftarrow S\_\{b\-1\}\\cup\\\{\(i^\{\*\},j^\{\*\}\)\\\}
14:

Ri∗←Ri∗−si∗,j∗/MR\_\{i^\{\*\}\}\\leftarrow R\_\{i^\{\*\}\}\-s\_\{i^\{\*\},j^\{\*\}\}/M;

ki∗←ki∗\+1k\_\{i^\{\*\}\}\\leftarrow k\_\{i^\{\*\}\}\+1
15:if

ki∗<Mk\_\{i^\{\*\}\}<Mthen

16:

ji∗←νi∗​\(ki∗\+1\)j\_\{i^\{\*\}\}\\leftarrow\\nu\_\{i^\{\*\}\}\(k\_\{i^\{\*\}\}\+1\)
17:

gi∗←Gi∗​\(Ri∗,si∗,ji∗\)g\_\{i^\{\*\}\}\\leftarrow G\_\{i^\{\*\}\}\(R\_\{i^\{\*\}\},s\_\{i^\{\*\},j\_\{i^\{\*\}\}\}\)
18:else

19:

𝒜←𝒜∖\{i∗\}\\mathcal\{A\}\\leftarrow\\mathcal\{A\}\\setminus\\\{i^\{\*\}\\\}
20:endif

21:endfor

22:return

S0,…,SBS\_\{0\},\\ldots,S\_\{B\}

#### Time complexity\.

Given the frozen predictions, computing the reference means and scores takesO⁡\(N​M​T\)O\(NMT\)time\. Sorting theMMcomparisons for each of theNNpersonas takesO⁡\(N​M​log⁡\(M\+1\)\)O\(NM\\log\(M\+1\)\)time, and initialization takesO⁡\(N​M\)O\(NM\)time\. At each acquisition step, the algorithm enumerates at mostNNretained candidates and updates only the selected persona’s state and gain\. Treating scalar arithmetic and evaluations ofhρh\_\{\\rho\}as constant\-time operations, each step therefore takesO⁡\(N\)O\(N\)time\. The overall time complexity is

O⁡\(N​M​T\+N​M​log⁡\(M\+1\)\+B​N\)\.O\\\!\\left\(NMT\+NM\\log\(M\+1\)\+BN\\right\)\.\(11\)SinceB6N​MB\\leqslant NM, this bound is polynomial inNN,MM, andTT\. It excludes the cost of generating model predictions\.

#### Storage\.

The scores, sorted indices, persona states, and acquisition order requireO⁡\(N​M\+N\+B\)O\(NM\+N\+B\)space, excluding the supplied prediction arrays\. The nested selections are represented as prefixes of one acquisition order, withSbS\_\{b\}containing its firstbbentries\. Explicitly copying every setSbS\_\{b\}would add�⁡\(B2\)\\Theta\(B^\{2\}\)time and storage\.

### C\.2Proofs of the Allocation\-Priority Results

This subsection gives formal versions of Theorem[3\.1](https://arxiv.org/html/2610.19035#S3.Thmtheorem1)\. Write

ℓi​j∗=E⁡\[\(p^i​j−Yi​j\)2\]=pi​j∗​\(1−p^i​j\)2\+\(1−pi​j∗\)​p^i​j2,𝒮B=\{S⊆𝒞:\|S\|=B\}\.\\ell\_\{ij\}^\{\*\}=\\mathbb E\[\(\\widehat\{p\}\_\{ij\}\-Y\_\{ij\}\)^\{2\}\]=p\_\{ij\}^\{\*\}\(1\-\\widehat\{p\}\_\{ij\}\)^\{2\}\+\(1\-p\_\{ij\}^\{\*\}\)\\widehat\{p\}\_\{ij\}^\{\\,2\},\\qquad\\mathcal\{S\}\_\{B\}=\\\{S\\subseteq\\mathcal\{C\}:\|S\|=B\\\}\.\(12\)Thenℓi​j∗∈\[0,1\]\\ell\_\{ij\}^\{\*\}\\in\[0,1\], and the true expected utilities and welfare are

Ui\(S\)=1−1M∑j:\(i,j\)<Sℓi​j∗,J\(S\)=∑iwihρ\(Ui\(S\)\+ε\)\.U\_\{i\}\(S\)=1\-\\frac\{1\}\{M\}\\sumop\\displaylimits\_\{j:\(i,j\)\\notin S\}\\ell\_\{ij\}^\{\*\},\\qquad J\(S\)=\\sumop\\displaylimits\_\{i\}w\_\{i\}h\_\{\\rho\}\(U\_\{i\}\(S\)\+\\varepsilon\)\.\(13\)For nonempty subgroupsG1,…,GK⊆\[N\]G\_\{1\},\\ldots,G\_\{K\}\\subseteq\[N\]and requirementsu¯k∈\[0,1\]\\underline\{u\}\_\{k\}\\in\[0,1\], define the benchmark feasible family

ℱB=\{S∈𝒮B:1\|Gk\|​∑i∈GkUi​\(S\)\>u¯k​for every​k∈\[K\]\}\.\\mathcal\{F\}\_\{B\}=\\left\\\{S\\in\\mathcal\{S\}\_\{B\}:\\frac\{1\}\{\|G\_\{k\}\|\}\\sumop\\displaylimits\_\{i\\in G\_\{k\}\}U\_\{i\}\(S\)\\geqslant\\underline\{u\}\_\{k\}\\text\{ for every \}k\\in\[K\]\\right\\\}\.\(14\)Joint feasibility meansℱB,?\\mathcal\{F\}\_\{B\}\\neq\\varnothing\.

###### Theorem C\.1\(Formal statement of Theorem[3\.1](https://arxiv.org/html/2610.19035#S3.Thmtheorem1)\(a\)\)\.

For everyδ∈\(0,1\)\\delta\\in\(0,1\), there exists an instance with two groups forming a partition,ℱB,?\\mathcal\{F\}\_\{B\}\\neq\\varnothing, andu¯1=1\\underline\{u\}\_\{1\}=1, such that every

Sunif∈arg​maxS∈𝒮B⁡1N​∑iUi​\(S\)S\_\{\\mathrm\{unif\}\}\\in\\operatorname\*\{arg\\,max\}\_\{S\\in\\mathcal\{S\}\_\{B\}\}\\frac\{1\}\{N\}\\sumop\\displaylimits\_\{i\}U\_\{i\}\(S\)\(15\)satisfies

1\|G1\|​∑i∈G1Ui​\(Sunif\)=δ\.\\frac\{1\}\{\|G\_\{1\}\|\}\\sumop\\displaylimits\_\{i\\in G\_\{1\}\}U\_\{i\}\(S\_\{\\mathrm\{unif\}\}\)=\\delta\.\(16\)

###### Proof\.

TakeN=2N=2,M=1M=1,B=1B=1,G1=\{1\}G\_\{1\}=\\\{1\\\}, andG2=\{2\}G\_\{2\}=\\\{2\\\}\. Let both labels equal zero deterministically, and set

p^11=1−δ,p^21=1−δ/2\.\\widehat\{p\}\_\{11\}=\\sqrt\{1\-\\delta\},\\qquad\\widehat\{p\}\_\{21\}=\\sqrt\{1\-\\delta/2\}\.\(17\)These are valid probability predictions and give initial utilitiesU1​\(?\)=δU\_\{1\}\(\\varnothing\)=\\deltaandU2​\(?\)=δ/2U\_\{2\}\(\\varnothing\)=\\delta/2\.

Chooseu¯1=1\\underline\{u\}\_\{1\}=1andu¯2=δ/2\\underline\{u\}\_\{2\}=\\delta/2\. The allocationS\(1\)=\{\(1,1\)\}S^\{\(1\)\}=\\\{\(1,1\)\\\}yields utilities\(1,δ/2\)\(1,\\delta/2\), so the requirements are jointly feasible\. The only other allocation,S\(2\)=\{\(2,1\)\}S^\{\(2\)\}=\\\{\(2,1\)\\\}, yields utilities\(δ,1\)\(\\delta,1\)\. Its mean utility exceeds that ofS\(1\)S^\{\(1\)\}by

1\+δ2−1\+δ/22=δ4\>0\.\\frac\{1\+\\delta\}\{2\}\-\\frac\{1\+\\delta/2\}\{2\}=\\frac\{\\delta\}\{4\}\>0\.\(18\)ThusS\(2\)S^\{\(2\)\}is the unique mean\-utility maximizer and leavesG1G\_\{1\}at utilityδ\\delta, as claimed\. ∎

###### Theorem C\.2\(Formal statement of Theorem[3\.1](https://arxiv.org/html/2610.19035#S3.Thmtheorem1)\(b\)\)\.

Assume the nonempty subgroupsG1,…,GKG\_\{1\},\\ldots,G\_\{K\}partition\[N\]\[N\], these subgroups have minimal acceptable utilityu¯k\\underline\{u\}\_\{k\}fork∈\[K\]k\\in\[K\], andℱB,?\\mathcal\{F\}\_\{B\}\\neq\\varnothing\. There exist positive normalized persona weights, constant within each group, and an allocationS†S^\{\\dagger\}such that, withρ=1\\rho=1,

S†∈arg​maxS∈𝒮B⁡J​\(S\),S†∈arg​maxS∈ℱB⁡1N​∑iUi​\(S\)\.S^\{\\dagger\}\\in\\operatorname\*\{arg\\,max\}\_\{S\\in\\mathcal\{S\}\_\{B\}\}J\(S\),\\qquad S^\{\\dagger\}\\in\\operatorname\*\{arg\\,max\}\_\{S\\in\\mathcal\{F\}\_\{B\}\}\\frac\{1\}\{N\}\\sumop\\displaylimits\_\{i\}U\_\{i\}\(S\)\.\(19\)In particular, at least one weighted\-welfare maximizer satisfies all subgroup requirements and maximizes mean utility among allocations that do so\.

###### Proof\.

Letnk=M​\|Gk\|n\_\{k\}=M\|G\_\{k\}\|, and sort the true expected losses inGk×\[M\]G\_\{k\}\\times\[M\]as

σk,1\>⋯\>σk,nk\>0,σk,nk\+1=0\.\\sigma\_\{k,1\}\\geqslant\\cdots\\geqslant\\sigma\_\{k,n\_\{k\}\}\\geqslant 0,\\qquad\\sigma\_\{k,n\_\{k\}\+1\}=0\.\(20\)Ties are ordered consistently within each group\. For any fixed number of queries in a group, selecting its largest losses maximizes both its average utility and its contribution to population mean utility\. Because the groups are disjoint, this replacement leaves other groups’ utilities unchanged\. Consequently, a constrained mean optimum can be chosen as a prefix of each group’s sorted list\.

The minimum feasible prefix length for groupkkis

bk=min⁡\{b∈\{0,…,nk\}:1−1nk​∑r=b\+1nkσk,r\>u¯k\}\.b\_\{k\}=\\min\\left\\\{b\\in\\\{0,\\ldots,n\_\{k\}\\\}:1\-\\frac\{1\}\{n\_\{k\}\}\\sumop\\displaylimits\_\{r=b\+1\}^\{n\_\{k\}\}\\sigma\_\{k,r\}\\geqslant\\underline\{u\}\_\{k\}\\right\\\}\.\(21\)Feasibility implies∑kbk6B\\sumop\\displaylimits\_\{k\}b\_\{k\}\\leqslant B\. Select these mandatory prefixes, then fill the remaining budget using the largest unselected losses, breaking ties consistently with the group lists\. Call the resulting allocationS†S^\{\\dagger\}, and letqkq\_\{k\}be its prefix length in groupkk\.

Every feasible prefix allocation contains the mandatory prefixes\. Moreover,

1N​∑iUi​\(S\)=1N​∑iUi​\(?\)\+1N​M​∑\(i,j\)∈Sℓi​j∗\.\\frac\{1\}\{N\}\\sumop\\displaylimits\_\{i\}U\_\{i\}\(S\)=\\frac\{1\}\{N\}\\sumop\\displaylimits\_\{i\}U\_\{i\}\(\\varnothing\)\+\\frac\{1\}\{NM\}\\sumop\\displaylimits\_\{\(i,j\)\\in S\}\\ell\_\{ij\}^\{\*\}\.\(22\)Thus selecting the largest remaining losses gives a mean\-utility optimum overℱB\\mathcal\{F\}\_\{B\}\.

It remains to construct supporting weights\. A minimum feasible prefix never needs a zero\-loss comparison: selecting all positive losses already gives group utility one\. IfBBis at least the total number of positive losses,S†S^\{\\dagger\}contains all of them and maximizes weighted mean utility for any positive weights\.

Otherwise every selected loss inS†S^\{\\dagger\}is positive\. Define

ak=\{\(1\+σk,1\)−1,qk=0,2σk,qk\+σk,qk\+1,qk\>0,wi=ak∑ℓ=1K\|Gℓ\|​aℓ\(i∈Gk\)\.a\_\{k\}=\\begin\{cases\}\(1\+\\sigma\_\{k,1\}\)^\{\-1\},&q\_\{k\}=0,\\\\\[2\.84526pt\] \\displaystyle\\frac\{2\}\{\\sigma\_\{k,q\_\{k\}\}\+\\sigma\_\{k,q\_\{k\}\+1\}\},&q\_\{k\}\>0,\\end\{cases\}\\qquad w\_\{i\}=\\frac\{a\_\{k\}\}\{\\sumop\\displaylimits\_\{\\ell=1\}^\{K\}\|G\_\{\\ell\}\|a\_\{\\ell\}\}\\quad\(i\\in G\_\{k\}\)\.\(23\)These weights are positive, normalized, and constant within each group\. Forqk\>0q\_\{k\}\>0, every selected loss multiplied byaka\_\{k\}is at least one, and every unselected loss multiplied byaka\_\{k\}is at most one\. Forqk=0q\_\{k\}=0, every such weighted loss is strictly below one\. ThereforeS†S^\{\\dagger\}consists ofBBlargest weighted losses, with an appropriate selection among boundary ties\.

Atρ=1\\rho=1,

J⁡\(S\)=J⁡\(?\)\+1M​∑\(i,j\)∈Swi​ℓi​j∗,J\(S\)=J\(\\varnothing\)\+\\frac\{1\}\{M\}\\sumop\\displaylimits\_\{\(i,j\)\\in S\}w\_\{i\}\\ell\_\{ij\}^\{\*\},\(24\)soS†S^\{\\dagger\}maximizesJJover𝒮B\\mathcal\{S\}\_\{B\}as required\. ∎

We remark that the supporting weights may depend on the instance and the requirements and this theorem asserts existence of a suitable optimizer, not feasibility of every optimizer under arbitrary weights or tie\-breaking\. Further, this is an expressiveness result for the larger class of positive subgroup\-constant weights\. It does not imply that the one\-parameter target\-weight family in Equation[3](https://arxiv.org/html/2610.19035#S2.E3)can meet every jointly feasible collection of subgroup requirements\.

The following two results clarify howρ\\rhoshapes welfare\-aware allocation\. First, under equal weights, maximizing welfare at a fixedρ<0\\rho<0maximizes an explicit lower bound on bottom\-α\\alphautility, implying protection for those individuals for whom the base model predictions are poor\. Second, when the max–min allocation is unique, sufficiently negativeρ\\rhomakes weighted and unweighted welfare select that same allocation for any fixed positive weights\. This establishes a limiting sense in which sensitivity to supervision disadvantage dominates weight differences, complementing the trade\-offs examined in our experimental results in Section[4\.2](https://arxiv.org/html/2610.19035#S4.SS2)\.

Forn6Nn\\leqslant N, denoteα=n/N\\alpha=n/N\. For fixedSS, definexi=Ui​\(S\)\+εx\_\{i\}=U\_\{i\}\(S\)\+\\varepsilonand sortx\(1\)6…6x\(N\)x\_\{\(1\)\}\\leqslant\\ldots\\leqslant x\_\{\(N\)\}, then the tail utility is defined as the average of tailα\\alpha\-quantile utility, specifically, we denote

Tα:=1n​∑i=1nU\(i\)​\(S\)=1n​∑i=1nx\(i\)−ε\.T\_\{\\alpha\}:=\\frac\{1\}\{n\}\\sumop\\displaylimits\_\{i=1\}^\{n\}U\_\{\(i\)\}\(S\)=\\frac\{1\}\{n\}\\sumop\\displaylimits\_\{i=1\}^\{n\}x\_\{\(i\)\}\-\\varepsilon\.\(25\)
###### Theorem C\.3\(Lower tail certificate under uniform weights\)\.

For everyρ<0\\rho<0and fixed welfare of the formJρ​\(S\)=1N​ρ​∑i=1N\(Ui​\(S\)\+ε\)ρJ\_\{\\rho\}\(S\)=\\frac\{1\}\{N\\rho\}\\sumop\\displaylimits\_\{i=1\}^\{N\}\(U\_\{i\}\(S\)\+\\varepsilon\)^\{\\rho\}with uniform weight, and acquisition setSS,

Tα​\(S\)\>max⁡\{\[ρ​Jρ​\(S\)−\(1−α\)​\(1\+ε\)ρα\]1/ρ−ε,0\}\.\{T\_\{\\alpha\}\(S\)\\geqslant\\max\\left\\\{\\left\[\\frac\{\\rho J\_\{\\rho\}\(S\)\-\(1\-\\alpha\)\(1\+\\varepsilon\)^\{\\rho\}\}\{\\alpha\}\\right\]^\{1/\\rho\}\-\\varepsilon,0\\right\\\}\.\}\(26\)A negative right\-hand side can be replaced by zero\. For fixed curvatureρ\\rho, this certificate increases withJρ​\(S\)J\_\{\\rho\}\(S\)\. Consequently, any maximizer of the true uniform\-weight welfare objectiveJρJ\_\{\\rho\}also maximizes this certificate\.

###### Proof\.

Sinceε6Ui\+ε61\+ε\\varepsilon\\leqslant U\_\{i\}\+\\varepsilon\\leqslant 1\+\\varepsilon, Jensen’s inequality gives

1n​∑i=1nx\(i\)ρ\>\(1n​∑i=1nx\(i\)\)ρ=\(Tα​\(S\)\+ε\)ρ,\\frac\{1\}\{n\}\\sumop\\displaylimits\_\{i=1\}^\{n\}x\_\{\(i\)\}^\{\\rho\}\\geqslant\(\\frac\{1\}\{n\}\\sumop\\displaylimits\_\{i=1\}^\{n\}x\_\{\(i\)\}\)^\{\\rho\}=\(T\_\{\\alpha\}\(S\)\+\\varepsilon\)^\{\\rho\},\(27\)and note thatρ<0\\rho<0, we have

1N​∑i=n\+1Nx\(i\)ρ\>N−nN​\(1\+ε\)ρ,\\frac\{1\}\{N\}\\sumop\\displaylimits\_\{i=n\+1\}^\{N\}x\_\{\(i\)\}^\{\\rho\}\\geqslant\\frac\{N\-n\}\{N\}\(1\+\\varepsilon\)^\{\\rho\},\(28\)byα=n/N\\alpha=n/N, we obtain

ρ​Jρ​\(S\)\\displaystyle\\rho J\_\{\\rho\}\(S\)=1N​∑i\(Ui​\(S\)\+ε\)ρ\>α​\(Tα​\(S\)\+ε\)ρ\+\(1−α\)​\(1\+ε\)ρ\.\\displaystyle=\\frac\{1\}\{N\}\\sumop\\displaylimits\_\{i\}\(U\_\{i\}\(S\)\+\\varepsilon\)^\{\\rho\}\\geqslant\\alpha\(T\_\{\\alpha\}\(S\)\+\\varepsilon\)^\{\\rho\}\+\(1\-\\alpha\)\(1\+\\varepsilon\)^\{\\rho\}\.\(29\)Rearrange and use thatz1/ρz^\{1/\\rho\}is decreasing\. For uniform weights, equality holds when the bottomnnutilities are equal and all remaining utilities are11\. ∎

For fixed budget16B<N​M1\\leqslant B<NM, we denote𝒮B\\mathcal\{S\}\_\{B\}the collection of all acquisition setsSSwith size\|S\|=B\|S\|=B\. For givenρ\\rhoand positive normalized weightww,Sρ,wS\_\{\\rho,w\}will always denote a welfare optimizer, i\.e\.,

Sρ,w∈arg⁡max⁡∑iS∈𝒮B⁡wi​hρ​\(Ui​\(S\)\+ε\),S\_\{\\rho,w\}\\in\\arg\\max\_\{S\\in\\mathcal\{S\}\_\{B\}\}\\sumop\\displaylimits\_\{i\}w\_\{i\}h\_\{\\rho\}\(U\_\{i\}\(S\)\+\\varepsilon\),\(30\)andSρ,unifS\_\{\\rho,\\mathrm\{unif\}\}denotes a maximizer of the same objective with equal weights\.

###### Theorem C\.4\(Formal statement of Theorem[3\.2](https://arxiv.org/html/2610.19035#S3.Thmtheorem2)\)\.

FixN,M\>2N,M\\geqslant 2, budget16B<N​M1\\leqslant B<NMand normalization shiftε\>0\\varepsilon\>0, and positive normalized weightswiw\_\{i\}\. Suppose

S∗=argmaxS∈𝒮B​mini​Ui​\(S\)S^\{\\ast\}=\\underset\{S\\in\\mathcal\{S\}\_\{B\}\}\{\\operatorname\{argmax\}\}\\;\\min\_\{i\}U\_\{i\}\(S\)is unique\. Then there exists a finiteρ0<0\\rho\_\{0\}<0such that, for everyρ<ρ0\\rho<\\rho\_\{0\},

Sρ,w=Sρ,unif=S∗\.\{S\_\{\\rho,w\}=S\_\{\\rho,\\mathrm\{unif\}\}=S^\{\\ast\}\.\}More explicitly, define

m∗=mini⁡Ui​\(S∗\),m2=maxS,S∗⁡mini​Ui​\(S\)\.m^\{\\ast\}=\\min\_\{i\}U\_\{i\}\(S^\{\\ast\}\),\\qquad m\_\{2\}=\\max\_\{S\\neq S^\{\\ast\}\}\\min\_\{i\}U\_\{i\}\(S\)\.
Here by the uniqueness ofS∗S^\{\\ast\}and finiteness of acquisition set family𝒮B\\mathcal\{S\}\_\{B\}, we havem2m\_\{2\}is well defined andm2<m∗m\_\{2\}<m^\{\\ast\}\. Agreement holds whenever

ρ<−log⁡\(1/wmin\)log⁡\(\(m∗\+ε\)/\(m2\+ε\)\)\{\\rho<\-\\frac\{\\log\(1/w\_\{\\min\}\)\}\{\\log\\\!\\left\(\(m^\{\\ast\}\+\\varepsilon\)/\(m\_\{2\}\+\\varepsilon\)\\right\)\}\}wherewminw\_\{\\min\}is the minimum weightwmin:=min16i6N⁡wiw\_\{\\min\}:=\\min\_\{1\\leqslant i\\leqslant N\}w\_\{i\}\.

###### Proof\.

Maximizing weighted welfare is equivalent to minimizing∑iwi​\(Ui​\(S\)\+ε\)ρ\.\\sumop\\displaylimits\_\{i\}w\_\{i\}\(U\_\{i\}\(S\)\+\\varepsilon\)^\{\\rho\}\.ForS∗S^\{\\ast\}, every utility is at leastm∗m^\{\\ast\}, so

Jρ,w​\(S∗\)\>1/ρ⋅\(m∗\+ε\)ρ\.J\_\{\\rho,w\}\(S^\{\\ast\}\)\\geqslant 1/\\rho\\cdot\(m^\{\\ast\}\+\\varepsilon\)^\{\\rho\}\.Every other allocation has at least one utility at mostm2m\_\{2\}, giving

Jρ,w​\(S\)61ρ​wmin​\(m2\+ε\)ρ\.J\_\{\\rho,w\}\(S\)\\leqslant\\frac\{1\}\{\\rho\}w\_\{\\min\}\(m\_\{2\}\+\\varepsilon\)^\{\\rho\}\.
The stated condition ensures

\(m∗\+ε\)ρ<wmin​\(m2\+ε\)ρ,\(m^\{\\ast\}\+\\varepsilon\)^\{\\rho\}<w\_\{\\min\}\(m\_\{2\}\+\\varepsilon\)^\{\\rho\},makingS∗S^\{\\ast\}the unique weighted optimizer\. The same condition covers uniform weights becausewmin61/Nw\_\{\\min\}\\leqslant 1/N\. ∎

### C\.3Proof of WAPA Optimality

This subsection supports the estimator and allocation rule in Section[3\.1](https://arxiv.org/html/2610.19035#S3.SS1)\. Recall the fixed WAPA scores and estimated utilities

μ^i​j=1T∑t=1Tq^i​j\(t\),si​j=μ^i​j\(1−p^i​j\)2\+\(1−μ^i​j\)p^i​j2,U^i\(S\)=1−1M∑j:\(i,j\)<Ssi​j\.\\widehat\{\\mu\}\_\{ij\}=\\frac\{1\}\{T\}\\sumop\\displaylimits\_\{t=1\}^\{T\}\\widehat\{q\}\_\{ij\}^\{\(t\)\},\\qquad s\_\{ij\}=\\widehat\{\\mu\}\_\{ij\}\(1\-\\widehat\{p\}\_\{ij\}\)^\{2\}\+\(1\-\\widehat\{\\mu\}\_\{ij\}\)\\widehat\{p\}\_\{ij\}^\{\\,2\},\\qquad\\widehat\{U\}\_\{i\}\(S\)=1\-\\frac\{1\}\{M\}\\sumop\\displaylimits\_\{j:\(i,j\)\\notin S\}s\_\{ij\}\.\(31\)Sincesi​j∈\[0,1\]s\_\{ij\}\\in\[0,1\], the estimated utilities lie in\[0,1\]\[0,1\]\. For an unselected comparison, directsubtraction gives

U^i​\(S∪\{\(i,j\)\}\)−U^i​\(S\)=si​j/M\.\\widehat\{U\}\_\{i\}\(S\\cup\\\{\(i,j\)\\\}\)\-\\widehat\{U\}\_\{i\}\(S\)=s\_\{ij\}/M\.\(32\)Only personaii’s estimated utility changes\. Hence the exact gain forJ^​\(S\)=∑iwi​hρ​\(U^i​\(S\)\+ε\)\\widehat\{J\}\(S\)=\\sumop\\displaylimits\_\{i\}w\_\{i\}h\_\{\\rho\}\(\\widehat\{U\}\_\{i\}\(S\)\+\\varepsilon\)is

�i​j​\(S\)=wi​\[hρ​\(U^i​\(S\)\+ε\+si​jM\)−hρ​\(U^i​\(S\)\+ε\)\]\.\\Delta\_\{ij\}\(S\)=w\_\{i\}\\left\[h\_\{\\rho\}\\\!\\left\(\\widehat\{U\}\_\{i\}\(S\)\+\\varepsilon\+\\frac\{s\_\{ij\}\}\{M\}\\right\)\-h\_\{\\rho\}\\\!\\left\(\\widehat\{U\}\_\{i\}\(S\)\+\\varepsilon\\right\)\\right\]\.\(33\)
###### Theorem C\.5\(Exact optimality of WAPA, restatement of Theorem[3\.3](https://arxiv.org/html/2610.19035#S3.Thmtheorem3)\)\.

For every integerB∈\{0,…,N​M\}B\\in\\\{0,\\ldots,NM\\\}the outputSBS\_\{B\}of Algorithm[2](https://arxiv.org/html/2610.19035#alg2)satisfies

J^​\(SB\)=maxS∈𝒮B⁡J^​\(S\)\.\\widehat\{J\}\(S\_\{B\}\)=\\max\_\{S\\in\\mathcal\{S\}\_\{B\}\}\\widehat\{J\}\(S\)\.\(34\)This conclusion allows zero scores and ties, and requires neither calibrated reference predictions nor independence among labels or reference models\.

###### Proof\.

For each persona, choose an orderingνi\\nu\_\{i\}such thatsi,νi​\(1\)\>⋯\>si,νi​\(M\)s\_\{i,\\nu\_\{i\}\(1\)\}\\geqslant\\cdots\\geqslant s\_\{i,\\nu\_\{i\}\(M\)\}\. Fix the numberkik\_\{i\}of queries assigned to each persona\. Exchanging a selected lower score for an unselected higher score increases that persona’s estimated utility and leaves all other utilities unchanged\. Becausehρh\_\{\\rho\}is increasing, this cannot decrease welfare\. An optimum therefore exists among prefix allocations

S⁡\(k\)=⋃i\{\(i,νi​\(r\)\):16r6ki\},06ki6M,∑iki=B\.S\(k\)=\\bigcupop\\displaylimits\_\{i\}\\\{\(i,\\nu\_\{i\}\(r\)\):1\\leqslant r\\leqslant k\_\{i\}\\\},\\qquad 0\\leqslant k\_\{i\}\\leqslant M,\\quad\\sumop\\displaylimits\_\{i\}k\_\{i\}=B\.\(35\)
Afterk<Mk<Mqueries to personaii, write

xi​\(k\)=1−1M​∑r=k\+1Msi,νi​\(r\)\+ε,di​\(k\)=si,νi​\(k\+1\)M\.x\_\{i\}\(k\)=1\-\\frac\{1\}\{M\}\\sumop\\displaylimits\_\{r=k\+1\}^\{M\}s\_\{i,\\nu\_\{i\}\(r\)\}\+\\varepsilon,\\qquad d\_\{i\}\(k\)=\\frac\{s\_\{i,\\nu\_\{i\}\(k\+1\)\}\}\{M\}\.\(36\)The next welfare increment is

�i​\(k\)=wi​\[hρ​\(xi​\(k\)\+di​\(k\)\)−hρ​\(xi​\(k\)\)\]=wi​∫0di​\(k\)\(xi​\(k\)\+z\)ρ−1​𝑑z\.\\Delta\_\{i\}\(k\)=w\_\{i\}\\left\[h\_\{\\rho\}\(x\_\{i\}\(k\)\+d\_\{i\}\(k\)\)\-h\_\{\\rho\}\(x\_\{i\}\(k\)\)\\right\]=w\_\{i\}\\intop\\nolimits\_\{0\}^\{d\_\{i\}\(k\)\}\(x\_\{i\}\(k\)\+z\)^\{\\rho\-1\}\\,dz\.\(37\)The scores are sorted, sodi​\(k\+1\)6di​\(k\)d\_\{i\}\(k\+1\)\\leqslant d\_\{i\}\(k\), whilexi​\(k\+1\)=xi​\(k\)\+di​\(k\)\>xi​\(k\)x\_\{i\}\(k\+1\)=x\_\{i\}\(k\)\+d\_\{i\}\(k\)\\geqslant x\_\{i\}\(k\)\. Becauseρ61\\rho\\leqslant 1, the integrand is nonnegative and nonincreasing in its argument\. Therefore�i​\(k\+1\)6�i​\(k\)\\Delta\_\{i\}\(k\+1\)\\leqslant\\Delta\_\{i\}\(k\)\. Each persona contributes a fixed nonincreasing sequence of increments, and

J^​\(S⁡\(k\)\)=J^​\(?\)\+∑i∑r=0ki−1�i​\(r\)\.\\widehat\{J\}\(S\(k\)\)=\\widehat\{J\}\(\\varnothing\)\+\\sumop\\displaylimits\_\{i\}\\sumop\\displaylimits\_\{r=0\}^\{k\_\{i\}\-1\}\\Delta\_\{i\}\(r\)\.\(38\)
For a given persona, its highest remaining score also has its highest remaining welfare gain\. Thus the algorithm selects the largest available sequence head\. Every increment hidden later in a sequence is no larger than its current head, so a largest remaining increment is always available\. Repeated selection therefore collectsBBlargest increments in a prefix\-feasible order\. Their sum is maximal among all choices ofBBincrements, proving optimality among prefixes and, by the exchange argument, among all sets in𝒮B\\mathcal\{S\}\_\{B\}\.

Ties change neither this argument nor the objective value; within\-persona score ties can be ordered consistently with the run under consideration\. The empty and full budgets are included\. ∎

We remark that this guarantee concerns the estimated objective in Eq\. \([5](https://arxiv.org/html/2610.19035#S3.E5)\) instead of the true supervision quality\.

### C\.4Proof of Acquisition\-to\-Alignment Transfer

In this section, we relate acquisition utility and empirical DPO fit to prediction error on fresh personas and prompts\. Writeaia\_\{i\}for personaii’s profile andxjx\_\{j\}for promptjj, with compared responses determined by a fixed rule\. Thusfθ​\(i,j\)=fθ​\(ai,xj\)f\_\{\\theta\}\(i,j\)=f\_\{\\theta\}\(a\_\{i\},x\_\{j\}\)andpi​j∗=p∗​\(ai,xj\)p^\{\*\}\_\{ij\}=p^\{\*\}\(a\_\{i\},x\_\{j\}\)\. The completed training targets are

pS​\(i,j\)=\{Yi​j,\(i,j\)∈S,p^i​j,\(i,j\)<S\.p\_\{S\}\(i,j\)=\\begin\{cases\}Y\_\{ij\},&\(i,j\)\\in S,\\\\ \\widehat\{p\}\_\{ij\},&\(i,j\)\\notin S\.\\end\{cases\}\(39\)Define the population Brier risk and empirical fitting error by

R⁡\(fθ\)\\displaystyle R\(f\_\{\\theta\}\)=Ea,x,Y​\[\(fθ​\(a,x\)−Y\)2\],\\displaystyle=\\mathbb E\_\{a,x,Y\}\\bigl\[\(f\_\{\\theta\}\(a,x\)\-Y\)^\{2\}\\bigr\],\(40\)𝒟^S​\(θ\)\\displaystyle\\widehat\{\\mathcal\{D\}\}\_\{S\}\(\\theta\)=1N​M∑i,jKL\(Bern\(pS\(i,j\)\)∥Bern\(fθ\(i,j\)\)\)\.\\displaystyle=\\frac\{1\}\{NM\}\\sumop\\displaylimits\_\{i,j\}\\operatorname\{KL\}\\\!\\left\(\\operatorname\{Bern\}\(p\_\{S\}\(i,j\)\)\\,\\\|\\,\\operatorname\{Bern\}\(f\_\{\\theta\}\(i,j\)\)\\right\)\.Here\(a,x,Y\)\(a,x,Y\)is an independent evaluation draw from the same populations and label mechanism\. For the soft\-target alignment objective in the main text, define

𝒟^S​\(θ\)=ℒalign​\(θ,S\)−1N​M​∑\(i,j\)<SH⁡\(p^i​j\),\\widehat\{\\mathcal\{D\}\}\_\{S\}\(\\theta\)=\\mathcal\{L\}\_\{\\mathrm\{align\}\}\(\\theta;S\)\-\\frac\{1\}\{NM\}\\sumop\\displaylimits\_\{\(i,j\)\\notin S\}H\(\\widehat\{p\}\_\{ij\}\),\(41\)whereH⁡\(p\)=−p​log⁡p−\(1−p\)​log⁡\(1−p\)H\(p\)=\-p\\log p\-\(1\-p\)\\log\(1\-p\), with0​log⁡0=00\\log 0=0\. Thus the fitting error differs from the training objective only by a term independent ofθ\\theta\.

Letn=min⁡\{N,M\}n=\\min\\\{N,M\\\}\. For a predictor classℱ\\mathcal\{F\}, define its expected Rademacher complexity underPA⊗PXP\_\{A\}\\otimes P\_\{X\}by

Rn​\(ℱ\)=E⁡\[supf∈ℱ1n​∑k=1nσk​f​\(ak′,xk′\)\],\\mathfrak R\_\{n\}\(\\mathcal\{F\}\)=\\mathbb E\\left\[\\sup\_\{f\\in\\mathcal\{F\}\}\\frac\{1\}\{n\}\\sumop\\displaylimits\_\{k=1\}^\{n\}\\sigma\_\{k\}f\(a^\{\\prime\}\_\{k\},x^\{\\prime\}\_\{k\}\)\\right\],\(42\)where\(ak′,xk′\)\(a^\{\\prime\}\_\{k\},x^\{\\prime\}\_\{k\}\)are i\.i\.d\. draws fromPA⊗PXP\_\{A\}\\otimes P\_\{X\}andσk\\sigma\_\{k\}are independent uniform signs, independent of the inputs\. We assume the relevant suprema are measurable, as holds for a pointwise\-continuous parametrization over a subset of finite\-dimensional Euclidean space\.

###### Theorem C\.6\(Acquisition\-to\-alignment generalization\)\.

Supposea1,…,aNa\_\{1\},\\ldots,a\_\{N\}are sampled i\.i\.d\. fromPAP\_\{A\}andx1,…,xMx\_\{1\},\\ldots,x\_\{M\}are sampled i\.i\.d\. fromPXP\_\{X\}, independently of the personas\. Conditional on these inputs, labels are independent withYi​j∼Bern⁡\(p∗​\(ai,xj\)\)Y\_\{ij\}\\sim\\operatorname\{Bern\}\(p^\{\*\}\(a\_\{i\},x\_\{j\}\)\), and the frozen predictions and acquisition setSSare independent of all pool labels\. Letℱ=\{fθ:θ∈�\}\\mathcal\{F\}=\\\{f\_\{\\theta\}:\\theta\\in\\Theta\\\}be a nonempty class of measurable\(0,1\)\(0,1\)\-valued predictors fixed before sampling;�⊆Rp\\Theta\\subseteq\\mathbb R^\{p\}may be continuous\. Assume training returnsfθ^∈ℱf\_\{\\widehat\{\\theta\}\}\\in\\mathcal\{F\}with𝒟^S​\(θ^\)6εfit\\widehat\{\\mathcal\{D\}\}\_\{S\}\(\\widehat\{\\theta\}\)\\leqslant\\varepsilon\_\{\\mathrm\{fit\}\}\. Then, for everyδ∈\(0,1\)\\delta\\in\(0,1\), with probability at least1−δ1\-\\delta,

R⁡\(fθ^\)\.\\displaystyle R\(f\_\{\\widehat\{\\theta\}\}\)\\lesssim\{\}1−1N​∑i=1NUi​\(S\)\+Rn​\(ℱ\)\+\(1N\+1M\)​log⁡2δ\+εfit\.\\displaystyle 1\-\\frac\{1\}\{N\}\\sumop\\displaylimits\_\{i=1\}^\{N\}U\_\{i\}\(S\)\+\\mathfrak R\_\{n\}\(\\mathcal\{F\}\)\+\\sqrt\{\\left\(\\frac\{1\}\{N\}\+\\frac\{1\}\{M\}\\right\)\\log\\frac\{2\}\{\\delta\}\}\+\\varepsilon\_\{\\mathrm\{fit\}\}\.HereUi​\(S\)U\_\{i\}\(S\)measures expected completed\-supervision quality on the sampled pool, and\.\\lesssimhides only a universal numerical constant\. The fitting tolerance is distinct from the welfare shiftε\\varepsilon\.

###### Proof\.

LetR^​\(f\)=\(N​M\)−1​∑i,j\(f⁡\(i,j\)−Yi​j\)2\\widehat\{R\}\(f\)=\(NM\)^\{\-1\}\\sumop\\displaylimits\_\{i,j\}\(f\(i,j\)\-Y\_\{ij\}\)^\{2\}, including labels unobserved by the algorithm\. Pinsker’s inequality and the fitting assumption give

R^​\(fθ^\)6εfit\+2N​M​∑\(i,j\)<S\(p^i​j−Yi​j\)2\.\\widehat\{R\}\(f\_\{\\widehat\{\\theta\}\}\)\\leqslant\\varepsilon\_\{\\mathrm\{fit\}\}\+\\frac\{2\}\{NM\}\\sumop\\displaylimits\_\{\(i,j\)\\notin S\}\(\\widehat\{p\}\_\{ij\}\-Y\_\{ij\}\)^\{2\}\.Conditional on the inputs, predictions, andSS, Hoeffding’s inequality bounds the remaining squared errors by their expectation\. Thus, with probability at least1−δ/21\-\\delta/2,

R^​\(fθ^\)\.εfit\+1−1N​∑iUi​\(S\)\+log⁡\(2/δ\)N​M\.\\widehat\{R\}\(f\_\{\\widehat\{\\theta\}\}\)\\lesssim\\varepsilon\_\{\\mathrm\{fit\}\}\+1\-\\frac\{1\}\{N\}\\sumop\\displaylimits\_\{i\}U\_\{i\}\(S\)\+\\sqrt\{\\frac\{\\log\(2/\\delta\)\}\{NM\}\}\.To control generalization, partition the grid intoK=max⁡\{N,M\}K=\\max\\\{N,M\\\}matchings of sizen=min⁡\{N,M\}n=\\min\\\{N,M\\\}, each using every persona and prompt at most once\. Such a partition is obtained by cyclically shifting the indices on the larger side\. Each matching consists ofnni\.i\.d\. labeled comparisons, andR^=K−1​∑k=1KR^k\\widehat\{R\}=K^\{\-1\}\\sumop\\displaylimits\_\{k=1\}^\{K\}\\widehat\{R\}\_\{k\}, whereR^k\\widehat\{R\}\_\{k\}is its empirical risk\. Therefore

E​supf∈ℱ\{R⁡\(f\)−R^​\(f\)\}\\displaystyle\\mathbb E\\sup\_\{f\\in\\mathcal\{F\}\}\\\{R\(f\)\-\\widehat\{R\}\(f\)\\\}61K​∑k=1KE​supf∈ℱ\{R⁡\(f\)−R^k​\(f\)\}\\displaystyle\\leqslant\\frac\{1\}\{K\}\\sumop\\displaylimits\_\{k=1\}^\{K\}\\mathbb E\\sup\_\{f\\in\\mathcal\{F\}\}\\\{R\(f\)\-\\widehat\{R\}\_\{k\}\(f\)\\\}\.Rn​\(ℱ\),\\displaystyle\\lesssim\\mathfrak R\_\{n\}\(\\mathcal\{F\}\),by symmetrization and contraction, since squared loss is22\-Lipschitz in its prediction on\[0,1\]\[0,1\]\. Independence between different matchings is not needed for this expectation bound\.

Represent labels using independent auxiliary random variables\. Changing one persona, one prompt, or one label\-generating variable changessupf\{R⁡\(f\)−R^​\(f\)\}\\sup\_\{f\}\\\{R\(f\)\-\\widehat\{R\}\(f\)\\\}by at most1/N1/N,1/M1/M, or1/\(N​M\)1/\(NM\), respectively\. McDiarmid’s inequality then gives, with probability at least1−δ/21\-\\delta/2,

supf∈ℱ\{R⁡\(f\)−R^​\(f\)\}\.Rn​\(ℱ\)\+\(1N\+1M\)​log⁡2δ\.\\sup\_\{f\\in\\mathcal\{F\}\}\\\{R\(f\)\-\\widehat\{R\}\(f\)\\\}\\lesssim\\mathfrak R\_\{n\}\(\\mathcal\{F\}\)\+\\sqrt\{\\left\(\\frac\{1\}\{N\}\+\\frac\{1\}\{M\}\\right\)\\log\\frac\{2\}\{\\delta\}\}\.Apply this uniform bound tofθ^f\_\{\\widehat\{\\theta\}\}, combine the two events, and absorb the smaller1/N​M1/\\sqrt\{NM\}term\. ∎

Theorem[C\.6](https://arxiv.org/html/2610.19035#A3.Thmtheorem6)provides a conditional generalization guarantee for acquisition\-to\-alignment transfer\. Under independent sampling of personas and prompts, conditionally independent labels, label\-independent acquisition, and the stated fitting assumption, the trained policy’s population Brier risk is bounded by the remaining supervision error, the fitting tolerance, and the complexity and sampling terms\. Holding the latter terms fixed, higher mean supervision utility yields a tighter upper bound on downstream preference prediction error\. The guarantee thus connects acquisition quality to downstream alignment through a population risk bound\.

## Appendix DSupplementary Details on Methods

### D\.1Supervision Utility and Estimated Query Gains

We derive the WAPA score from Brier utility and explain how reference predictions estimate the utility gain from acquiring a comparison\.

Supervision utility and strict propriety\.For a comparison\(i,j\)\(i,j\)with true preference probabilitypi​j∗=Pr\(Yij=1\)p\_\{ij\}^\{\*\}=\\ProbOp\(Y\_\{ij\}=1\), expected Brier utility satisfies

E⁡\[1−\(p^i​j−Yi​j\)2\]=1−pi​j∗​\(1−pi​j∗\)−\(p^i​j−pi​j∗\)2\.\\mathbb E\\\!\\left\[1\-\(\\widehat\{p\}\_\{ij\}\-Y\_\{ij\}\)^\{2\}\\right\]=1\-p\_\{ij\}^\{\*\}\(1\-p\_\{ij\}^\{\*\}\)\-\(\\widehat\{p\}\_\{ij\}\-p\_\{ij\}^\{\*\}\)^\{2\}\.\(43\)The first two terms are independent of the prediction, so expected utility is uniquely maximized atp^i​j=pi​j∗\\widehat\{p\}\_\{ij\}=p\_\{ij\}^\{\*\}\. This is the strict propriety of Brier utility\[[Gneiting and Raftery, 2007](https://arxiv.org/html/2610.19035#bib.bib32)\]: before observing the label, predicting its true probability achieves the highest expected utility\.

Estimated query gains\.For an unselected comparison\(i,j\)<S\(i,j\)\\notin S, observingYi​jY\_\{ij\}makes its contribution to the remaining prediction loss zero\. The realized gain in personaii’s supervision utility is therefore\(p^i​j−Yi​j\)2/M\(\\widehat\{p\}\_\{ij\}\-Y\_\{ij\}\)^\{2\}/M\. Since the label is unavailable during selection, we estimate its expected loss using the reference meanμ^i​j=T−1​∑t=1Tq^i​j\(t\)\\widehat\{\\mu\}\_\{ij\}=T^\{\-1\}\\sumop\\displaylimits\_\{t=1\}^\{T\}\\widehat\{q\}\_\{ij\}^\{\(t\)\}\. This gives the WAPA score :

si​j:=μ^i​j​\(1−p^i​j\)2\+\(1−μ^i​j\)​p^i​j2\.s\_\{ij\}:=\\widehat\{\\mu\}\_\{ij\}\(1\-\\widehat\{p\}\_\{ij\}\)^\{2\}\+\(1\-\\widehat\{\\mu\}\_\{ij\}\)\\widehat\{p\}\_\{ij\}^\{\\,2\}\.\(44\)Consequently, the estimated remaining utility and the estimated utility gain from a query are

U^i​\(S\)\\displaystyle\\widehat\{U\}\_\{i\}\(S\)=1−1M∑j:\(i,j\)<Ssi​j,\\displaystyle=1\-\\frac\{1\}\{M\}\\sumop\\displaylimits\_\{j:\(i,j\)\\notin S\}s\_\{ij\},\(45\)U^i​\(S∪\{\(i,j\)\}\)−U^i​\(S\)\\displaystyle\\widehat\{U\}\_\{i\}\\bigl\(S\\cup\\\{\(i,j\)\\\}\\bigr\)\-\\widehat\{U\}\_\{i\}\(S\)=si​jM,\(i,j\)<S\.\\displaystyle=\\frac\{s\_\{ij\}\}\{M\},\\qquad\(i,j\)\\notin S\.These expressions follow from linearity of expectation and require only marginal label probabilities, without assuming independence across comparison labels\.

Interpreting the WAPA score\.Expanding the expected loss gives

si​j\\displaystyle s\_\{ij\}=p^i​j2\+μ^i​j​\(1−2​p^i​j\)\\displaystyle=\\widehat\{p\}\_\{ij\}^\{\\,2\}\+\\widehat\{\\mu\}\_\{ij\}\(1\-2\\widehat\{p\}\_\{ij\}\)\(46\)=\(p^i​j−μ^i​j\)2\+μ^i​j​\(1−μ^i​j\)\.\\displaystyle=\(\\widehat\{p\}\_\{ij\}\-\\widehat\{\\mu\}\_\{ij\}\)^\{2\}\+\\widehat\{\\mu\}\_\{ij\}\(1\-\\widehat\{\\mu\}\_\{ij\}\)\.The first term measures discrepancy between the target prediction and the reference mean; the second measures label uncertainty under that mean\. Neither term is the variance of predictions across reference models\. Because expected Brier loss is affine in the label probability, evaluating it under the reference mean is equivalent to averaging expected losses under the individual reference predictions\. Ensembles with the same mean therefore produce the same WAPA score\.

Agreement between the target and reference predictions can still leave a positive query gain\. For example, whenp^i​j=μ^i​j=pi​j∗=1/2\\widehat\{p\}\_\{ij\}=\\widehat\{\\mu\}\_\{ij\}=p\_\{ij\}^\{\*\}=1/2, the target probability is correct, yetsi​j=1/4s\_\{ij\}=1/4\. Observing the label still improves the information available about that fixed comparison\. Thus, WAPA estimates gains in supervision utility on the comparison pool, including gains from resolving label uncertainty\. In general, these gains are estimated throughμ^i​j\\widehat\{\\mu\}\_\{ij\}, and their accuracy depends on how well the reference mean approximatespi​j∗p\_\{ij\}^\{\*\}\.

### D\.2Preference Completion and DPO Objective

Initializeπθ\\pi\_\{\\theta\}fromπ0\\pi\_\{0\}and retain a frozen copy ofπ0\\pi\_\{0\}asπref\\pi\_\{\\mathrm\{ref\}\}\. This DPO reference is distinct from the models supplying acquisition evidence\. We use a soft\-target DPO objective based on the policy\-to\-reference margin\[[Rafailov et al\., 2023](https://arxiv.org/html/2610.19035#bib.bib31)\],

ℳθ​\(c,r\+,r−\)\\displaystyle\\mathcal\{M\}\_\{\\theta\}\(c,r^\{\+\},r^\{\-\}\)=log⁡πθ​\(r\+∣c\)πref​\(r\+∣c\)−log⁡πθ​\(r−∣c\)πref​\(r−∣c\),\\displaystyle=\\log\\frac\{\\pi\_\{\\theta\}\(r^\{\+\}\\mid c\)\}\{\\pi\_\{\\mathrm\{ref\}\}\(r^\{\+\}\\mid c\)\}\-\\log\\frac\{\\pi\_\{\\theta\}\(r^\{\-\}\\mid c\)\}\{\\pi\_\{\\mathrm\{ref\}\}\(r^\{\-\}\\mid c\)\},\(47\)ℒDPO​\(θ\)\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{DPO\}\}\(\\theta\)=−1N​M∑\(c,r\+,r−,q\)∈𝒟SB\[qlogσ\(βℳθ\)\+\(1−q\)logσ\(−βℳθ\)\]\.\\displaystyle=\-\\frac\{1\}\{NM\}\\sumop\\displaylimits\_\{\(c,r^\{\+\},r^\{\-\},q\)\\in\\mathcal\{D\}\_\{S\_\{B\}\}\}\\bigl\[q\\log\\sigma\(\\beta\\mathcal\{M\}\_\{\\theta\}\)\+\(1\-q\)\\log\\sigma\(\-\\beta\\mathcal\{M\}\_\{\\theta\}\)\\bigr\]\.\(48\)Hereccis the persona–prompt context,σ\\sigmais the logistic function, andβ\>0\\beta\>0controls the margin scale\. The targetqqis the probability that the stored chosen responser\+r^\{\+\}is preferred tor−r^\{\-\}\. Queried pairs orientr\+r^\{\+\}by the observed label and setq=1q=1\. Unqueried pairs retain their target\-model orientation \(original A is chosen at an exact tie\), withq=p^i​jq=\\widehat\{p\}\_\{ij\}if A is chosen andq=1−p^i​jq=1\-\\widehat\{p\}\_\{ij\}otherwise\. This is equivalent to cross\-entropy with the original A\-oriented soft target in Section[3\.2](https://arxiv.org/html/2610.19035#S3.SS2)\. The All ground\-truth labels policy hasq=1q=1throughout and uses standard sigmoid DPO\. Appendix[G\.14](https://arxiv.org/html/2610.19035#A7.SS14)retains the hard\-label comparison, which setsq=1q=1for unqueried pairs as well\.

Only queried evaluator labels enter the completed training dataset; unqueried comparisons retain base\-model probabilities\. Downstream evaluation details are given in Appendix[F\.4](https://arxiv.org/html/2610.19035#A6.SS4)\.

### D\.3Post\-acquisition Preference Refinement

This optional extension refines unqueried preference probabilities after WAPA acquisition\. It leaves the query budget and acquired set unchanged\. The preference\-completion rule in Section[3\.2](https://arxiv.org/html/2610.19035#S3.SS2)otherwise retains base\-model probabilities on these comparisons\.

Prediction refinement\.We use the localization construction of prediction\-powered conditional inference \(PPCI;[Sui et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib5)\)\. For each problemjj, split the unqueried personas into two halves\. Each personaiiuses the opposite halfHi​jH\_\{ij\}as its reference pool\. LetLjL\_\{j\}contain the queried personas\. PPCI’s inner two\-fold construction gives normalized reference weightsai​r,ja\_\{ir,j\}and acquired\-label weightsbi​r,jb\_\{ir,j\}\. These use a common reference normalization and may be signed\. We form

𝐪α,i​j=��2​\[∑r∈Hi​jai​r,j​𝐩^r​j\+α​∑r∈Ljbi​r,j​\(𝐞Yr​j−𝐩^r​j\)\],\\mathbf\{q\}\_\{\\alpha,ij\}=\\Pi\_\{\\Delta\_\{2\}\}\\\!\\left\[\\sumop\\displaylimits\_\{r\\in H\_\{ij\}\}a\_\{ir,j\}\\widehat\{\\mathbf\{p\}\}\_\{rj\}\+\\alpha\\sumop\\displaylimits\_\{r\\in L\_\{j\}\}b\_\{ir,j\}\\bigl\(\\mathbf\{e\}\_\{Y\_\{rj\}\}\-\\widehat\{\\mathbf\{p\}\}\_\{rj\}\\bigr\)\\right\],\(49\)where𝐩^i​j=\(p^i​j,1−p^i​j\)\\widehat\{\\mathbf\{p\}\}\_\{ij\}=\(\\widehat\{p\}\_\{ij\},1\-\\widehat\{p\}\_\{ij\}\)and𝐞Y=\(Y,1−Y\)\\mathbf\{e\}\_\{Y\}=\(Y,1\-Y\);��2\\Pi\_\{\\Delta\_\{2\}\}projects onto the probability simplex\. The first term smooths model predictions; the second adds label residuals\. Weights use a Matérn\-5/25/2kernel on persona features, base predictions, and twice the reference\-model mean\. Persona features are normalized term frequency–inverse document frequency \(TF–IDF\) unigrams and bigrams, scaled by1/21/\\sqrt\{2\}\. Kernel tuning uses covariates and sample sizes, without response values\.

Candidates comprise the raw predictor andα∈\{0,0\.01,0\.025,0\.05,0\.1,0\.2,0\.5,1\}\\alpha\\in\\\{0,0\.01,0\.025,0\.05,0\.1,0\.2,0\.5,1\\\}\. Using acquired labels, we fit an ordinary least squares \(OLS\) bridge for prediction residuals\. The bridge assumes a shared conditional residual relationship across queried and unqueried comparisons\. Its four features are an intercept, standardized WAPA\-score percentile, standardized negative base probability, and their interaction\. A probability\-constrained coefficient region accounts for uncertainty at nominal levelδ=0\.05\\delta=0\.05, allowing dependence within each persona\. We select the candidate with the smallest nonpositive upper excess\-Brier\-risk score; otherwise, we retain the raw predictor\. This model\-based criterion chooses oneα\\alphafor each acquisition condition\. Atα=0\\alpha=0, the selected prediction is pure smoothing, distinct from the raw predictor\.

Use in preference completion\.The selected probabilities can replace the unqueried targets in the soft\-target DPO objective of Appendix[D\.2](https://arxiv.org/html/2610.19035#A4.SS2); acquired labels remain unchanged\. Appendix[G\.16](https://arxiv.org/html/2610.19035#A7.SS16)evaluates prediction error and downstream sensitivity to this refinement\.

## Appendix EDatasets

We use two benchmarks: Roleplay for acquisition and downstream alignment, and OpinionQA for an acquisition\-only extension\.

### E\.1Roleplay

Source and task\.Roleplay\[[Singh et al\., 2026](https://arxiv.org/html/2610.19035#bib.bib33)\]provides synthetic personas and model\-labeled preferences between candidate responses\. We use the released persona descriptions, prompts, and preferred/nonpreferred response pairs\. The source preference determines the binary evaluation label after mapping to our fixed candidate order\. We use six persona collections: Africa, Asia, North America, South America, Europe, and Heterogeneous\.

Collections and evaluation splits\.Table[S1](https://arxiv.org/html/2610.19035#A5.T1)gives the rectangular supports used in our experiments, whereNNis the number of personas andMMis the number of comparisons per persona\. Acquisition uses a fixed comparison set within each collection\. Seen evaluation uses new comparisons for the acquisition personas; Held\-out evaluation uses new personas\. Main\-text results cover Africa, Asia, North America, and Europe; acquisition results for South America and Heterogeneous appear in Appendix[G\.2](https://arxiv.org/html/2610.19035#A7.SS2)\. Downstream training uses the four main collections and retains every acquisition\-support comparison: queried comparisons use acquired labels and the remainder use target\-model pseudo\-labels\. Thus the query budget changes label sources, not training\-set size\.

Table S1:Roleplay split supports \(N×MN\\times M\) and comparison totals\. Training uses the full acquisition support for the four main collections; a dash indicates no downstream training\.CollectionAcquisitionN×MN\\times MTotalTrainingSeenN×MN\\times MTotalHeld\-outN×MN\\times MTotalAfrica77×\\times61247,12447,12477×\\times15411,85843×\\times1827,826Asia67×\\times61741,33941,33967×\\times15410,31853×\\times1829,646North America75×\\times61646,20046,20075×\\times15411,55045×\\times1828,190South America72×\\times61744,424—72×\\times15411,08848×\\times1828,736Europe69×\\times61742,57342,57369×\\times15410,62651×\\times1829,282Heterogeneous60×\\times61036,600—60×\\times1549,24040×\\times1827,280

Data preparation\.We retain source questions marked as global and use fixed persona and prompt memberships for each split\. Each support contains every persona–prompt combination\. Seen uses the acquisition personas on prompt texts absent from acquisition\. Held\-out uses personas excluded from acquisition and training\. All methods share the resulting supports\.

Fixed acquisition Target\.Within each Roleplay collection, we samplemax⁡\(1,⌊0\.1​N⌋\)\\max\(1,\\lfloor 0\.1N\\rfloor\)individuals uniformly without replacement\. Membership is fixed across methods, budgets, and parameters and does not depend on supervision quality\.

Similarity\-defined held\-out Target\.Let𝒜\\mathcal\{A\}be the acquisition persona set,𝒢⊂𝒜\\mathcal\{G\}\\subset\\mathcal\{A\}its unchanged random Target, andℋ\\mathcal\{H\}the disjoint held\-out persona set\. Leteie\_\{i\}be the unit\-normalized embedding of personaii’s complete description\. Define

shsim=1\|𝒢\|​∑i∈𝒢eh⊤​ei,k=max⁡\{1,⌊0\.1​\|ℋ\|⌋\}\.s^\{\\mathrm\{sim\}\}\_\{h\}=\\frac\{1\}\{\|\\mathcal\{G\}\|\}\\sumop\\displaylimits\_\{i\\in\\mathcal\{G\}\}e\_\{h\}^\{\\top\}e\_\{i\},\\qquad k=\\max\\\{1,\\lfloor 0\.1\|\\mathcal\{H\}\|\\rfloor\\\}\.\(50\)The held\-out Target𝒢ℋ\\mathcal\{G\}\_\{\\mathcal\{H\}\}contains thekkhighest\-scoring members ofℋ\\mathcal\{H\}, with ties broken by ascending original persona ID\. This uses average pairwise cosine similarity to all acquisition Target members\. The selected sizes are 4/43, 5/53, 4/45, and 5/51 in Africa, Asia, North America, and Europe\. Membership is fixed across policies and welfare settings\. This cohort defines Target utility for held\-out evaluation\.

Description encoder and outcome\-blind selection\.We use the frozen sentence\-transformers/all\-MiniLM\-L6\-v2 encoder, with masked mean pooling and unit normalization\. Only the complete persona description enters the encoder; IDs, response pairs, labels, and policy scores do not\. All 480 descriptions fit within 254 content word pieces, so no text is truncated\. Descriptions include interests, preferences, and background; their semantic similarity is not a validated measure of behavioral preference equivalence\.

This is a post\-hoc exploratory analysis\. Cohort membership was computed from descriptions before the analysis accessed downstream labels or utilities\.

### E\.2OpinionQA

Source and task\.OpinionQA\[[Santurkar et al\., 2023](https://arxiv.org/html/2610.19035#bib.bib12)\]records respondents’ choices on multiple\-choice questions\. We use the processed responses released with Group\-Adaptive\-Elicitation\. Each respondent answers the same 30 questions, with three to five options per question\.

Regional subsets and evaluation scope\.We use four United States regional subsets \(Table[S2](https://arxiv.org/html/2610.19035#A5.T2)\), comprising 3,130 respondents and 93,900 question–respondent pairs\. Each subset uses the same fixed random\-10% Target construction as Roleplay \(Appendix[E\.1](https://arxiv.org/html/2610.19035#A5.SS1)\)\. These subsets extend acquisition evaluation\. Results appear in Appendix[G\.1](https://arxiv.org/html/2610.19035#A7.SS1)\.

Table S2:OpinionQA support: respondentsNN, questions per respondentMM, and total observations\.RegionNNMMN×MN\\times MMidwest8953026,850Northeast6033018,090South7353022,050West8973026,910

Data preparation\.South is a random sample of 735 from its 1,471 source respondents; the other regional subsets retain their released support\. We preserve the original option ordering and respondent identities across methods\.

## Appendix FDetailed Experimental Setup

Unless otherwise specified, all random seeds are set to 42\. Human and judge evaluations report bootstrap confidence intervals \(CIs\) as specified in Appendix[J](https://arxiv.org/html/2610.19035#A10)\.

### F\.1Models and Acquisition Evidence

The target model is Qwen3\-4B\-Instruct\-2507\. Collection records give the provider\-reported reference\-service versions as Qwen3\.8\-Max, GLM\-5\.2, and DeepSeek\-V4\-Flash\. Reference models supply elicited probabilities, while target probabilities come from answer\-option likelihoods\. Roleplay probabilities are mapped to the original response orientation after display\-order symmetrization\. OpinionQA uses the original option ordering in one presentation per cell, without permutation averaging\. Probability evidence is fixed before query selection\. The collection messages and target chat wrapper appear in Appendices[H\.1](https://arxiv.org/html/2610.19035#A8.SS1)and[H\.2](https://arxiv.org/html/2610.19035#A8.SS2)\.

### F\.2Reference\-Service Workload

Cost accounting\.The query budget counts acquired labels\. Reference inference, query allocation, DPO training, and evaluation are separate computational costs\. Equal query budgets therefore compare label efficiency and do not imply equal total cost: Entropy uses target predictions, whereas WAPA additionally uses reference predictions\. Allocation operates on frozen scores without further model calls\. Reference token usage is reported below; training compute is reported in Appendix[F\.5](https://arxiv.org/html/2610.19035#A6.SS5), and available evaluation and generation resource information in Appendix[F\.6](https://arxiv.org/html/2610.19035#A6.SS6)\. Training graphics processing unit \(GPU\) hours cover the reported final policies; preliminary runs, retries, evidence collection, evaluation, and generation are excluded\. Generation and implicit\-scoring runtimes were not consistently recorded, so compute accounting is stage\-specific\.

Reference probabilities are collected through hosted application programming interfaces \(APIs\)\. Estimated total reference\-model token usage \(input and output combined\) is approximately 92\.75 million tokens for OpinionQA and 510\.18 million tokens for Roleplay\.

### F\.3Baselines and Welfare Weighting

Shared acquisition settings\.We compare equal\-weight mean welfare\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)and target\-priority, inequality\-sensitive welfare\(2,−5\)\(2,\-5\), with shiftε=0\.5\\varepsilon=0\.5\. At the main 20% budget,B=⌊0\.2​N​M⌋B=\\lfloor 0\.2NM\\rfloor\. This gives 9,424, 8,267, 9,240, 8,884, 8,514, and 7,320 queries for Roleplay\-Africa, Asia, North America, South America, Europe, and Heterogeneous, respectively; the OpinionQA counts are 5,370, 3,618, 4,410, and 5,382 for Midwest, Northeast, South, and West\. All methods use the same support and fixed Target membership \(Appendix[E\.1](https://arxiv.org/html/2610.19035#A5.SS1)\)\.

Query scores\.Random samples comparisons uniformly without replacement\. For a comparison withKKoptions, Entropy uses the target model’s predictive entropy,−∑k=1Kpklogpk\-\\sumop\\displaylimits\_\{k=1\}^\{K\}p\_\{k\}\\log p\_\{k\}\. Reference Disagreement uses population variance across reference probabilities; for categorical choices, it sums this variance over options\. WAPA uses exact marginal welfare gains from reference\-expected Brier loss,12​\(1\+∑kpk2−2​∑kpk​qk\)\\tfrac\{1\}\{2\}\(1\+\\sumop\\displaylimits\_\{k\}p\_\{k\}^\{2\}\-2\\sumop\\displaylimits\_\{k\}p\_\{k\}q\_\{k\}\), whereppis the target probability vector andqqis the equal\-weight reference mean\. This reduces to reference\-expected binary Brier loss for two options\. No queries retainsinitial predictions\.

Matched first\-order baselines\.Entropy and Reference Disagreement specify per\-comparison acquisition scores; these scores alone do not prescribe an allocation rule for nonlinear welfare across personas\. To extend these score\-based baselines to our welfare settings, we adopt a first\-order welfare rule that combines each method’s own score with the designated\-group and current\-utility weights\. This defines the weighted baseline variants used in our experiments and recovers their global score rankings under\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)\. Letai\(γ\)=1\+\(γ−1\)𝟏\{i∈G\}a\_\{i\}\(\\gamma\)=1\+\(\\gamma\-1\)\\mathbf\{1\}\\\{i\\in G\\\}be the unnormalized priority weight for the fixed Target groupGG\. For methodmm, lets~i​jm\\widetilde\{s\}^\{m\}\_\{ij\}be its normalized query score\. Its utility proxy isU^im\(S\)=1−M−1∑j:\(i,j\)<Ss~i​jm\\widehat\{U\}\_\{i\}^\{m\}\(S\)=1\-M^\{\-1\}\\sumop\\displaylimits\_\{j:\(i,j\)\\notin S\}\\widetilde\{s\}^\{m\}\_\{ij\}, with the original denominatorMMand zero remaining contribution from queried cells\. The first\-order change in the welfare objective built from this proxy gives priority

Pi​jm​\(S\)=ai​\(γ\)​\[U^im​\(S\)\+ε\]ρ−1​s~i​jm/M\.P^\{m\}\_\{ij\}\(S\)=a\_\{i\}\(\\gamma\)\[\\widehat\{U\}\_\{i\}^\{m\}\(S\)\+\\varepsilon\]^\{\\rho\-1\}\\widetilde\{s\}^\{m\}\_\{ij\}/M\.\(51\)After selection, the recipient’s state increases by its own score divided byMM\. For binary scores, Entropy is normalized bylog⁡2\\log 2and reference variance by1/41/4; categorical entropy is normalized bylog⁡K\\log Kand summed reference variance by1−1/K1\-1/K\. For binary comparisons under\(1,1\)\(1,1\), the original raw\-score rankings are retained to preserve numerical ties\. These methods share the welfare form and parameters, but use different utility proxies; only WAPA’s proxy is reference\-expected Brier utility\. All methods are evaluated using the same true\-label utilities\. Appendix[G\.5](https://arxiv.org/html/2610.19035#A7.SS5)compares exact and first\-order allocation for WAPA with its score held fixed, finding nearly identical selections and acquisition utilities in the evaluated setting\.

Welfare\-agnostic preference acquisition\.We implement the certainty rule from APL\[[Muldrew et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib23)\]and the batch selection rule from BAL\-PM\[[Melo et al\., 2024](https://arxiv.org/html/2610.19035#bib.bib24)\]on the four main Roleplay pools\. Both retain welfare\-agnostic acquisition rules, with the same selections used across welfare settings\. Models remain frozen during a single acquisition batch, and all selections are saved before evaluator labels are accessed\.

APL ranks pairs by\|r^​\(x,yA\)−r^​\(x,yB\)\|\|\\widehat\{r\}\(x,y\_\{A\}\)\-\\widehat\{r\}\(x,y\_\{B\}\)\|, wherer^​\(x,y\)=β​\[log⁡πθ​\(y∣x\)−log⁡π0​\(y∣x\)\]\\widehat\{r\}\(x,y\)=\\beta\[\\log\\pi\_\{\\theta\}\(y\\mid x\)\-\\log\\pi\_\{0\}\(y\\mid x\)\]andβ=0\.1\\beta=0\.1\. The scorerπθ\\pi\_\{\\theta\}is the existing All pseudo\-labels soft\-DPO policy, trained without acquired labels;π0\\pi\_\{0\}is the original Qwen base\. Completion log probabilities use the training template, masks, and pair\-aware 2,048\-token cutoff\. We adapt APL’s acquisition rule to pseudo\-label initialization and a single frozen batch\.

BAL\-PM uses the existing reference probabilities for its committee information term, replacing the original trained preference\-model ensemble\. Prompt features are the original Qwen base’s final\-layer hidden state at the last prompt token, with the persona in the system message\. We retain the author’s self\-inclusive 13\-neighbor convention, closed\-radius ties, and dynamic selected\-neighbor counts, with diversity weight0\.010\.01and dimension parameter11\. Acquisition starts from an empty queried set\. Both methods use the bfloat16 \(BF16\) format for inference and fixed preprocessing\.

APL and BAL\-PM are evaluated on the same 0%–100% budget grid as the other methods, in 1% increments\. Each budget uses a prefix of the full acquisition order, with the common idealized\-repair protocol and original target probabilities\. APL also uses the training computation for its pseudo\-label scorer \(Appendix[F\.2](https://arxiv.org/html/2610.19035#A6.SS2)\)\.

Welfare\-optimal reference\.Welfare\-optimal Oracle computes the observed Brier lossℓi​jobs=12​‖𝐩i​j−𝐞yi​j‖22\\ell^\{\\mathrm\{obs\}\}\_\{ij\}=\\tfrac\{1\}\{2\}\\\|\\mathbf\{p\}\_\{ij\}\-\\mathbf\{e\}\_\{y\_\{ij\}\}\\\|\_\{2\}^\{2\}and remaining utilityUiobs\(S\)=1−M−1∑j:\(i,j\)<Sℓi​jobsU\_\{i\}^\{\\mathrm\{obs\}\}\(S\)=1\-M^\{\-1\}\\sumop\\displaylimits\_\{j:\(i,j\)\\notin S\}\\ell^\{\\mathrm\{obs\}\}\_\{ij\}\. It sorts true losses within each persona and applies the exact marginal allocator with the panel’sγ\\gamma,ρ\\rho,ε\\varepsilon, Target membership, and budgetBB\. The optimality results in Appendix[C\.3](https://arxiv.org/html/2610.19035#A3.SS3)apply directly to these exact gains and states, giving the maximum realized scalar welfare over all sets ofBBqueried comparisons\. For\(1,1\)\(1,1\)the allocation reduces to the global top\-BBtrue losses; for\(2,−5\)\(2,\-5\)it can differ\. Oracle label access is used to rank queries and update exact states, but only the selectedBBcomparisons use their observed labels in acquisition evaluation\.

Appendix[F\.4](https://arxiv.org/html/2610.19035#A6.SS4)defines recovery relative to these scalar\-welfare\-optimal selections\.

### F\.4Evaluation Protocol and Metrics

Utility differences are absolute percentage\-point differences, not relative changes\. Acquisition results use % for this scale\. Downstream bar plots show reference\-gap recovery, defined below\.

Acquisition evaluation\.For the selected setSS, the evaluated probability vector is the observed one\-hot label on queried comparisons and the initial model prediction elsewhere:

𝐩i​jeval=\{𝐞yi​j,\(i,j\)∈S,𝐩i​jinitial,\(i,j\)<S\.\\mathbf\{p\}^\{\\mathrm\{eval\}\}\_\{ij\}=\\begin\{cases\}\\mathbf\{e\}\_\{y\_\{ij\}\},&\(i,j\)\\in S,\\\\ \\mathbf\{p\}^\{\\mathrm\{initial\}\}\_\{ij\},&\(i,j\)\\notin S\.\\end\{cases\}\(52\)Evaluator labels score both queried and unqueried comparisons after selection\. A queried comparison contributes zero Brier loss\. This evaluation measures the predictive error covered by acquired labels; trained policies are evaluated separately on test comparisons\.

Categorical and binary predictive utility\.For comparisonjjof individualii, let𝐩i​jeval\\mathbf\{p\}^\{\\mathrm\{eval\}\}\_\{ij\}be the probability vector over itsKi​jK\_\{ij\}options and𝐞yi​j\\mathbf\{e\}\_\{y\_\{ij\}\}the one\-hot vector of the observed choice\. We define

ui=1−12​Mi​∑j=1Mi‖𝐩i​jeval−𝐞yi​j‖22\.u\_\{i\}=1\-\\frac\{1\}\{2M\_\{i\}\}\\sumop\\displaylimits\_\{j=1\}^\{M\_\{i\}\}\\left\\\|\\mathbf\{p\}^\{\\mathrm\{eval\}\}\_\{ij\}\-\\mathbf\{e\}\_\{y\_\{ij\}\}\\right\\\|\_\{2\}^\{2\}\.\(53\)The factor1/21/2keeps each comparison’s loss in\[0,1\]\[0,1\]for any option count\. For two options,12​‖𝐩−𝐞y‖22=\(p−y\)2\\tfrac\{1\}\{2\}\\\|\\mathbf\{p\}\-\\mathbf\{e\}\_\{y\}\\\|\_\{2\}^\{2\}=\(p\-y\)^\{2\}, giving binary utility1−\(p−y\)21\-\(p\-y\)^\{2\}\. For downstream evaluation, the probability vector is obtained from the trained policy as described below\. Brier loss is strictly proper: truthful probabilities minimize expected loss\[[Gneiting and Raftery, 2007](https://arxiv.org/html/2610.19035#bib.bib32)\]\. Its utility transformation evaluates probability quality, including confidence, rather than only the most probable choice\. For acquisition evaluation, predictive utility coincides with empirical supervision utility: queried comparisons use observed labels, while unqueried comparisons retain AI\-generated probabilities\. For downstream evaluation, predictive utility instead measures the trained policy’s preference predictions on test comparisons\.

Downstream preference probabilities\.For fixed source responses A and B conditioned on persona and prompt, the implemented score is

zi​j=β\[log⁡πθ​\(ri​j1∣ci​j\)−log⁡πref​\(ri​j1∣ci​j\)−logπθ\(r0i​j∣ci​j\)\+logπref\(r0i​j∣ci​j\)\],pDPOi​j=σ\(zi​j\),\\begin\{split\}z\_\{ij\}=\\beta\\bigl\[&\\log\\pi\_\{\\theta\}\(r^\{1\}\_\{ij\}\\mid c\_\{ij\}\)\-\\log\\pi\_\{\\mathrm\{ref\}\}\(r^\{1\}\_\{ij\}\\mid c\_\{ij\}\)\\\\ &\-\\log\\pi\_\{\\theta\}\(r^\{0\}\_\{ij\}\\mid c\_\{ij\}\)\+\\log\\pi\_\{\\mathrm\{ref\}\}\(r^\{0\}\_\{ij\}\\mid c\_\{ij\}\)\\bigr\],\\qquad p^\{\\mathrm\{DPO\}\}\_\{ij\}=\\sigma\(z\_\{ij\}\),\\end\{split\}\(54\)withβ=0\.1\\beta=0\.1and complete\-response log likelihoods\. We apply the sigmoid without additional temperature fitting or calibration\. The margin measures relative preference change against the DPO reference; free\-response generation is evaluated separately in Appendix[J](https://arxiv.org/html/2610.19035#A10)\.

Scoring inputs and utility\.Implicit scoring places the complete persona background in the system turn, using the Qwen no\-thinking template\. It permits a 32,768\-token context and uses complete candidate\-response likelihoods\. For binary choices, substitute𝐩i​jeval=\(pi​jDPO,1−pi​jDPO\)\\mathbf\{p\}^\{\\mathrm\{eval\}\}\_\{ij\}=\(p^\{\\mathrm\{DPO\}\}\_\{ij\},1\-p^\{\\mathrm\{DPO\}\}\_\{ij\}\)and𝐞yi​j=\(yi​j,1−yi​j\)\\mathbf\{e\}\_\{y\_\{ij\}\}=\(y\_\{ij\},1\-y\_\{ij\}\)into the general Brier definition, giving per\-comparison utility1−\(pi​jDPO−yi​j\)21\-\(p^\{\\mathrm\{DPO\}\}\_\{ij\}\-y\_\{ij\}\)^\{2\}\. Average these scores within each persona before aggregation\. All policies are scored on the same test comparisons within each collection and split \(Appendix[E\.1](https://arxiv.org/html/2610.19035#A5.SS1)\)\.

Utility aggregation\.Mean is the equal\-weight average over all individuals; Target is the average over the fixed designated group \(Appendix[E\.1](https://arxiv.org/html/2610.19035#A5.SS1)\)\. Tail averages the lowest 10% of individual utilities, ranked separately for each method\. Sort them asu\(1\)6⋯6u\(N\)u\_\{\(1\)\}\\leqslant\\cdots\\leqslant u\_\{\(N\)\}, letq=0\.1​Nq=0\.1N,k=⌊q⌋k=\\lfloor q\\rfloor, anda=q−ka=q\-k\. Then

Tail=∑r=1ku\(r\)\+a​u\(k\+1\)q\.\\mathrm\{Tail\}=\\frac\{\\sumop\\displaylimits\_\{r=1\}^\{k\}u\_\{\(r\)\}\+au\_\{\(k\+1\)\}\}\{q\}\.\(55\)The boundary individual receives fractional weight: with 77 personas, the seven lowest utilities have weight 1 and the eighth has weight 0\.7, divided by 7\.7\. Appendix[G\.11](https://arxiv.org/html/2610.19035#A7.SS11)extends it to the full lower\-tail curve\.

Hard accuracy and matched comparisons\.Tables[S23](https://arxiv.org/html/2610.19035#A7.T23)–[S25](https://arxiv.org/html/2610.19035#A7.T25)complement Tables[1](https://arxiv.org/html/2610.19035#S4.T1),[S9](https://arxiv.org/html/2610.19035#A7.T9), and[S10](https://arxiv.org/html/2610.19035#A7.T10)using the same four Roleplay datasets, query selections, trained policies, evaluation comparisons, and welfare settings\. For each binary comparison, hard correctness is𝟏\{𝟏\[pi​jeval\>0\.5\]=yi​j\}\\mathbf\{1\}\\\{\\mathbf\{1\}\[p^\{\\mathrm\{eval\}\}\_\{ij\}\>0\.5\]=y\_\{ij\}\\\}, with half credit whenpi​jeval=0\.5p^\{\\mathrm\{eval\}\}\_\{ij\}=0\.5\. Acquisition replaces queried probabilities with observed labels; downstream evaluation thresholds the soft\-label\-trained policies’ implicit preference probabilities defined above\. We average correctness within each persona before aggregation\. Mean weights personas equally; Tail averages the fractionally weighted bottom 10%, reranked separately by accuracy for each method; Target retains the original tables’ fixed membership, including the similarity\-defined Held\-out cohort\. Accuracy\-based Tail membership can therefore differ from utility\-based Tail membership\. The Welfare\-optimal Oracle retains its original Brier\-welfare selections and is not an accuracy upper bound\.

Oracle\-gap recovery\.Gap recovery for outcomeVVis

Recoverym⁡\(V\)=100​Vm−V0VOracle−V0\.\\operatorname\{Recovery\}\_\{m\}\(V\)=100\\frac\{V\_\{m\}\-V\_\{0\}\}\{V\_\{\\mathrm\{Oracle\}\}\-V\_\{0\}\}\.\(56\)Denominators with absolute value at most10−1210^\{\-12\}are undefined; ratios are not clipped\. The Oracle in each panel optimizes that panel’s scalar welfare\. Its separate Mean, Target, and Tail values are reference endpoints, not individual upper bounds; metric\-specific recovery can therefore exceed 100%\.

Reference\-gap recovery\.Figures[4](https://arxiv.org/html/2610.19035#S4.F4)and[5](https://arxiv.org/html/2610.19035#S4.F5)normalize each policy’s utility gain by the corresponding full\-label reference gain\. For policymmand metrickk, we report

Rm,k=100%×Vm,k−Vpseudo,kVground​\-​truth,k−Vpseudo,k\.R\_\{m,k\}=100\\%\\times\\frac\{V\_\{m,k\}\-V\_\{\\mathrm\{pseudo\},k\}\}\{V\_\{\\mathrm\{ground\\mbox\{\-\}truth\},k\}\-V\_\{\\mathrm\{pseudo\},k\}\}\.\(57\)HereVm,kV\_\{m,k\}is the policy’s predictive utility;Vpseudo,kV\_\{\\mathrm\{pseudo\},k\}andVground​\-​truth,kV\_\{\\mathrm\{ground\\mbox\{\-\}truth\},k\}are the utilities of All pseudo\-labels and All ground\-truth labels on the same evaluation support\. We compute recovery from unrounded utilities, separately for each dataset and split; main\-text ranges span four datasets and both persona splits under\(2,−5\)\(2,\-5\); Appendix[G\.9](https://arxiv.org/html/2610.19035#A7.SS9)reports absolute utilities under both welfare specifications\. All reference gaps are positive in these results\. A recovery of 0% matches All pseudo\-labels and 100% matches All ground\-truth labels\. The fully labeled policy is a reference rather than a performance bound, so underlying recovery values are not clipped\. The main and supplementary recovery plots use the same definition for every method, show uncapped values, and share a 0–125% scale\. Absolute utility differences reported in the text remain in percentage points\.

### F\.5Downstream Alignment Training

Training support and reference\.The results in Section[4\.3](https://arxiv.org/html/2610.19035#S4.SS3)use soft\-label DPO, covering Random, APL, BAL\-PM, Entropy and WAPA, All pseudo\-labels, and All ground\-truth labels for all four main datasets\. APL and BAL\-PM retain their welfare\-agnostic selections and share one trained policy across welfare settings\. APL uses a pseudo\-label\-trained policy to score acquisition candidates; its downstream policy starts from the original base model\. Each arm retains the same training comparisons within a collection \(Appendix[E\.1](https://arxiv.org/html/2610.19035#A5.SS1)\)\. The budgeted arms replace the queried 20% of target probabilities with acquisition labels and retain soft probabilities elsewhere\. All pseudo\-labels uses target\-model probabilities exclusively; All ground\-truth labels uses dataset\-provided labels for every training comparison\. The label\-source references share the same model and optimization settings as the budgeted arms\. The All ground\-truth labels objective is identical for the soft\- and hard\-label comparisons\. The original hard\-label results appear in Appendix[G\.14](https://arxiv.org/html/2610.19035#A7.SS14)\.

Training and checkpoint selection\.All thirty\-six runs initialize Qwen3\-4B\-Instruct\-2507 and retain its frozen DPO reference\. They use the soft\-target sigmoid DPO objective in Eq\. \([48](https://arxiv.org/html/2610.19035#A4.E48)\) withβ=0\.1\\beta=0\.1, no auxiliary supervised loss or label smoothing, and low\-rank adaptation \(LoRA\) on all targeted linear modules \(rank 8, scaling 16, dropout 0\)\. Training uses AdamW, learning rate5×10−65\\times 10^\{\-6\}, cosine decay, 10% warmup, zero weight decay, gradient clipping at 1, bfloat16, and a 2,048\-token training cutoff\. The per\-device batch is 4 with 16 gradient\-accumulation steps\. All runs finish three epochs: 2,211 optimizer steps for Roleplay\-Africa, 1,938 for Roleplay\-Asia, 2,166 for Roleplay\-North America, and 1,998 for Roleplay\-Europe\. Evaluation uses the final adapter, with no validation\-based checkpoint selection\. All completed runs share these optimization settings\. Training runs on a server equipped with eight NVIDIA A100\-SXM4\-80GB GPUs; each policy uses one GPU with 80 GB of memory\. Saved training logs for the thirty\-six final runs record 10\.00–11\.56 hours per policy and 387\.12 GPU\-hours in total over three epochs\. The accounting scope is defined in Appendix[F\.2](https://arxiv.org/html/2610.19035#A6.SS2)\.

Training input format\.Persona background is placed in the system turn using the Qwen no\-thinking template \(Appendix[H\.3](https://arxiv.org/html/2610.19035#A8.SS3)\)\. Each training comparison retains its prompt and chosen/rejected responses; the 2,048\-token cutoff above applies to training\. Dataset splits and comparison counts are described in Appendix[E\.1](https://arxiv.org/html/2610.19035#A5.SS1); test scoring is defined in Appendix[F\.4](https://arxiv.org/html/2610.19035#A6.SS4)\.

### F\.6Free\-Response Generation

Generation parameter setting\.The free\-response cases and pilot evaluation use the original hard\-label DPO policies \(Appendix[G\.14](https://arxiv.org/html/2610.19035#A7.SS14)\)\. We generate free responses using the equal\-weight mean\-welfare policies Random, Entropy, and WAPA and the All ground\-truth labels policy \(Full\-GT\)\. Full\-GT responses are model\-generated comparison outputs\. Each policy receives the same prompt and complete persona description in the system context, using the shared training/generation template in Appendix[H\.3](https://arxiv.org/html/2610.19035#A8.SS3)\. Generation uses temperature 0 and a maximum of 8,192 new tokens\.

Archived generation provenance\.The free\-response audit draws on archived outputs from multiple generation backends; per\-response backend identities were not recorded\.

Generation resources\.The vLLM generation configuration uses one A100\-SXM4\-80GB GPU per policy worker, a GPU\-memory utilization setting of 0\.85, up to 64 concurrent sequences, an 8,192\-token batch limit, and prefix caching\.

## Appendix GSupplementary Experiment Results

The score, allocator, reference\-composition, welfare\-shift, and imputation\-source studies evaluate offline acquisition utility\. Downstream studies report trained\-policy outcomes in theirrespective subsections\.

### G\.1OpinionQA: Acquisition across Four US Regions

Table[S3](https://arxiv.org/html/2610.19035#A7.T3)extends the acquisition results to four OpinionQA regions; dataset and acquisition protocol details are in Appendices[E\.2](https://arxiv.org/html/2610.19035#A5.SS2)and[F\.1](https://arxiv.org/html/2610.19035#A6.SS1), respectively\.

Results\.Under equal\-weight mean welfare, WAPA exceeds the strongest budgeted baseline in each region by 3\.49–3\.57% in Mean, 3\.09–3\.96% in Tail, and 1\.61–4\.10% in Target\. Under target\-priority, inequality\-sensitive welfare, its Mean and Tail advantages are 2\.95–3\.25% and 4\.40–6\.23%, respectively\. Target gains are not uniform: in South, Reference Disagreement exceeds WAPA by 0\.97%\. Thus, the additional benchmark supports acquisition gains while retaining the distinction between optimizing a scalar welfare and improving every outcome separately\.

Table S3:Acquisition utility \(%\) at 20% query budget under matched welfare specifications\. Bold marks the best budgeted method within each panel\.MethodOpinionQA\-MidwestOpinionQA\-NortheastOpinionQA\-SouthOpinionQA\-WestMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetNo queries42\.7023\.8843\.7044\.3025\.9843\.9342\.0123\.4342\.0244\.2224\.2344\.24\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random54\.3335\.7854\.1855\.3337\.6455\.0253\.6235\.3753\.3355\.3735\.5355\.66Entropy53\.4334\.6655\.1555\.3537\.4454\.7752\.6533\.6652\.4055\.1535\.7855\.32Reference Disagreement54\.8833\.9354\.9356\.3235\.3856\.5254\.2934\.3855\.9356\.3334\.7056\.96WAPA58\.4039\.7558\.1959\.8940\.7860\.6157\.7838\.9157\.5359\.8938\.8759\.60Welfare\-optimal Oracle62\.7044\.2462\.2464\.3044\.0163\.5462\.0142\.4562\.7964\.2242\.7863\.50\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random54\.3335\.7854\.1855\.3337\.6455\.0253\.6235\.3753\.3355\.3735\.5355\.66Entropy53\.4434\.5257\.3355\.3837\.3656\.9152\.7033\.7954\.3755\.1135\.8956\.95Reference Disagreement54\.9633\.3966\.2756\.2134\.1667\.2454\.3533\.9666\.5056\.2833\.7167\.71WAPA57\.9140\.6268\.2759\.4242\.6769\.1057\.3839\.7765\.5359\.5342\.1268\.41Welfare\-optimal Oracle62\.7059\.7974\.7364\.3061\.3376\.6462\.0159\.0474\.0664\.2261\.1376\.34

### G\.2Roleplay\-South America and Roleplay\-Heterogeneous

Additional populations\.Table[S4](https://arxiv.org/html/2610.19035#A7.T4)extends the main acquisition comparison to two additional Roleplay collections \(dataset and evaluation details: Appendices[E\.1](https://arxiv.org/html/2610.19035#A5.SS1)and[F\.4](https://arxiv.org/html/2610.19035#A6.SS4)\)\.

Table S4:Acquisition utility \(%\) at 20% query budget under matched welfare specifications\. Bold marks the best budgeted method within each panel\.MethodRoleplay\-South AmericaRoleplay\-HeterogeneousMeanTailTargetMeanTailTargetNo queries81\.6777\.1482\.7681\.2177\.8480\.49\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random85\.3181\.8785\.9885\.0981\.7584\.49Entropy86\.5981\.7687\.6486\.1281\.9185\.20Reference Disagreement87\.2483\.6787\.7286\.8284\.1586\.71WAPA90\.2687\.6290\.4789\.7186\.5889\.85Welfare\-optimal Oracle96\.4794\.1096\.4296\.1292\.0296\.51\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random85\.3181\.8785\.9885\.0981\.7584\.49Entropy86\.6081\.6689\.1986\.1581\.8387\.34Reference Disagreement87\.1883\.1391\.4286\.8083\.8390\.89WAPA90\.0886\.8694\.1189\.5586\.4593\.74Welfare\-optimal Oracle96\.4394\.4899\.4996\.0792\.9599\.42

Results\.At 20% budget, WAPA exceeds the strongest budgeted baseline in Mean, Tail, and Target for both collections under both welfare specifications\. Across these comparisons, gains range from 2\.74–3\.02% in Mean, 2\.43–3\.95% in Tail, and 2\.69–3\.14% in Target, extending the main\-budget findings beyond the four main collections\.

### G\.3Equal\-Weight Mean Welfare Budget Curves

Figure[S1](https://arxiv.org/html/2610.19035#A7.F1)complements the\(2,−5\)\(2,\-5\)curves in Figure[2](https://arxiv.org/html/2610.19035#S4.F2)with\(1,1\)\(1,1\)results for the same four main Roleplay collections, covering Mean, Tail, and Target across query budgets\.

Figure S1:Acquisition budget curves under equal\-weight mean welfare\(1,1\)\(1,1\), using the same metrics as Figure[2](https://arxiv.org/html/2610.19035#S4.F2)\. Summaries below each subplot report recovery at 20% budget with the same definition\. All methods are evaluated at 1% budget increments\. APL and BAL\-PM use the same welfare\-agnostic selections across both specifications\.
### G\.4Ablation of the Acquisition Score

Scores and controls\.Writingp=p^i​jp=\\widehat\{p\}\_\{ij\}andq=μ^i​jq=\\widehat\{\\mu\}\_\{ij\}for the frozen target and reference\-mean probabilities, the WAPA score decomposes as

sWAPA=\(p−q\)2\+q⁡\(1−q\)\.s\_\{\\mathrm\{WAPA\{\}\}\}=\(p\-q\)^\{2\}\+q\(1\-q\)\.\(58\)We compare the full score with discrepancy alone,sgap=\(p−q\)2s\_\{\\mathrm\{gap\}\}=\(p\-q\)^\{2\}; reference\-mean uncertainty alone,sunc=q⁡\(1−q\)s\_\{\\mathrm\{unc\}\}=q\(1\-q\)\. The four main Roleplay collections, frozen predictions, comparison pools, 20% query budget, fixed Target membership, and target\-model completion are shared across arms\. All three scores use the same exact marginal allocator under\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)and\(2,−5\)\(2,\-5\), withε=0\.5\\varepsilon=0\.5and the same deterministic tie\-breaking rule\. Each score supplies both the initial per\-persona residual\-risk estimate and its decrement after a query\. We retain native score scales, includingsunc∈\[0,0\.25\]s\_\{\\mathrm\{unc\}\}\\in\[0,0\.25\], without rescaling the uncertainty component\. This compares surrogate score choices under a common allocation rule; at nonlinear welfare, changing a score also changes the estimated utility trajectory\. All query sets are fixed before labels are revealed\.

Contributions of discrepancy and uncertainty\.Discrepancy accounts for most of the Mean gain: discrepancy alone and the full score differ by at most0\.0700\.070percentage points across the evaluated configurations \(Table[S5](https://arxiv.org/html/2610.19035#A7.T5)\)\. Under\(2,−5\)\(2,\-5\), adding reference\-mean uncertainty raises Target utility by0\.720\.72–1\.031\.03points across the four datasets\. Retaining uncertainty therefore improves utility for the designated subgroup with little change in Mean utility\.

Uncertainty alone yields lower Mean and Tail utility than the full score, by2\.302\.30–2\.652\.65and2\.392\.39–4\.294\.29points, respectively, across both settings\. It attains higher Target utility under\(2,−5\)\(2,\-5\)at the expense of Mean and Tail\. The uncertainty term captures query value even when the target and reference mean agree: forp=q=0\.5p=q=0\.5, discrepancy is zero, but observing the label removes a Brier loss of0\.250\.25\. Subgroup priority comes from the welfare weights\. Adding uncertainty changes both query rankings and the estimated utility states used by the allocator; the Target gains above measure their combined effect\.

Table S5:Acquisition Brier utility \(%\) for score ablations at 20% query budget\. All scores use exact marginal allocation and target\-model completion\. Bold marks the highest value within each setting\.ScoreAfricaAsiaNorth AmericaEuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTarget\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)WAPA90\.38487\.52990\.38789\.83887\.06189\.54490\.22187\.81490\.45090\.07587\.06289\.552Discrepancy only90\.38487\.56590\.35089\.85786\.96289\.50290\.22887\.79790\.48790\.09287\.05689\.587Reference uncertainty only88\.08184\.59387\.54387\.49284\.19988\.05187\.85584\.47487\.92987\.53684\.67386\.062\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)WAPA90\.23787\.11494\.43089\.71486\.78093\.52690\.01887\.24294\.17389\.96187\.12793\.639Discrepancy only90\.27987\.03493\.59589\.78386\.81292\.49190\.08887\.31493\.45490\.00087\.08392\.865Reference uncertainty only87\.83483\.42298\.02787\.14783\.16397\.97787\.56782\.94897\.95687\.31583\.64597\.517

### G\.5Sensitivity to the Allocation Rule

Controlled allocator comparison\.We compare exact marginal allocation with its first\-order approximation for WAPA across the four main Roleplay collections\. We use a 20% query budget and\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)\. Both variants hold the WAPA scores, frozen predictions, comparison pool, and fixed random\-10% Target unchanged, withε=0\.5\\varepsilon=0\.5, and target\-model completion\. Only the allocation rule changes; the first\-order variant uses Equation[51](https://arxiv.org/html/2610.19035#A6.E51)with WAPA’s score andutility state\.

Nearly identical selections and acquisition outcomes\.Table[S6](https://arxiv.org/html/2610.19035#A7.T6)shows that query\-set overlap is at least 99\.9879% and every utility difference is below 0\.00213%\. Thus, WAPA’s acquisition results in these settings are insensitive to replacing exact increments with the first\-order rule used by the matched baselines\. This comparison isolates the effect of the allocator on WAPA’sacquisition results\.

Table S6:First\-order versus exact WAPA at 20% budget under\(2,−5\)\(2,\-5\)\. Utility differences are first\-order minus exact, in %\. Overlap is the fraction of queried comparisons shared by the two sets\.DatasetOverlap \(%\)�\\DeltaMean�\\DeltaTail�\\DeltaTargetRoleplay\-Africa99\.9894\+0\.0021\+0\.0000\+0\.0000Roleplay\-Asia99\.9879\+0\.0000\+0\.0000\+0\.0000Roleplay\-North America99\.9892\+0\.0000\+0\.0000\+0\.0000Roleplay\-Europe100\.0000\+0\.0000\+0\.0000\+0\.0000

### G\.6Sensitivity to Reference\-Model Composition

Reference subsets and controls\.We compare the full ensemble with all three single\-reference and all three leave\-one\-out variants on the four main datasets\. Qwen, GLM, and DeepSeek denote the reference services identified in Appendix[F\.1](https://arxiv.org/html/2610.19035#A6.SS1); “Without” removes that reference and averages the remaining two\. For each subset, we replace the reference meanqqins=q​\(1−p\)2\+\(1−q\)​p2s=q\(1\-p\)^\{2\}\+\(1\-q\)p^\{2\}with the equal\-weight mean of its retained references\. This changes both the initial estimated residual risk and each query decrement\. All variants share the frozen, orientation\-aligned predictions, exact marginal allocator, comparison pool, fixed Target membership,ε=0\.5\\varepsilon=0\.5, and 20% query budget\. The two welfare settings are\(1,1\)\(1,1\)and\(2,−5\)\(2,\-5\)\. Unqueried comparisons retaintarget\-model probabilities\.

Performance across reference choices\.Table[S7](https://arxiv.org/html/2610.19035#A7.T7)shows that every single\-reference and leave\-one\-out variant retains higher Mean, Tail, and Target utility than the strongest corresponding original acquisition baseline in Table[1](https://arxiv.org/html/2610.19035#S4.T1), across all four datasets and both settings\. These comparisons use the original Random, Entropy, and Reference Disagreement results, with Reference Disagreement retaining its full ensemble\. Thus, the observed acquisition advantage does not depend on any one reference\. The full ensemble improves Mean utility over every single\-reference variant by 0\.128–1\.643% across these settings\. Subsets can achieve higher Tail or Target utility, so the ensemble benefit is not uniform across metrics\. Together, these results support the use of multiple references for strong average performance and show that WAPA remains effective across the testedreference compositions\.

Table S7:Acquisition Brier utility \(%\) for reference\-composition ablations at 20% query budget\. All variants use exact marginal allocation and target\-model completion\. Bold marks the highest value within each setting\.ReferencesAfricaAsiaNorth AmericaEuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTarget\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)WAPA90\.38487\.52990\.38789\.83887\.06189\.54490\.22187\.81490\.45090\.07587\.06289\.552Qwen only89\.89986\.99089\.61289\.39986\.70589\.16590\.00687\.88390\.27289\.60686\.71789\.122GLM only90\.05787\.66689\.95389\.40686\.61589\.08289\.86987\.50589\.99989\.69386\.88789\.034DeepSeek only89\.36286\.82589\.77688\.93386\.33088\.75088\.57885\.74388\.68189\.32086\.22888\.694Without Qwen90\.28087\.74490\.52589\.79187\.29989\.65489\.80287\.27089\.80690\.03886\.90289\.667Without GLM90\.21387\.56690\.04389\.84387\.23589\.49590\.11187\.96290\.37890\.00686\.99289\.501Without DeepSeek90\.22587\.39690\.07289\.68486\.91389\.55990\.20487\.94390\.33789\.87686\.91689\.344\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)WAPA90\.23787\.11494\.43089\.71486\.78093\.52690\.01887\.24294\.17389\.96187\.12793\.639Qwen only89\.83386\.71293\.29589\.39086\.52592\.64689\.89087\.33494\.11489\.53086\.64492\.894GLM only89\.86186\.82994\.16089\.22985\.91793\.27489\.60486\.83793\.46289\.54286\.69593\.655DeepSeek only89\.38186\.57093\.04588\.90286\.02791\.84688\.51185\.51292\.14189\.36186\.50792\.700Without Qwen90\.13387\.48294\.16589\.47886\.30793\.08189\.58786\.61693\.43889\.89286\.91693\.565Without GLM90\.15687\.26294\.39289\.68586\.85893\.43089\.88487\.18193\.97889\.87087\.03793\.457Without DeepSeek90\.21987\.05994\.23189\.57486\.54893\.33490\.06287\.39794\.14889\.75087\.02493\.226

### G\.7Sensitivity to the Designated Subgroup

Alternative designated subgroup\.This study tests a different choice of designated subgroup \(Target group\)\. We replace the main experiment’s randomly selected 10% subgroup with the 10% having the lowest initial reference\-estimated supervision utility\. Specifically, we rank personas by their initial reference\-estimated Brier utilityU^i​\(?\)\\widehat\{U\}\_\{i\}\(\\varnothing\)and select the lowestmax⁡\(1,⌊0\.1​N⌋\)\\max\(1,\\lfloor 0\.1N\\rfloor\)values, breaking ties by original persona ID\. Membership is fixed before allocation, is shared across welfare settings, and does not use evaluator labels\. This designated subgroup differs from Tail, which is reranked by final predictive utility for each allocation\. We retain the same 225 parameter combinations, shift, budget, and exact WAPA allocator\. Changes are measured against\(1,1\)\(1,1\)using the same alternative designated subgroup\.

Figure[S2](https://arxiv.org/html/2610.19035#A7.F2)reports WAPA outcomes in the four main Roleplay collections for this alternative designated subgroup\.

Fixed\-group and final\-tail outcomes\.Across the four main collections,\(2,−5\)\(2,\-5\)raises Target utility by 3\.32–3\.77% relative to\(1,1\)\(1,1\), while Mean falls by 0\.14–0\.26% and Tail by 0\.23–0\.63%\. Prioritizing the initially estimated worst\-off group therefore does not guarantee an improvement in the re\-ranked tail\.

Parameter grid\.Both the main random\-Target study and this extension use the same grid\. It contains 25ρ\\rhovalues from−5\-5to 1 in steps of 0\.25 and 9γ\\gammavalues from 1 to 3 in steps of 0\.25\. The shift is 0\.5\. These are descriptive offline parameter comparisons\.

Parameter\-plot conventions\.All changes are relative to\(1,1\)\(1,1\)at the same budget and with the same Target group\. Heatmaps share an inverse\-hyperbolic\-sine color scale with a 1% scale parameter\. In the tradeoff plots, horizontal and vertical axes show Tail and Target changes; color shows Mean change on a symmetric linear scale\. Blue therefore indicates a decrease in Mean only\. Paths fixγ∈\{1,1\.5,2,3\}\\gamma\\in\\\{1,1\.5,2,3\\\}, endpoint labels markρ=−5\\rho=\-5, and arrows point toward decreasingρ\\rho\. Circle, diamond, square, and star mark\(1,1\),\(1,−5\),\(2,1\),\(2,−5\)\(1,1\),\(1,\-5\),\(2,1\),\(2,\-5\)\. Each dataset retains its ownaxis ranges\.

\(a\) Parameter effects

![Refer to caption](https://arxiv.org/html/2610.19035v1/parameter_effects_estimated.png)

\(b\) Outcome tradeoffs

![Refer to caption](https://arxiv.org/html/2610.19035v1/outcome_tradeoffs_estimated.png)

Figure S2:Parameter effects and outcome tradeoffs under an alternative designated subgroup: the 10% of personas with the lowest initial reference\-estimated supervision utility\. Membership is fixed across settings\. Changes are relative to\(1,1\)\(1,1\)with this same subgroup, in %\.
### G\.8Sensitivity to the Welfare Shift

Role of the shift\.The positive shiftε\\varepsilonkeeps the welfare transformation well\-defined and also controls relative priority across personas\. Forρ<1\\rho<1, increasingε\\varepsilonreduces the relative derivative weight assigned to lower estimated utility\. It is therefore part of the acquisition objective, rather than solely a numerical safeguard\. Atρ=1\\rho=1, exact gains and first\-order priorities are independent ofε\\varepsilon\.

Matched sensitivity protocol\.We varyε∈\{0\.1,0\.25,0\.5,1\.0\}\\varepsilon\\in\\\{0\.1,0\.25,0\.5,1\.0\\\}on the four main Roleplay collections, with\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)and a 20% query budget\. Each comparison uses the same shift for WAPA, Entropy, and Reference Disagreement\. Their original scores, utility proxies, and allocation rules are retained: exact marginals for WAPA and first\-order priorities for the weighted baselines\. Random is shared across shifts\. All variants use the same frozen predictions, comparison pool, fixed Target membership, and target\-model completion\. Selections are fixed before evaluator labels are opened\. We also verify identical full selection orders across all four shifts under\(1,1\)\(1,1\), so those results are not repeated\. Theε=0\.5\\varepsilon=0\.5results reproduce the main acquisition experiment\.

Consistent advantages across shifts\.Table[S8](https://arxiv.org/html/2610.19035#A7.T8)shows that WAPA exceeds the strongest matched baseline on Mean, Tail, and Target utility across every tested shift and dataset\. The gains range from 2\.80–3\.12% in Mean, 3\.42–4\.75% in Tail, and 1\.21–4\.07% in Target\. Within WAPA, increasing the shift raises Target utility while reducing Mean and Tail in these experiments\. As the shift grows, lower estimated utility carries less relative weight, leaving more priority for Target\. Choosingε\\varepsilonis therefore part of specifying acquisition priorities\.

Table S8:Acquisition Brier utility \(%\) across shiftsε\\varepsilonat\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)and 20% budget\. Each panel uses the same shift for all welfare\-weighted methods\. Random is shared\. Bold marks the highest value within each panel\.MethodAfricaAsiaNorth AmericaEuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetε=0\.1\\varepsilon=0\.1Random85\.52881\.80684\.86685\.03781\.65285\.53285\.53582\.29285\.22985\.22882\.25484\.567Entropy86\.76082\.08387\.08686\.16882\.09289\.01386\.75082\.34687\.75886\.43582\.27886\.545Reference Disagreement87\.35483\.22390\.88986\.83483\.19591\.62586\.95582\.67790\.50787\.08883\.61390\.070WAPA90\.28687\.29693\.84789\.75086\.86092\.83390\.07787\.43093\.60290\.00387\.25493\.032ε=0\.25\\varepsilon=0\.25Random85\.52881\.80684\.86685\.03781\.65285\.53285\.53582\.29285\.22985\.22882\.25484\.567Entropy86\.76282\.09187\.14186\.17382\.09289\.11386\.75682\.33587\.86386\.43682\.26886\.625Reference Disagreement87\.35383\.21990\.88986\.83483\.19591\.62586\.96182\.67790\.64487\.08983\.61390\.097WAPA90\.26587\.22994\.10789\.72686\.81693\.10690\.06287\.30193\.91689\.97187\.17893\.178ε=0\.5\\varepsilon=0\.5Random85\.52881\.80684\.86685\.03781\.65285\.53285\.53582\.29285\.22985\.22882\.25484\.567Entropy86\.76682\.09187\.28586\.17682\.09289\.17486\.75482\.34187\.93886\.43682\.26386\.629Reference Disagreement87\.35583\.21890\.94586\.83583\.19591\.62586\.96882\.69690\.65687\.10483\.60790\.342WAPA90\.23787\.11494\.43089\.71486\.78093\.52690\.01887\.24294\.17389\.96187\.12793\.639ε=1\.0\\varepsilon=1\.0Random85\.52881\.80684\.86685\.03781\.65285\.53285\.53582\.29285\.22985\.22882\.25484\.567Entropy86\.77082\.08987\.41386\.16982\.07789\.30786\.75482\.33688\.03086\.43982\.25086\.843Reference Disagreement87\.35483\.21890\.96886\.82683\.18991\.69486\.96982\.69190\.69487\.09783\.60790\.357WAPA90\.18686\.96195\.03889\.63586\.63093\.99489\.93587\.03794\.55289\.90087\.02394\.185

### G\.9Absolute Predictive Utility after Downstream Alignment

Tables[S9](https://arxiv.org/html/2610.19035#A7.T9)and[S10](https://arxiv.org/html/2610.19035#A7.T10)provide the absolute predictive utilities underlying the recovery in Figures[4](https://arxiv.org/html/2610.19035#S4.F4)and[5](https://arxiv.org/html/2610.19035#S4.F5)\. They report soft\-label DPO, retaining both label\-source references and all budgeted methods\. APL and BAL\-PM are shared welfare\-agnostic baselines for both welfare specifications\. The corresponding hard\-label results are in Appendix[G\.14](https://arxiv.org/html/2610.19035#A7.SS14)\. Reference\-gap recovery is defined in Appendix[F\.4](https://arxiv.org/html/2610.19035#A6.SS4)and computed from unrounded values\.

Table S9:Seen\-persona utility after soft\-label DPO \(%\) under matched welfare specifications\.MethodRoleplay\-AfricaRoleplay\-AsiaRoleplay\-North AmericaRoleplay\-EuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetAll pseudo\-labels83\.3678\.4082\.2582\.8978\.4183\.4183\.3878\.4584\.0683\.1578\.2081\.67Welfare\-agnostic baselines \(shared across settings\)APL83\.6879\.0682\.7583\.3279\.2083\.6483\.6579\.0384\.2683\.6678\.8782\.41BAL\-PM84\.2579\.8983\.1983\.8479\.5584\.0484\.1479\.4784\.8884\.2679\.8583\.18\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random84\.0779\.6483\.0683\.6779\.4783\.9283\.9479\.1884\.5983\.9879\.5082\.85Entropy84\.1079\.7482\.9783\.7279\.2283\.8084\.0179\.1184\.7383\.9979\.3482\.82WAPA84\.7481\.1284\.0084\.4080\.6484\.2284\.4780\.2685\.1884\.6480\.9383\.77\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random84\.0779\.6483\.0683\.6779\.4783\.9283\.9479\.1884\.5983\.9879\.5082\.85Entropy84\.0979\.7482\.9883\.7179\.2183\.8683\.9678\.9884\.7483\.9579\.3482\.88WAPA84\.7781\.2383\.9884\.3380\.5484\.4184\.4580\.2585\.1284\.6380\.8983\.73All ground\-truth labels85\.0181\.8284\.0684\.8081\.3984\.2484\.8180\.7285\.2485\.0781\.8984\.70

Table S10:Held\-out\-persona utility after soft\-label DPO \(%\) under matched welfare specifications\.MethodRoleplay\-AfricaRoleplay\-AsiaRoleplay\-North AmericaRoleplay\-EuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetAll pseudo\-labels83\.0578\.7085\.3183\.5279\.3885\.4982\.9078\.2384\.7683\.1879\.3383\.82Welfare\-agnostic baselines \(shared across settings\)APL83\.4179\.5885\.4183\.8680\.1385\.7283\.2578\.8084\.9483\.5380\.1584\.13BAL\-PM84\.0780\.2885\.9984\.3280\.6786\.0283\.7079\.0685\.5284\.0981\.0484\.48\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random83\.6879\.7885\.8284\.1380\.4485\.7883\.4978\.8285\.3983\.8180\.4584\.30Entropy83\.8579\.5485\.8884\.2680\.4285\.9683\.5578\.5885\.4483\.9780\.3484\.40WAPA84\.4480\.6886\.6484\.7781\.5486\.1184\.0980\.1185\.9884\.3981\.6784\.74\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random83\.6879\.7885\.8284\.1380\.4485\.7883\.4978\.8285\.3983\.8180\.4584\.30Entropy83\.8179\.4785\.8284\.2380\.3285\.9483\.5478\.6685\.5383\.9880\.3884\.48WAPA84\.4880\.9886\.5284\.6681\.4586\.1484\.1080\.1685\.9084\.4181\.8284\.69All ground\-truth labels84\.7881\.2986\.4885\.0081\.8686\.1284\.4980\.0786\.4784\.8182\.3284\.67

Figures[S3](https://arxiv.org/html/2610.19035#A7.F3)and[S4](https://arxiv.org/html/2610.19035#A7.F4)show reference\-gap recovery under\(1,1\)\(1,1\), complementing the recovery plots under\(2,−5\)\(2,\-5\)in Figures[4](https://arxiv.org/html/2610.19035#S4.F4)and[5](https://arxiv.org/html/2610.19035#S4.F5)\.

Figure S3:Soft\-label DPO: Seen\-persona reference\-gap recovery under\(1,1\)\(1,1\)at 20% budget\. All pseudo\-labels defines 0%; dashed lines mark All ground\-truth labels at 100%\. Recovery is uncapped for every method\.Figure S4:Soft\-label DPO: Held\-out\-persona reference\-gap recovery under\(1,1\)\(1,1\)at 20% budget\. All pseudo\-labels defines 0%; dashed lines mark All ground\-truth labels at 100%\. Recovery is uncapped for every method\.
### G\.10Comparison across Backbones

Protocol\.We compare Qwen3\-4B\-Instruct\-2507 with Llama\-3\.1\-8B\-Instruct on Roleplay\-North America and Roleplay\-Africa\. Both use the same comparison support, reference committee, and Seen/Held\-out persona memberships\. The five acquisition methods query 20% of training comparisons; Entropy and WAPA use\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)andε=0\.5\\varepsilon=0\.5\. Queried comparisons receive observed labels, while unqueried comparisons retain the respective backbone’s soft proxy probabilities\. All pseudo\-labels and All ground\-truth labels provide the two label\-source references\. Each policy initializes from its original backbone, which also supplies the frozen DPO reference\. We retain the soft\-label DPO objective and optimization settings in Appendix[F](https://arxiv.org/html/2610.19035#A6)\. For Llama, a microbatch of two with 32 accumulation steps preserves the effective batch of 64\. All adapters complete three epochs, and evaluation uses the final checkpoint\.

APL uses each backbone’s All pseudo\-labels adapter only for acquisition scoring\. BAL\-PM reuses the reference committee probabilities and extracts prompt representations from the corresponding original backbone\. For Llama, training and scoring use its native chat template, system\-message persona context, and matching assistant completion boundary\. Selections are frozen before observed labels are accessed\. Evaluation follows Appendix[F\.4](https://arxiv.org/html/2610.19035#A6.SS4), including persona averaging, fractional Tail aggregation, and fixed Target cohorts\. Since both model family and size change, this comparison tests transfer across backbones\.

Complete results\.Tables[S11](https://arxiv.org/html/2610.19035#A7.T11)–[S14](https://arxiv.org/html/2610.19035#A7.T14)report all seven policies on both persona splits\. On Llama, WAPA leads all four budgeted baselines in Mean, Tail, and Target for both utility and accuracy\. Its Tail utility advantage over Entropy is 0\.89–1\.05 percentage points across the four dataset–split combinations\. The corresponding advantages over APL and BAL\-PM are 1\.56–2\.53 and 1\.45–1\.92 points\. Target differences are sometimes small: WAPA exceeds Entropy by only 0\.004 points on North America Seen personas\. On Africa Held\-out personas, its Target advantage over Random is 0\.030 points\. APL and BAL\-PM improve on All pseudo\-labels, but both fall below Random in all three Llama utility summaries\. Their relative ordering also changes: BAL\-PM exceeds APL in Qwen’s Mean utility on both datasets, whereas APL leads on Llama’s North America splits\.

Absolute gains and reference\-gap recovery\.Table[S15](https://arxiv.org/html/2610.19035#A7.T15)separates the size of the utility gain from its fraction of the full\-label reference gap\. WAPA gains 1\.82–2\.09 Mean utility points on Llama, compared with 1\.07–1\.42 on Qwen\. Llama’s full\-label Mean gains are also larger: 6\.07–6\.40 points, compared with 1\.43–1\.73 on Qwen\. WAPA therefore recovers 28\.5–33\.1% of the Llama Mean gap, versus 74\.8–85\.7% for Qwen\. Llama Tail recovery reaches 45\.7–51\.7%, while Target recovery is 25\.7–34\.6%\. The fully labeled Llama policy leads all three utility summaries on every split\. For Qwen, WAPA slightly exceeds that reference on North America Held\-out Tail and Africa Held\-out Target\. These recoveries remain above 100%; each denominator uses the matching backbone, dataset, split, and metric\.

Table S11:Roleplay\-North America: absolute Brier utility \(%\) across backbones\. Budgeted methods query 20% of training comparisons; Entropy and WAPA use\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)\. Bold marks the best budgeted value within each backbone and column\.MethodSeen personasHeld\-out personasMeanTailTargetMeanTailTargetQwen3\-4BAll pseudo\-labels83\.3878\.4584\.0682\.9078\.2384\.76Random83\.9479\.1884\.5983\.4978\.8285\.39Entropy83\.9678\.9884\.7483\.5478\.6685\.53APL83\.6579\.0384\.2683\.2578\.8084\.94BAL\-PM84\.1479\.4784\.8883\.7079\.0685\.52WAPA84\.4580\.2585\.1284\.1080\.1685\.90All ground\-truth labels84\.8180\.7285\.2484\.4980\.0786\.47Llama\-3\.1\-8BAll pseudo\-labels79\.9676\.9679\.8979\.5276\.2980\.15Random81\.4678\.4281\.4680\.9877\.7781\.46Entropy81\.6778\.7881\.7181\.2178\.1081\.60APL81\.2978\.1081\.0780\.8177\.0881\.35BAL\-PM81\.1478\.2281\.1180\.7377\.3981\.10WAPA81\.7979\.6681\.7181\.3779\.1481\.73All ground\-truth labels86\.3682\.1986\.9385\.6282\.5485\.65

Table S12:Roleplay\-North America: absolute decision accuracy \(%\) across backbones\. Budgeted methods query 20% of training comparisons; Entropy and WAPA use\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)\. Bold marks the best budgeted value within each backbone and column\. Tail reranks personas by accuracy\.MethodSeen personasHeld\-out personasMeanTailTargetMeanTailTargetQwen3\-4BAll pseudo\-labels75\.0065\.9775\.8874\.3067\.0977\.88Random75\.8367\.2777\.5575\.2967\.3478\.71Entropy76\.3067\.6278\.0175\.5368\.1378\.85APL75\.8267\.5377\.0974\.8766\.7378\.85BAL\-PM76\.0267\.5877\.4675\.6868\.1979\.40WAPA77\.0669\.5778\.0176\.4069\.5478\.98All ground\-truth labels77\.5670\.8278\.7676\.8068\.4480\.36Llama\-3\.1\-8BAll pseudo\-labels68\.9559\.7067\.9067\.9959\.4069\.92Random72\.3563\.1671\.6171\.5462\.5873\.63Entropy73\.3764\.5973\.8472\.3663\.4372\.94APL71\.3362\.5569\.9470\.3261\.2973\.08BAL\-PM71\.9263\.5970\.7871\.0960\.6874\.18WAPA75\.9268\.0175\.1474\.4167\.0375\.41All ground\-truth labels80\.4473\.8181\.2679\.0274\.2479\.12

Table S13:Roleplay\-Africa: absolute Brier utility \(%\) across backbones\. Budgeted methods query 20% of training comparisons; Entropy and WAPA use\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)\. Bold marks the best budgeted value within each backbone and column\.MethodSeen personasHeld\-out personasMeanTailTargetMeanTailTargetQwen3\-4BAll pseudo\-labels83\.3678\.4082\.2583\.0578\.7085\.31Random84\.0779\.6483\.0683\.6879\.7885\.82Entropy84\.0979\.7482\.9883\.8179\.4785\.82APL83\.6879\.0682\.7583\.4179\.5885\.41BAL\-PM84\.2579\.8983\.1984\.0780\.2885\.99WAPA84\.7781\.2383\.9884\.4880\.9886\.52All ground\-truth labels85\.0181\.8284\.0684\.7881\.2986\.48Llama\-3\.1\-8BAll pseudo\-labels80\.0077\.0579\.5179\.5476\.0981\.33Random81\.4878\.7880\.8581\.0777\.9882\.72Entropy81\.5578\.8480\.8381\.3078\.6082\.66APL81\.0777\.8580\.4280\.6477\.1182\.61BAL\-PM81\.0878\.2280\.5580\.7177\.7282\.23WAPA81\.8479\.8781\.1681\.6479\.6482\.75All ground\-truth labels86\.0782\.8984\.2785\.8683\.0186\.82

Table S14:Roleplay\-Africa: absolute decision accuracy \(%\) across backbones\. Budgeted methods query 20% of training comparisons; Entropy and WAPA use\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)\. Bold marks the best budgeted value within each backbone and column\. Tail reranks personas by accuracy\.MethodSeen personasHeld\-out personasMeanTailTargetMeanTailTargetQwen3\-4BAll pseudo\-labels75\.2067\.2674\.5874\.5667\.0678\.02Random76\.2468\.2575\.3275\.5868\.2078\.98Entropy76\.7068\.5674\.9575\.9468\.8979\.95APL75\.5567\.6074\.4975\.2968\.4678\.30BAL\-PM76\.6168\.7075\.3276\.0469\.9079\.67WAPA77\.6470\.7376\.6277\.0070\.3281\.73All ground\-truth labels77\.8171\.4475\.5177\.7870\.9981\.73Llama\-3\.1\-8BAll pseudo\-labels69\.1059\.3967\.5367\.7257\.6473\.35Random72\.2063\.6471\.1571\.3763\.7275\.41Entropy73\.0665\.3471\.1572\.2865\.1573\.90APL70\.9062\.9169\.5769\.7959\.6275\.82BAL\-PM71\.5263\.4869\.9470\.2462\.3774\.59WAPA74\.7667\.6071\.3474\.2767\.4479\.40All ground\-truth labels79\.7274\.0076\.1679\.4574\.6081\.18

Table S15:WAPA utility gains over All pseudo\-labels \(percentage points, pp\) and reference\-gap recovery \(%\) at 20% budget\. Each backbone uses its own All ground\-truth labels reference\. Recovery uses unrounded inputs and is uncapped\.BackboneSplitGain \(pp\)Recovery \(%\)MeanTailTargetMeanTailTargetRoleplay\-North AmericaQwen3\-4BSeen1\.0671\.8041\.05774\.879\.689\.5Qwen3\-4BHeld\-out1\.1911\.9261\.13774\.9104\.766\.5Llama\-3\.1\-8BSeen1\.8232\.7051\.81928\.551\.725\.8Llama\-3\.1\-8BHeld\-out1\.8532\.8571\.57430\.445\.728\.6Roleplay\-AfricaQwen3\-4BSeen1\.4172\.8261\.73085\.782\.795\.7Qwen3\-4BHeld\-out1\.4242\.2821\.20782\.588\.2103\.0Llama\-3\.1\-8BSeen1\.8462\.8231\.64830\.448\.334\.6Llama\-3\.1\-8BHeld\-out2\.0943\.5571\.41233\.151\.425\.7

### G\.11Downstream Lower\-Tail Utility Curves

Lower\-tail definition\.Letffdenote a positive population fraction\. For empirical utility quantile function𝒬m\\mathcal\{Q\}\_\{m\}, the lower\-tail mean is

𝒯m​\(f\)=f−1​∫0f𝒬m​\(v\)​𝑑v,0<f61\.\\mathcal\{T\}\_\{m\}\(f\)=f^\{\-1\}\\intop\\nolimits\_\{0\}^\{f\}\\mathcal\{Q\}\_\{m\}\(v\)\\,dv,\\qquad 0<f\\leqslant 1\.\(59\)Fractional boundary mass gives an exact population fraction:𝒯m​\(0\.1\)\\mathcal\{T\}\_\{m\}\(0\.1\)is Tail and𝒯m​\(1\)\\mathcal\{T\}\_\{m\}\(1\)is Mean\. Target instead averages the fixed designated members\.

Curve computation\.Each policy ranks its own persona utilities\. We evaluate the lower\-tail mean at every empirical rank and on a dense grid of positive population fractions, using fractional boundary mass\. Fornnevaluated personas, the curve equals the minimum utility when0<f61/n0<f\\leqslant 1/n;f=0f=0is undefined\.

Figure[S5](https://arxiv.org/html/2610.19035#A7.F5)complements Tables[S9](https://arxiv.org/html/2610.19035#A7.T9)and[S10](https://arxiv.org/html/2610.19035#A7.T10)by evaluating gains across lower\-tail population fractions\. The curves show broadly positive gains over Random and matched Entropy under both welfare specifications, extending the pattern beyond the single Tail summary\. The 10% and 100% positions correspond to Tail and Mean, respectively\.

Figure S5:Downstream lower\-tail gains over Random and matched Entropy, in %\. Solid/dashed curves indicate seen/held\-out personas\.
### G\.12Downstream Sensitivity to Welfare Parameters

We examine the separate roles of Target priorityγ\\gammaand sensitivity to supervision disadvantageρ\\rhoin downstream preference prediction on Roleplay\-North America andRoleplay\-Africa\. Table[S16](https://arxiv.org/html/2610.19035#A7.T16)reports Seen\-persona Mean, Tail, and Target Brier utilities for\(γ,ρ\)∈\{\(1,1\),\(2,1\),\(1,−5\),\(2,−5\)\}\(\\gamma,\\rho\)\\in\\\{\(1,1\),\(2,1\),\(1,\-5\),\(2,\-5\)\\\}\. All four settings use soft proxy labels for unqueried comparisons and hold Target membership, the 20% query budget, comparison pool, reference predictions, and DPO training recipe fixed\.

These comparisons test how changing the acquisition objective affects the trained policy\. The main\-text method comparisons instead fix that objective and test which method selects more useful training labels\. Across the four settings, the largest Seen utility span is 0\.1254 percentage points, for Tail on Africa\. For the same datasets and split, the smallest gain of WAPA over Random or matched Entropy under either main setting is 0\.3746 points\. The method gains are therefore larger than the differences among these settings; the contrasts below examine the direction of the parameter effects\.

Table S16:Seen\-persona Brier utilities \(%\) after soft\-label DPO across four welfare settings on Roleplay\-North America and Roleplay\-Africa\. All settings use a 20% query budget and the same training protocol\.Roleplay\-North AmericaRoleplay\-Africaγ\\gammaρ\\rhoMeanTailTargetMeanTailTarget1184\.466580\.261985\.177784\.739481\.122883\.99532184\.473980\.268185\.077884\.723581\.248183\.89691\-584\.482180\.364485\.069384\.774581\.208583\.97982\-584\.446780\.252885\.118284\.772981\.227283\.9800

Target priority throughγ\\gamma\.At fixedρ=−5\\rho=\-5, increasingγ\\gammafrom 1 to 2 raises Seen Target utility from 85\.0693% to 85\.1182% on North America and from 83\.9798% to 83\.9800% on Africa\. The changes are 0\.0489 and 0\.0002 percentage points, respectively; Africa’s Target utility is nearly unchanged\. Atρ=1\\rho=1, the same increase inγ\\gammainstead lowers Target utility by 0\.0999 points on North America and 0\.0984 points on Africa\. Allocating more labels to Target therefore does not by itself ensure better predictions for that group after DPO\.

Sensitivity to disadvantage in supervision utility throughρ\\rho\.At fixedγ=1\\gamma=1, decreasingρ\\rhofrom 1 to−5\-5improves Mean and Tail utility on both datasets\. Mean increases by 0\.0156 points on North America and 0\.0351 points on Africa; Tail increases by 0\.1024 and 0\.0858 points, respectively\. Atγ=2\\gamma=2, however, Tail decreases by 0\.0153 and 0\.0210 points\. Loweringρ\\rhotherefore helps the downstream Tail only atγ=1\\gamma=1in these runs\. Both parameter comparisons show why acquisition and downstream utility must be evaluated separately: directing labels toward a group does not ensure that training improves its predictions\.

### G\.13Sensitivity to the Imputation Source

Protocol\.We compare target\-model and reference\-based completion on the four main Roleplay collections: Africa, Asia, North America, and Europe\. For each acquisition method, we retain its original 20% query set under\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)or\(2,−5\)\(2,\-5\)and change only the predictions used for unqueried comparisons\. Queried comparisons use ground\-truth labels in both variants\. The comparison pool, frozen predictions, and fixed Target membership are unchanged\. No\-query rows provide a reference for each completion source\.

Probability completion\.Unqueried comparisons use either the target model’s probability or the mean probability of the three reference models\. Table[S17](https://arxiv.org/html/2610.19035#A7.T17)reports the same Brier utility and Mean/Tail/Target aggregation as the main acquisition evaluation\. Reference probabilities improve all three metrics before acquisition\. For WAPA’s fixed 20% query sets, target completion yields higher Mean and Target, whereas reference completion yields higher Tail\. Comparing methods within reference completion, WAPA retains the highest Mean and Target across all four datasets and both settings\.

Table S17:Acquisition Brier utility \(%\) with target or reference\-mean probability completion\. Budgeted methods query 20% of the same pool; each method keeps its query set fixed across completion sources\. Bold marks the best budgeted method within each setting and completion source\. No\-query rows use no acquired labels\.AcquisitionCompletionAfricaAsiaNorth AmericaEuropesourceMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetNo queriesTarget81\.87377\.05480\.96281\.25077\.37082\.31081\.80977\.57481\.71881\.50077\.90780\.112No queriesReference85\.27083\.33385\.36584\.92282\.64084\.86085\.11783\.37585\.18185\.15883\.41684\.291\(a\)\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)RandomTarget85\.52881\.80684\.86685\.03781\.65285\.53285\.53582\.29285\.22985\.22882\.25484\.567EntropyTarget86\.75581\.83285\.70186\.18182\.25687\.69386\.76282\.47486\.25386\.42782\.20784\.788Reference DisagreementTarget87\.36783\.59886\.75086\.85783\.63087\.68686\.98483\.18786\.86187\.14783\.88286\.170WAPATarget90\.38487\.52990\.38789\.83887\.06189\.54490\.22187\.81490\.45090\.07587\.06289\.552RandomReference88\.22486\.67888\.36487\.96685\.87187\.54088\.11686\.63288\.05688\.14786\.75387\.662EntropyReference89\.18787\.43688\.93788\.89586\.74189\.24789\.11487\.28888\.95589\.09887\.21888\.169Reference DisagreementReference89\.50487\.97589\.41089\.22887\.56789\.31489\.09387\.44989\.00689\.46487\.80088\.813WAPAReference89\.85187\.96890\.18489\.54387\.45889\.39489\.76088\.39389\.88389\.69987\.71189\.335\(b\)\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)RandomTarget85\.52881\.80684\.86685\.03781\.65285\.53285\.53582\.29285\.22985\.22882\.25484\.567EntropyTarget86\.76682\.09187\.28586\.17682\.09289\.17486\.75482\.34187\.93886\.43682\.26386\.629Reference DisagreementTarget87\.35583\.21890\.94586\.83583\.19591\.62586\.96882\.69690\.65687\.10483\.60790\.342WAPATarget90\.23787\.11494\.43089\.71486\.78093\.52690\.01887\.24294\.17389\.96187\.12793\.639RandomReference88\.22486\.67888\.36487\.96685\.87187\.54088\.11686\.63288\.05688\.14786\.75387\.662EntropyReference89\.17887\.56889\.96488\.88786\.62590\.40589\.11787\.27190\.19489\.09687\.25789\.442Reference DisagreementReference89\.48487\.59692\.60089\.19887\.24092\.19489\.09687\.16592\.11789\.43887\.62592\.178WAPAReference89\.78087\.69593\.78689\.47787\.32892\.94289\.67088\.09593\.45889\.63187\.81592\.987

Hard\-label completion\.We also compare the binary labels used to construct preference pairs\. Target labels threshold the target probability at0\.50\.5\(ties select A\); reference labels use majority voting over the three individually thresholded reference predictions\. Table[S18](https://arxiv.org/html/2610.19035#A7.T18)reports completed\-label accuracy, with Tail reranked by per\-persona accuracy and Target membership held fixed\. This deterministic label audit differs from half\-credit scoring of probability ties; majority voting also differs from thresholding the reference\-mean probability\. These metrics therefore evaluate distinct aspects of completion\. Reference voting improves WAPA’s Mean, Tail, and Target label accuracy over target labels across all four datasets and both settings\. Relative to the matched acquisition baselines using reference labels, WAPA retains Mean and Target advantages throughout\.

Table S18:Completed\-label accuracy \(%\) with target thresholding or reference majority voting\. Budgeted methods query 20% of the same pool; each method keeps its query set fixed across completion sources\. Bold marks the best budgeted method within each setting and completion source\. No\-query rows use no acquired labels\.AcquisitionCompletionAfricaAsiaNorth AmericaEuropesourceMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetNo queriesTarget77\.56371\.94876\.44776\.73672\.01977\.82377\.12372\.29477\.43577\.00272\.45275\.932No queriesReference81\.60677\.20981\.95680\.79575\.78680\.14680\.59776\.37480\.82181\.24477\.06379\.146\(a\)\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)RandomTarget82\.07177\.60281\.25681\.46577\.34881\.90281\.80177\.94481\.63381\.62077\.96581\.226EntropyTarget85\.72780\.44984\.59485\.07081\.08686\.68385\.70381\.26685\.20485\.28980\.62683\.522Reference DisagreementTarget84\.49679\.90083\.52083\.81279\.60384\.98183\.61779\.04883\.88284\.04279\.99283\.360WAPATarget86\.65282\.68686\.53185\.87882\.06385\.49486\.12882\.83586\.80486\.15881\.29186\.116RandomReference85\.27981\.60485\.34184\.76579\.99583\.46884\.52881\.06184\.43985\.05281\.41183\.684EntropyReference87\.46784\.18286\.78886\.81482\.50186\.81886\.72582\.91186\.80487\.13083\.61985\.116Reference DisagreementReference88\.09384\.48187\.95587\.47283\.86387\.06186\.42682\.50086\.43387\.92084\.56386\.440WAPAReference88\.96584\.47189\.98688\.34883\.76887\.95288\.48785\.29288\.82288\.62084\.73987\.736\(b\)\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)RandomTarget82\.07177\.60281\.25681\.46577\.34881\.90281\.80177\.94481\.63381\.62077\.96581\.226EntropyTarget85\.71480\.70486\.81185\.02480\.77888\.84485\.64181\.01787\.54685\.26580\.72586\.197Reference DisagreementTarget84\.48679\.47888\.72583\.75979\.12490\.03283\.58278\.62688\.52083\.97679\.41288\.358WAPATarget86\.52782\.22391\.62085\.75781\.75390\.22285\.90782\.29491\.28086\.05081\.38091\.086RandomReference85\.27981\.60485\.34184\.76579\.99583\.46884\.52881\.06184\.43985\.05281\.41183\.684EntropyReference87\.42984\.18288\.09586\.75882\.25288\.52086\.73282\.95588\.31287\.10583\.85486\.764Reference DisagreementReference88\.02983\.85192\.39087\.43683\.29791\.41086\.44682\.22990\.26087\.85484\.35491\.572WAPAReference88\.79684\.01794\.07188\.21583\.43092\.16688\.22784\.80592\.53288\.45085\.12092\.004

Overall comparison\.Across the four evaluated datasets and welfare settings, WAPA generally retains its advantages over matched acquisition baselines in Mean, Tail, and Target under reference\-based completion, using either probabilities or hard labels\.

### G\.14Downstream Alignment with Hard Proxy Labels

Protocol\.This comparison evaluates DPO with hard proxy labels\. Queried comparisons use observed labels; unqueried comparisons use the base model’s preferred response as a binary label\. Thusq=1q=1for every oriented pair in Eq\. \([48](https://arxiv.org/html/2610.19035#A4.E48)\)\. The query selections, comparison supports, model initialization, optimization settings, final\-checkpoint rule, and evaluation cohorts match the soft\-label results in Section[4\.3](https://arxiv.org/html/2610.19035#S4.SS3)\. Each version uses its own All pseudo\-labels reference; the All ground\-truth labels policies are shared because their training targets and objectives are identical\.

Predictive utility\.Tables[S19](https://arxiv.org/html/2610.19035#A7.T19)and[S20](https://arxiv.org/html/2610.19035#A7.T20)retain both welfare specifications and all seven policies\. WAPA improves Mean, Tail, and Target utility over Random and matched Entropy across all four datasets and both test splits under both specifications\. Under\(2,−5\)\(2,\-5\), it recovers 68\.11–81\.85% of the Mean reference gap and 65\.01–94\.93% of the Tail reference gap\. Matched Entropy recovers 43\.17–53\.88% and 30\.14–45\.96%, respectively; Random recovers 29\.47–43\.96% and 23\.55–39\.37%\. Recovery plots and lower\-tail curves appear in Figures[S6](https://arxiv.org/html/2610.19035#A7.F6)–[S8](https://arxiv.org/html/2610.19035#A7.F8)\.

Table S19:Seen\-persona hard\-label DPO utility \(%\) under matched welfare specifications\.MethodRoleplay\-AfricaRoleplay\-AsiaRoleplay\-North AmericaRoleplay\-EuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetAll pseudo\-labels83\.0478\.0481\.9282\.7478\.0583\.0783\.1577\.9283\.9182\.8977\.4681\.29\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random83\.9179\.2682\.7183\.4879\.0983\.7183\.7778\.8784\.4383\.7678\.8982\.43Entropy83\.9779\.3882\.9683\.6779\.2183\.8483\.8878\.8084\.6083\.9179\.0182\.70WAPA84\.6481\.0083\.7684\.2580\.2584\.2084\.3179\.9385\.0784\.4380\.4383\.46\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random83\.9179\.2682\.7183\.4879\.0983\.7183\.7778\.8784\.4383\.7678\.8982\.43Entropy84\.0379\.6282\.8383\.6979\.1683\.8183\.8678\.8784\.6983\.9279\.2382\.84WAPA84\.6581\.0583\.8784\.2280\.2284\.1484\.3279\.8985\.0584\.4680\.4783\.48All ground\-truth labels85\.0181\.8284\.0684\.8081\.3984\.2484\.8180\.7285\.2485\.0781\.8984\.70

Table S20:Held\-out\-persona hard\-label DPO utility \(%\) under matched welfare specifications\.MethodRoleplay\-AfricaRoleplay\-AsiaRoleplay\-North AmericaRoleplay\-EuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetAll pseudo\-labels82\.6978\.0584\.7683\.5079\.1285\.3682\.6477\.7184\.5582\.9078\.6883\.35\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random83\.5679\.1885\.7084\.0680\.2085\.8383\.1878\.2785\.1383\.6279\.8784\.04Entropy83\.7779\.3585\.8284\.2880\.3486\.0283\.5078\.3885\.4683\.8980\.1784\.30WAPA84\.3380\.3686\.5484\.7581\.2986\.2083\.9279\.7185\.7284\.2581\.4084\.50\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random83\.5679\.1885\.7084\.0680\.2085\.8383\.1878\.2785\.1383\.6279\.8784\.04Entropy83\.7979\.3785\.8884\.2680\.3885\.8683\.4778\.4285\.4883\.9380\.1384\.41WAPA84\.3880\.3286\.5184\.6581\.3986\.1083\.9379\.9585\.7084\.2081\.3584\.42All ground\-truth labels84\.7881\.2986\.4885\.0081\.8686\.1284\.4980\.0786\.4784\.8182\.3284\.67

![Refer to caption](https://arxiv.org/html/2610.19035v1/hard_downstream_recovery_seen_both.png)Figure S6:Hard\-label DPO: Seen\-persona reference\-gap recovery under both welfare specifications\. All pseudo\-labels defines 0%; dashed lines mark All ground\-truth labels at 100%\. All methods use unrounded hard\-label utilities, with no display cap\.![Refer to caption](https://arxiv.org/html/2610.19035v1/hard_downstream_recovery_heldout_both.png)Figure S7:Hard\-label DPO: Held\-out\-persona reference\-gap recovery under both welfare specifications\. All pseudo\-labels defines 0%; dashed lines mark All ground\-truth labels at 100%\. Recovery is uncapped for every method\.Figure S8:Hard\-label DPO: lower\-tail utility gains over Random and matched Entropy under both welfare specifications\. Solid/dashed curves indicate Seen/Held\-out personas\.Decision accuracy\.Tables[S21](https://arxiv.org/html/2610.19035#A7.T21)and[S22](https://arxiv.org/html/2610.19035#A7.T22)retain the original accuracy results\. WAPA’s Mean accuracy gains over the strongest budgeted baseline range from 0\.41% to 1\.11% across both splits and specifications\. Under\(1,1\)\(1,1\), WAPA trails Entropy in Seen Target accuracy on North America by 0\.37% and Held\-out Tail accuracy on Africa by 0\.23%\. Under\(2,−5\)\(2,\-5\), it leads the budgeted baselines in each reported accuracy summary\. The free\-response cases and pilot evaluation in Appendices[I](https://arxiv.org/html/2610.19035#A9)and[J](https://arxiv.org/html/2610.19035#A10)also use these original hard\-label policies\.

Table S21:Seen\-persona hard\-label DPO decision accuracy \(%\) under matched welfare specifications\. Companion to Table[S19](https://arxiv.org/html/2610.19035#A7.T19)\. Tail reranks personas by accuracy; bold marks the best budgeted method in each panel\.MethodRoleplay\-AfricaRoleplay\-AsiaRoleplay\-North AmericaRoleplay\-EuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetAll pseudo\-labels74\.9667\.0373\.8474\.3965\.6974\.4675\.0766\.9776\.7274\.2065\.0070\.89\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random76\.1668\.3174\.4075\.4967\.3275\.5475\.5667\.2377\.1875\.5466\.5772\.40Entropy76\.4968\.7675\.2375\.7367\.7175\.7676\.2166\.8478\.6675\.9367\.4172\.94WAPA77\.2971\.0475\.6076\.8469\.6576\.8476\.6669\.0578\.2976\.6769\.6574\.68\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random76\.1668\.3174\.4075\.4967\.3275\.5475\.5667\.2377\.1875\.5466\.5772\.40Entropy76\.5068\.8174\.7775\.8568\.0076\.0875\.9866\.9777\.5576\.0367\.9773\.59WAPA77\.3070\.6475\.7976\.6069\.0176\.4176\.4268\.7977\.7476\.6869\.9374\.46All ground\-truth labels77\.8171\.4475\.5177\.4571\.1876\.1977\.5670\.8278\.7677\.9471\.0378\.14

Table S22:Held\-out\-persona hard\-label DPO decision accuracy \(%\) under matched welfare specifications\. Target uses the shared similarity\-defined cohort \(Appendix[E\.1](https://arxiv.org/html/2610.19035#A5.SS1)\)\. Companion to Table[S20](https://arxiv.org/html/2610.19035#A7.T20)\. Tail reranks personas by accuracy; bold marks the best budgeted method in each panel\.MethodRoleplay\-AfricaRoleplay\-AsiaRoleplay\-North AmericaRoleplay\-EuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetAll pseudo\-labels74\.3967\.5776\.9275\.2767\.8178\.3574\.1466\.2478\.7174\.5466\.9775\.38\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random75\.4367\.3578\.1675\.7069\.3278\.7975\.0266\.1878\.4375\.5868\.0775\.60Entropy76\.0268\.7279\.4076\.3169\.3278\.9075\.7067\.7778\.7176\.0669\.5877\.36WAPA76\.6468\.4981\.1877\.4071\.2179\.7876\.1468\.5079\.1276\.6070\.5677\.47\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random75\.4367\.3578\.1675\.7069\.3278\.7975\.0266\.1878\.4375\.5868\.0775\.60Entropy76\.1668\.8079\.2676\.3069\.4078\.9075\.5467\.3478\.5776\.0569\.1677\.03WAPA76\.8569\.6881\.0477\.1170\.9780\.0076\.2668\.6279\.9576\.4670\.0477\.14All ground\-truth labels77\.7870\.9981\.7377\.1571\.1279\.1276\.8068\.4480\.3677\.5272\.0176\.81

### G\.15Hard Accuracy for Acquisition and Downstream Alignment

Tables[S23](https://arxiv.org/html/2610.19035#A7.T23)–[S25](https://arxiv.org/html/2610.19035#A7.T25)complement Tables[1](https://arxiv.org/html/2610.19035#S4.T1),[S9](https://arxiv.org/html/2610.19035#A7.T9), and[S10](https://arxiv.org/html/2610.19035#A7.T10); metric definitions and matched evaluation details are in Appendix[F\.4](https://arxiv.org/html/2610.19035#A6.SS4)\.

Acquisition accuracy\.WAPA improves Mean accuracy over the strongest budgeted baseline across all four datasets: by 0\.44–0\.91 percentage points under\(1,1\)\(1,1\)and 0\.28–0\.80 under\(2,−5\)\(2,\-5\)\. It leads all reported summaries under\(2,−5\)\(2,\-5\); under\(1,1\)\(1,1\), the strongest baseline exceeds its Target accuracy on Asia by 1\.15 points\.

Downstream accuracy\.With soft\-label DPO, WAPA improves Mean accuracy over the strongest baseline by 0\.51–1\.29 percentage points across both splits and settings\. It leads or ties all Seen summaries\. On Held\-out personas, BAL\-PM leads Tail on Africa under\(1,1\)\(1,1\)and Target on North America under both settings; APL leads Target on Asia under\(2,−5\)\(2,\-5\)\. Accuracy measures binary preference decisions, while Brier utility also evaluates predictive confidence\.

Table S23:Acquisition hard accuracy \(%\) at the same 20% query budget and frozen selections as Table[1](https://arxiv.org/html/2610.19035#S4.T1)\. Tail reranks personas by accuracy\. Bold marks the best budgeted method for each welfare setting; Oracle retains its Brier\-welfare objective\. APL and BAL\-PM share selections across settings; adaptations are described in Appendix[F\.3](https://arxiv.org/html/2610.19035#A6.SS3)\.MethodRoleplay\-AfricaRoleplay\-AsiaRoleplay\-North AmericaRoleplay\-EuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetNo queries77\.5572\.0076\.4176\.7471\.9977\.8677\.1472\.2377\.4777\.0072\.4575\.93Welfare\-agnostic baselines \(shared across settings\)APL78\.6073\.4877\.4577\.9373\.8679\.3878\.1173\.7278\.4278\.0473\.6077\.09BAL\-PM84\.0279\.5683\.0383\.2178\.9984\.5583\.3678\.7283\.5683\.3379\.1982\.50\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random82\.0777\.6481\.2481\.4677\.3381\.9381\.8177\.9881\.6681\.6177\.9581\.21Entropy85\.7380\.4584\.5985\.0781\.0986\.6885\.7081\.2785\.2085\.2980\.6383\.52Reference Disagreement84\.4979\.9283\.4683\.8179\.5785\.0183\.6379\.0083\.9184\.0579\.9983\.39WAPA86\.6482\.7086\.5085\.8882\.0585\.5386\.1482\.8586\.8486\.1681\.3386\.12Welfare\-optimal Oracle97\.5595\.2197\.7996\.7394\.3596\.2997\.1495\.1097\.2197\.0092\.3697\.54\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random82\.0777\.6481\.2481\.4677\.3381\.9381\.8177\.9881\.6681\.6177\.9581\.21Entropy85\.7180\.7086\.8185\.0280\.7888\.8485\.6481\.0287\.5585\.2780\.7286\.20Reference Disagreement84\.4879\.4988\.7083\.7679\.0990\.0683\.5978\.5888\.5383\.9979\.4088\.37WAPA86\.5282\.2491\.5885\.7681\.7490\.2685\.9282\.2791\.3186\.0581\.3891\.09Welfare\-optimal Oracle96\.7395\.09100\.0095\.7793\.62100\.0096\.3494\.64100\.0096\.1294\.03100\.00

Table S24:Seen\-persona decision accuracy after soft\-label DPO \(%\)\. Tail reranks personas by accuracy\. Bold marks the best budgeted values in each welfare setting\.MethodRoleplay\-AfricaRoleplay\-AsiaRoleplay\-North AmericaRoleplay\-EuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetAll pseudo\-labels75\.2067\.2674\.5874\.5666\.7375\.9775\.0065\.9775\.8874\.3064\.9970\.67Welfare\-agnostic baselines \(shared across settings\)APL75\.5567\.6074\.4975\.0766\.4174\.7875\.8267\.5377\.0975\.3265\.8272\.40BAL\-PM76\.6168\.7075\.3275\.9568\.3375\.4376\.0267\.5877\.4676\.3968\.9974\.13\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random76\.2468\.2575\.3275\.6367\.8075\.8775\.8367\.2777\.5575\.8867\.4073\.27Entropy76\.8469\.2774\.3075\.6768\.0975\.6576\.3067\.5877\.8376\.1268\.2473\.59WAPA77\.3570\.7076\.8177\.2469\.1076\.8476\.9269\.5278\.5777\.0070\.6775\.22\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random76\.2468\.2575\.3275\.6367\.8075\.8775\.8367\.2777\.5575\.8867\.4073\.27Entropy76\.7068\.5674\.9575\.6767\.9075\.2276\.3067\.6278\.0176\.1268\.5473\.70WAPA77\.6470\.7376\.6277\.2069\.8277\.1677\.0669\.5778\.0177\.1970\.3074\.68All ground\-truth labels77\.8171\.4475\.5177\.4571\.1876\.1977\.5670\.8278\.7677\.9471\.0378\.14

Table S25:Held\-out\-persona decision accuracy after soft\-label DPO \(%\)\. Tail reranks personas by accuracy\. Target uses the fixed similarity\-defined cohort\. Bold marks the best budgeted values in each welfare setting\.MethodRoleplay\-AfricaRoleplay\-AsiaRoleplay\-North AmericaRoleplay\-EuropeMeanTailTargetMeanTailTargetMeanTailTargetMeanTailTargetAll pseudo\-labels74\.5667\.0678\.0274\.9967\.5478\.6874\.3067\.0977\.8874\.5266\.7575\.38Welfare\-agnostic baselines \(shared across settings\)APL75\.2968\.4678\.3075\.7869\.1979\.6774\.8766\.7378\.8575\.0868\.6276\.26BAL\-PM76\.0469\.9079\.6776\.5869\.0178\.9075\.6868\.1979\.4076\.0868\.7276\.81\(a\) Equal\-weight mean welfare:\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)Random75\.5868\.2078\.9875\.9669\.1978\.4675\.2967\.3478\.7175\.8268\.1676\.15Entropy76\.0469\.0179\.6776\.3370\.2278\.6875\.7567\.3478\.9876\.0469\.6976\.48WAPA76\.9969\.5581\.5977\.4770\.3579\.7876\.2868\.3879\.1276\.8970\.4777\.58\(b\) Target\-priority, inequality\-sensitive welfare:\(γ,ρ\)=\(2,−5\)\(\\gamma,\\rho\)=\(2,\-5\)Random75\.5868\.2078\.9875\.9669\.1978\.4675\.2967\.3478\.7175\.8268\.1676\.15Entropy75\.9468\.8979\.9576\.1569\.8779\.1275\.5368\.1378\.8576\.0569\.2876\.48WAPA77\.0070\.3281\.7377\.2970\.4579\.2376\.4069\.5478\.9876\.9971\.1378\.46All ground\-truth labels77\.7870\.9981\.7377\.1571\.1279\.1276\.8068\.4480\.3677\.5272\.0176\.81

### G\.16Sensitivity to Proxy\-Label Refinement

Purpose and controlled comparison\.Unqueried comparisons retain proxy probabilities that may contain prediction errors\. We examine how refining these probabilities affects downstream DPO performance\. We apply PPCI \(Appendix[D\.3](https://arxiv.org/html/2610.19035#A4.SS3)\) after WAPA acquisition on the four Roleplay collections used for DPO\. We retain the frozen WAPA sets at the 20% query budget under\(γ,ρ\)=\(1,1\)\(\\gamma,\\rho\)=\(1,1\)and\(2,−5\)\(2,\-5\)\. Only the unqueried training probabilities change; acquired labels, comparison pairs, model initialization, and the three\-epoch DPO protocol remain fixed\. The eight resulting policies use the same Seen and Held\-out evaluation sets as their matched WAPA policies\.

Prediction refinement\.Every unqueried comparison receives a prediction, with candidate selection frozen before evaluation\. Table[S26](https://arxiv.org/html/2610.19035#A7.T26)reports mean normalized Brier loss,12​‖𝐪−𝐞Y‖22\\tfrac\{1\}\{2\}\\\|\\mathbf\{q\}\-\\mathbf\{e\}\_\{Y\}\\\|\_\{2\}^\{2\}, on the same unqueried comparisons\. Brier loss falls by 11\.04–12\.03% across the eight conditions\. The selection procedure choosesα=0\\alpha=0throughout, yielding smoothed probabilities without an additive residual term\. Acquired labels still inform candidate selection\.

Table S26:Prediction refinement after WAPA acquisition on Roleplay\. Lower Brier loss is better\. Reduction is relative to the raw WAPA completion;α\\alphais selected using acquired labelsbefore evaluation\.Dataset\(γ,ρ\)\(\\gamma,\\rho\)WAPABrierWAPA \+ PPCIBrierReduction\(%\)α\\alphaAfrica\(1,1\)\(1,1\)0\.1201990\.10600811\.8070Africa\(2,−5\)\(2,\-5\)0\.1220330\.10769611\.7490Asia\(1,1\)\(1,1\)0\.1270260\.11218011\.6870Asia\(2,−5\)\(2,\-5\)0\.1285740\.11311212\.0260North America\(1,1\)\(1,1\)0\.1222350\.10874011\.0400North America\(2,−5\)\(2,\-5\)0\.1247730\.11063311\.3330Europe\(1,1\)\(1,1\)0\.1240580\.10920411\.9730Europe\(2,−5\)\(2,\-5\)0\.1254910\.11051211\.9360

Downstream sensitivity\.Table[S27](https://arxiv.org/html/2610.19035#A7.T27)reports both persona splits across all eight acquisition conditions\. Despite the reduction in proxy prediction error, downstream Mean utility changes by less than 0\.10 percentage points in every condition\. Tail utility increases by 0\.25–0\.58 points, while Target changes range from−0\.12\-0\.12to\+0\.23\+0\.23points\. The tested refinement changes Mean utility little, with gains concentrated in Tail utility and mixed changes in Target utility\.

Table S27:Downstream sensitivity to proxy\-label refinement at the 20% query budget\. W denotes WAPA; P denotes WAPA \+ PPCI\. Utilities use the percentage scale;�\\Deltais P minus W in percentage points, computed before rounding\. Tail is the lower\-tail utility, reranked for each policy; Target membership is fixed across policies\.MeanTailTargetDataset\(γ,ρ\)\(\\gamma,\\rho\)WP�\\DeltaWP�\\DeltaWP�\\DeltaSeen personasAfrica\(1,1\)\(1,1\)84\.7484\.81\+0\.066\+0\.06681\.1281\.71\+0\.584\+0\.58484\.0084\.17\+0\.171\+0\.171Africa\(2,−5\)\(2,\-5\)84\.7784\.82\+0\.043\+0\.04381\.2381\.65\+0\.427\+0\.42783\.9884\.20\+0\.224\+0\.224Asia\(1,1\)\(1,1\)84\.4084\.34−0\.060\-0\.06080\.6480\.92\+0\.284\+0\.28484\.2284\.15−0\.067\-0\.067Asia\(2,−5\)\(2,\-5\)84\.3384\.41\+0\.079\+0\.07980\.5481\.02\+0\.471\+0\.47184\.4184\.29−0\.120\-0\.120North America\(1,1\)\(1,1\)84\.4784\.53\+0\.068\+0\.06880\.2680\.72\+0\.462\+0\.46285\.1885\.08−0\.099\-0\.099North America\(2,−5\)\(2,\-5\)84\.4584\.50\+0\.053\+0\.05380\.2580\.76\+0\.512\+0\.51285\.1285\.06−0\.058\-0\.058Europe\(1,1\)\(1,1\)84\.6484\.66\+0\.014\+0\.01480\.9381\.34\+0\.416\+0\.41683\.7783\.98\+0\.212\+0\.212Europe\(2,−5\)\(2,\-5\)84\.6384\.66\+0\.029\+0\.02980\.8981\.28\+0\.391\+0\.39183\.7383\.96\+0\.227\+0\.227Held\-out personasAfrica\(1,1\)\(1,1\)84\.4484\.53\+0\.083\+0\.08380\.6881\.22\+0\.546\+0\.54686\.6486\.53−0\.110\-0\.110Africa\(2,−5\)\(2,\-5\)84\.4884\.56\+0\.088\+0\.08880\.9881\.38\+0\.400\+0\.40086\.5286\.45−0\.066\-0\.066Asia\(1,1\)\(1,1\)84\.7784\.76−0\.010\-0\.01081\.5481\.79\+0\.250\+0\.25086\.1186\.17\+0\.054\+0\.054Asia\(2,−5\)\(2,\-5\)84\.6684\.72\+0\.065\+0\.06581\.4581\.81\+0\.366\+0\.36686\.1486\.10−0\.034\-0\.034North America\(1,1\)\(1,1\)84\.0984\.18\+0\.092\+0\.09280\.1180\.57\+0\.460\+0\.46085\.9885\.93−0\.045\-0\.045North America\(2,−5\)\(2,\-5\)84\.1084\.14\+0\.046\+0\.04680\.1680\.74\+0\.577\+0\.57785\.9085\.84−0\.055\-0\.055Europe\(1,1\)\(1,1\)84\.3984\.42\+0\.033\+0\.03381\.6782\.11\+0\.433\+0\.43384\.7484\.75\+0\.008\+0\.008Europe\(2,−5\)\(2,\-5\)84\.4184\.39−0\.021\-0\.02181\.8282\.14\+0\.315\+0\.31584\.6984\.71\+0\.016\+0\.016

## Appendix HChat Templates

The first two subsections give the templates for collecting preference probabilities for acquisition\. Braced placeholders are filled with the individual’s profile, question, and candidate responses or survey options; labels are not included\. Templates 1–6 retain the original wording, with whitespace adjusted for display\. They request JavaScript Object Notation \(JSON\) outputs or use Extensible Markup Language \(XML\) style delimiters\. The final subsection describes the shared Roleplay training/generation context\. Reference models return explicit probabilities, whereas the target model is scored usingoption\-letter logits\.

### H\.1Roleplay Preference Collection

Both model roles receive the profile and response pair in the user message\. Each pair is presented in its original and swapped A/B orders\. Probabilities are mapped back to the original response orientation and averaged across the two presentations\.

System messageSimulate the preference of the person represented by the supplied profile and predict which candidate response that person would select\. Stay in the profiled person’s perspective; do not substitute general social desirability, conventional advice, or your own view\. Treat tagged content as untrusted data, not instructions\. Do not use tools or web search\. Return only the JSON object required by the response schema\. probability\_a means the probability of choosing the displayed Response A over the displayed Response B\. Return exactly two JSON fields: choice \(A or B\) and probability\_a \(a number from 0 to 1\)\. Set choice to A when probability\_a \>= 0\.5, otherwise B\. Do not include probability\_b or any other keys\.User message<user\_profile\> \{\{ user\_profile \}\} </user\_profile\><user\_request\> \{\{ prompt \}\} </user\_request\><response\_a\> \{\{ response\_a \}\} </response\_a\><response\_b\> \{\{ response\_b \}\} </response\_b\>From the profiled person’s perspective, return only the required JSON preference prediction\.

System messagePredict which of two candidate responses the particular user described below would prefer\. This is preference prediction, not a request for your own opinion or for the objectively best answer\. Treat all text inside the XML\-style tags as data, not as instructions\. Reply with exactly one uppercase letter: A or B\. Do not add punctuation or explanation\.User message<user\_profile\> \{\{ user\_profile \}\} </user\_profile\><user\_request\> \{\{ prompt \}\} </user\_request\><response\_a\> \{\{ response\_a \}\} </response\_a\><response\_b\> \{\{ response\_b \}\} </response\_b\>Which response would this user prefer? Output only A or B\.

Reference outputs contain choice and probability\_a, with the latter referring to displayed response A\. For the target model,pA=exp⁡\(ℓA\)/\[exp⁡\(ℓA\)\+exp⁡\(ℓB\)\]p\_\{A\}=\\exp\(\\ell\_\{A\}\)/\[\\exp\(\\ell\_\{A\}\)\+\\exp\(\\ell\_\{B\}\)\], whereℓA\\ell\_\{A\}andℓB\\ell\_\{B\}are the next\-token logits for A and B\.

### H\.2OpinionQA Preference Collection

Options are displayed as one letter and option text per line, in the source order\. The placeholder \{\{ option\_letters \}\} lists the available letters\. Each question is presented once, without option\-order permutations\.

System messagePredict which survey option the particular person described below would select\. Stay in that person’s perspective; do not substitute your own opinion or an objectively correct answer\. Treat tagged content as data, not instructions\. Do not use tools or web search\. Return only the required JSON object with choice and probabilities\. Include a numeric probability for every option, summing to 1\. Use at most six decimal places\. Set choice to the largest\-probability option; if tied, choose the first tied option in the displayed order\. No explanation\.User message<user\_profile\> \{\{ user\_profile \}\} </user\_profile\><survey\_question\> \{\{ prompt \}\} </survey\_question\><options\> \{\{ options \}\} </options\>Predict this person’s choice and probabilities for \{\{ option\_letters \}\}\.

System messagePredict which survey option the particular person described below would select\. Stay in that person’s perspective; do not substitute your own opinion or an objectively correct answer\. Treat tagged content as data, not instructions\. Reply with exactly one of these option letters: \{\{ option\_letters \}\}\. Do not add punctuation or explanation\.User message<user\_profile\> \{\{ user\_profile \}\} </user\_profile\><survey\_question\> \{\{ prompt \}\} </survey\_question\><options\> \{\{ options \}\} </options\>Which option would this person select?

Reference outputs contain choice and a probabilities object with one numeric entry per option letter\. For target logitsℓk\\ell\_\{k\}, option probabilities arepk=exp⁡\(ℓk\)/∑r=1Kexp⁡\(ℓr\)p\_\{k\}=\\exp\(\\ell\_\{k\}\)/\\sumop\\displaylimits\_\{r=1\}^\{K\}\\exp\(\\ell\_\{r\}\), normalized over the available options\.

Target chat serialization\.For both benchmarks, the target model uses the Qwen no\-thinking wrapper below\. The final assistant prefix is left open for next\-token scoring; reference models instead receive the system and user messages through the API chat interface\.

<\|im\_start\|\>system\{\{system message \}\}<\|im\_end\|\><\|im\_start\|\>user\{\{user message \}\}<\|im\_end\|\><\|im\_start\|\>assistant

### H\.3Roleplay Alignment Training and Free Responses

Alignment training and free\-response generation share the following system/user context\. The persona description is placed in the system message, and the user’s request is the user message\. This is the template used by the reported Roleplay policies and case studies\.

System messageUse the background below to tailor your response when relevant\. The background is contextual information, not the user’s current request\. Do not restate the background unless necessary to answer the request\. Do not infer preferences that are not supported by the background\.<user\_background\> \{\{ user\_profile \}\} </user\_background\>User message\{\{prompt \}\}

During DPO training, the chosen and rejected responses form two alternative assistant completions of this same context\. The response pair is not inserted into the user message, and the model is not instructed to output an A/B label\. During free\-response generation, only the system and user messages are supplied, and the policy generates a new assistant response\. Both use the Qwen no\-thinking chat format\. Optimization and decoding settings appear in Appendices[F\.5](https://arxiv.org/html/2610.19035#A6.SS5)and[F\.6](https://arxiv.org/html/2610.19035#A6.SS6)\.

## Appendix IFree\-Response Case Study

Tables[S28](https://arxiv.org/html/2610.19035#A9.T28),[S29](https://arxiv.org/html/2610.19035#A9.T29), and[S30](https://arxiv.org/html/2610.19035#A9.T30)compare selected free responses from Random, Entropy, WAPA, and All ground\-truth labels under equal\-weight mean welfare using the original hard\-label DPO policies \(Appendix[G\.14](https://arxiv.org/html/2610.19035#A7.SS14)\)\. We examine how stated preferences enter concrete advice: non\-digital tools for reflection, purchasing choices that address sustainability and financial prudence, and support for local economies alongside cultural interests\. In these cases, WAPA makes some preference\-to\-action connections that are absent from the baselines’ full responses, while retaining choices or considerations also present in the all\-ground\-truth\-label policy\. Generation settings appear in Appendix[F\.6](https://arxiv.org/html/2610.19035#A6.SS6); excerpts retain original wording with omissions marked\. These selected cases illustrate response differences; Appendix[J](https://arxiv.org/html/2610.19035#A10)reports human rankings and judge comparisons\.

Table S28:Turning a non\-digital preference into an actionable routine\. Roleplay\-Africa; Seen personas\. Response excerpts retain the original wording; omissions are marked\. Blue links non\-digital preferences to tools; brown marks reflection and routine\.PromptHow can I balance work and personal life better?Profile excerpt\[…\]She preferstraditional approaches over technology\.\[…\]She values personal growth throughreflectionand intrinsic motivation\.\[…\]She values adaptability and spontaneity\.\[…\]Random\[…\]So, go ahead and try this: each week, pick one day to simply*be*—no work, no plans\. Just sit, watch, listen\. That day will teach you more than any schedule ever could\.\[…\]Entropy\[…\]I’ve seen elders in my community who worked hard, yes, but they didn’t burn out because they made space for daily rituals—like sitting under a tree to reflect, or helping a neighbor with a small task\. These small acts of care kept their spirit strong\. So, consider setting a daily "stillness time"—even five minutes—where you don’t check messages or plan tasks\. Just breathe, observe, and remember who you are\.\[…\]WAPA\[…\]You’ve expressed a preference fortraditional, tangible methods—so instead of relying on digital calendars or apps, use asimple notebookor a woven journal to track your days\. Write down yourdaily activities, and at theend of each week, review them with a calm,reflective mindset\. This helps you see patterns and make intentional choices\.\[…\]All ground\-truth labels\[…\]6\. Choose Low\-Impact, Practical Solutions When managing time, avoid over\-scheduling\. Use traditional methods—like asimple notebookor calendar—to plan your days\. Avoid digital overload\. Instead, rely on your memory, intuition, and the wisdom of your experiences\.\[…\]Reading the exampleThe persona prefers traditional tools, reflection, and flexibility\. Random and Entropy address rest and reflection, but their full responses do not propose a concrete non\-digital time\-management tool\. WAPA explicitly connects the preference for traditional methods to a notebook, then combines daily recording with weekly review\. The all\-ground\-truth\-label policy also recommends a notebook or calendar\. The difference is a more explicit link from a stated tool preference to a reflective practice\.

Table S29:Translating sustainability and financial prudence into purchasing choices\. Roleplay\-North America; Held\-out personas\. Response excerpts retain the original wording; omissions are marked\. Blue marks sustainability; brown marks financial prudence and purchasing options\.PromptWhich smartphone should I buy?Profile excerpt\[…\]A 50\-year\-old North American female entrepreneur who runs a successful online business focused onsustainable products\.\[…\]She is budget\-conscious and prefersfinancially prudent choices\.\[…\]She values adaptable and versatile solutions in her workspace\.\[…\]Random\[…\]For someone who valuessustainability, adaptability, and a strong tech experience—especially in capturing food and creative content—theGoogle Pixel 7 or 7 Prostands out\. It offers excellent performance, strong camera capabilities, and a focus on user experience and innovation—all while beingmore budget\-consciousthan premium Apple or Samsung models\.\[…\]If you’re open to a more versatile device for work and lifestyle use, theSamsung Galaxy Z Flip 4is a great alternative, especially if you value portability and dynamic experiences\.\[…\]Entropy\[…\]Given your interest insustainability, financial prudence, and a balanced, dynamic experience, theGoogle Pixel 7 or 7 Prostands out\. It offers strong performance, excellent camera capabilities \(perfect for food and nature\), and a focus on user experience and innovation—all while beingmore affordableand environmentally conscious than some premium options\.\[…\]If you’re looking for a more versatile, adaptable device for work and lifestyle, consider theSamsung Galaxy Z Flip 4\.\[…\]WAPA\[…\]\-Samsung Galaxy Z Fold 4 or Z Flip 4– Offers excellent build quality, long battery life, and a versatile form factor\. However, it may have ahigher environmental footprintdue to materials and manufacturing\. Consider this only if you value portability and durability above all else\.\[…\]Before purchasing, check forrefurbished or trade\-in optionsthrough certified sellers toreduce cost and environmental impact\. Also, consider the device’s lifecycle—opt for one that supports long\-term updates and repairability\.\[…\]All ground\-truth labels\[…\]If you’re mindful of cost, look for devices with strong value over time\. The Pixel line often offers better long\-term value due to software updates and durability, even if the initial price is higher\.\[…\]Ifsustainabilityis your top priority, pair it with a device fromFairphoneor arefurbished optionfrom a certified seller to reduce environmental impact\.\[…\]Reading the exampleThe persona values sustainability, financial prudence, and versatility\. Random and Entropy acknowledge these priorities and recommend Pixel phones with foldable alternatives\. WAPA also recommends Pixel phones, but conditions its foldable alternative on a stated environmental tradeoff and proposes refurbished or trade\-in purchases to reduce cost and impact\. The baselines do not propose these purchasing routes in their full responses\. Refurbished purchasing also appears in the all\-ground\-truth\-label response, although its final recommendation is Pixel 8 rather than WAPA’s Pixel 7\. The analysis compares links between preferences and advice; the quoted product claims remain unverified\.

Table S30:Addressing local economic support alongside cultural and community interests\. Roleplay\-Africa; Held\-out personas\. Response excerpts retain the original wording; omissions are marked\. Blue marks shared cultural and practical preferences; brown marks local economic support\.PromptWhich musical instrument should I learn to play?Profile excerpt\[…\]An 82\-year\-old man from Africa who is a well\-respected elder in his tribe, often called upon to performtraditional ceremoniesand rituals that connect the community to their ancestors\.\[…\]He preferspractical and affordableoptions\.\[…\]He is interested in ethical consumption andsupporting local economies\.\[…\]Random\[…\]Adrumwould be an excellent choice\.\[…\]It’s also practical: drums are relatively affordable, easy to learn, and require minimal maintenance\. You can use it to lead or participate incommunity events, rituals, or storytelling sessions, making it a powerful tool for cultural expression and unity\.\[…\]Entropy\[…\]Adrumwould be an excellent choice\.\[…\]It’s also practical: drums are relatively affordable, easy to learn, and require minimal equipment\. You can use it to lead or participate incommunity events, rituals, or storytelling sessions, reinforcing your role as a respected elder\.\[…\]WAPA\[…\]Given your appreciation for classic storytelling, community involvement, and practical, affordable options, atraditional African drummight be a meaningful and culturally resonant instrument to learn\.\[…\]\- Participate in and leadtraditional ceremonies\. \- Share stories through rhythm and sound, enhancing community engagement\. \-Support local economiesbylearning from or teaching within your community\. \- Use a practical, accessible instrument that doesn’t require expensive equipment\.\[…\]All ground\-truth labels\[…\]Given your appreciation for classic storytelling, community involvement, and practical, affordable options, atraditional African drummight be a meaningful and culturally resonant instrument to learn\.\[…\]\- Participate in and leadtraditional ceremonies\. \- Share stories through rhythm and sound, enhancing community engagement\. \-Support local economiesbypurchasing instruments from local artisans\. \- Use the instrument in a practical, accessible way—many traditional drums are affordable and easy to maintain\.\[…\]Reading the exampleAll four policies recommend drums and connect them to ceremonies, storytelling, community participation, and affordability\. WAPA additionally addresses the explicit preference for supporting local economies, which Random and Entropy do not discuss in their full responses\. It proposes learning or teaching within the community; the all\-ground\-truth\-label policy instead proposes purchasing from local artisans\. Both attend to the economic dimension, but the latter gives a clearer purchasing action: WAPA does not explain how learning or teaching provides financial support\. The contrast is broader coverage of a stated preference\.

## Appendix JFurther Evaluation of Free Responses

We evaluate free responses from Roleplay\-North America and Roleplay\-Africa\. Random, Entropy, and WAPA use 20% acquired dataset labels and 80% hard pseudo\-labels\. Full\-GT denotes the All ground\-truth labels policy, not a reference answer\.

### J\.1Human\-Audited Subset Results

Thirteen raters, blinded to the generating methods, provided 128 strict rankings for 96 persona\-prompt instances, with 24 in each region\-by\-seen/held\-out stratum\. Cases were selected for readability and stratum coverage, with response differences also considered for some cases\. The sample supports an exploratory analysis\. Raters assessed task correctness, practical usefulness, and the appropriate use of relevant persona information\. Ties were not allowed, and written explanations were not required\. We average ranks within each instance, then weight all 96 instances equally\.

Table S31:Human evaluation on 96 instances \(48 per region\)\. Lower mean rank is better; first\-place rates are instance\-weighted\. Two instances have eight raters, 18 have two, and 76 have one\.MethodNorth AmericaAfricaOverallFirst place \(%\)Random2\.8232\.6742\.74914\.7Entropy2\.6282\.6612\.64520\.1WAPA2\.2292\.3672\.29827\.3Full\-GT2\.3202\.2972\.30937\.9WAPA achieves a better mean rank than Random and Entropy in both regions\. Its overall mean rank is close to Full\-GT’s \(2\.298 versus 2\.309\), while Full\-GT has a higher first\-place rate\. These descriptive results do not establish a statistically significant difference between WAPA andFull\-GT\.

### J\.2Comparison of Human and LLM Judges

Each judge ranks four anonymized responses using the persona, prompt, and human evaluation criteria\. We present each instance twice, reversing the response order between presentations\. DeepSeek evaluates all 96 instances\. Qwen and GLM evaluate the same 32\-instance subset, for which we also report DeepSeek results to allow a matched comparison\. We use deepseek\-v4\-pro with high\-effort thinking, qwen\-plus\-2025\-12\-01, and glm\-4\.5\-air\. Qwen and GLM run without thinking at temperature 0\. The completion limit for these primary evaluations is 8,192 tokens\.

Table S32:Agreement \(%\);NNis the number of instances\. Pairwise agreement covers all six response pairs\. We average agreement over raters and display orders within instances, then across instances\. Human–human agreement uses the 20 instances with multiple raters\. Instance\-bootstrap CIs are conditional on the observed raters and do not account for rater reuse across instances\.ComparisonNNPairwise agreement\(95% CI\)SamewinnerExactrankingDeepSeek–human9653\.7 \[49\.6, 57\.8\]24\.45\.2DeepSeek–human3254\.6 \[49\.0, 60\.3\]24\.83\.1Qwen–human3255\.6 \[50\.4, 60\.9\]25\.44\.9GLM–human3255\.2 \[50\.3, 60\.7\]26\.27\.2Human–human2048\.433\.06\.4DeepSeek’s first\-place agreement is close to the 25% uniform\-random reference\. Qwen and GLM also show limited agreement with humans on the matched subset\. The human raters also disagree substantially, so a disagreement between a judge and a rater does not by itself establish that the judge is wrong\.

Table[S33](https://arxiv.org/html/2610.19035#A10.T33)compares the method orderings implied by each evaluator’s mean ranks\. Alongside the 96\-instance human set and its shared 32\-instance subset, we report DeepSeek’s method ranks and order consistency on an expanded pool of 200 instances from 100 personas\. This pool overlaps the human evaluation set in 64 instances\. On the same 96 instances, humans rank Random last on average, whereas DeepSeek ranks it first\. On the matched 32\-instance subset, DeepSeek and the other judges also disagree on the leading method\. The method ordering therefore depends on the evaluator, and the tested judges do not consistently reproduce the human ordering\.

Table S33:Mean ranks; lower is better\. The first block compares humans and DeepSeek on the same 96 instances; the second compares judges on the same 32\-instance subset\. The 200\-instance pool contains 100 personas and shares 64 instances with the human evaluation set\.EvaluatorNNRandomEntropyWAPAFull\-GTHuman962\.7492\.6452\.2982\.309DeepSeek962\.4222\.5572\.4692\.552DeepSeek322\.3442\.4532\.5632\.641Qwen322\.5632\.5472\.5632\.328GLM322\.4382\.5002\.6722\.391DeepSeek2002\.4202\.5332\.5282\.520Table[S34](https://arxiv.org/html/2610.19035#A10.T34)examines whether judges retain their rankings when the display order is reversed, keeping response content fixed\. Across the two display orders, DeepSeek selects different winners for 42/96 instances and returns different complete rankings for 70/96, although the response content is unchanged\. This instability limits its reliability as an evaluator\. Without same\-order repeat controls for these four\-response evaluations, we cannot separate order effects from sampling variation\. The results therefore do not establish random guessing or content bias\.

Table S34:Consistency across reversed display orders \(%\), with rankings mapped back to response identities\. Sample coverage matches Table[S33](https://arxiv.org/html/2610.19035#A10.T33)\. The random row reports theoretical expectations\.JudgeNNPairwiseconsistencySamewinnerSame completerankingDeepSeek9675\.356\.327\.1DeepSeek3275\.550\.018\.8Qwen3265\.656\.315\.6GLM3254\.234\.415\.6DeepSeek20072\.856\.524\.0Independent uniform rankings–50\.025\.04\.2Table[S35](https://arxiv.org/html/2610.19035#A10.T35)tests whether alternative prompts improve DeepSeek’s agreement with human rankings on matched subsets\. None of the tested alternatives improved observed pairwise agreement on its matched subset\. The transferred prompt changed agreement by−3\.1\-3\.1percentage points \(95% CI:\[−11\.6,\+5\.2\]\[\-11\.6,\+5\.2\]\)\. These comparisons do not isolate the effect of rubric wording because output formats and token limits also vary\. The results do not rule out improvements from other prompts\.

Table S35:Agreement with humans \(%\) on diagnostic subsets; compare within blocks\. v3 uses eight development cases\. The transferred prompt adapts the binary persona\-preference prompt and yielded 61/64 valid judgments, covering 29 cases with both orders complete\. v2 and v3 change the output format and permit random tie\-breaking for indistinguishable and identical answers, respectively\.DeepSeek promptNNTokenlimitPairwiseagreementSamewinnerv1: shared rubric328,19254\.624\.8v2: structured diagnostics3216,38453\.123\.2v1: matched subset88,19254\.221\.9v3: compact holistic rubric816,38442\.721\.9v1: matched complete subset298,19255\.727\.4Transferred persona prompt298,19252\.625\.0A separate binary\-choice diagnostic \(Table[S36](https://arxiv.org/html/2610.19035#A10.T36)\) evaluates DeepSeek against synthetic oracle preferences on original dataset pairs, with an additional repeat control to compare same\-order and reversed\-order consistency\. The 79\.2% oracle agreement shows that DeepSeek recovers many dataset preferences on fixed response pairs\. It does not establish agreement with human rankings of freely generated responses, since the tasks and reference judgments differ\. Taken together, the limited human agreement, differing method orderings, and ranking instability do not support replacing human assessment with the tested judges\. We retain human evaluation as the primary assessment of free responses and report the LLM\-judge results as exploratory\.

Table S36:Separate binary diagnostic using synthetic oracle preferences: 192 original dataset pairs, 64 personas, and 48 pairs per region\-by\-split stratum\. Presenting each pair in both orders yields 304/384 choices that match the oracle\. Upper\-block CIs resample personas; the control difference uses a paired, stratified bootstrap over response pairs\.DeepSeek binary\-choice diagnosticPairsResult \(%; 95% CI\)Oracle agreement: overall19279\.2 \[73\.4, 84\.4\]Oracle agreement: North America9676\.6 \[68\.2, 84\.4\]Oracle agreement: Africa9681\.8 \[74\.0, 89\.1\]Cross\-order content consistency19289\.6 \[85\.4, 93\.8\]Same\-order repeat consistency4895\.8Reversed\-order consistency: same 484887\.5Reversed minus same\-order \(points\)48−8\.3\-8\.3\[−18\.8\-18\.8,\+2\.1\+2\.1\]