Linear Social Choice with Few Queries: A Moment-Based Approach

2026-03-19

AI Summary

This work addresses the fundamental challenge in social choice of balancing social welfare and fairness under extremely low communication budgets—specifically, when each voter provides only one or two feedback signals. The authors model voter preferences as draws from an unknown type distribution and recover its moments (e.g., mean, variance) as statistical summaries of candidate utilities. Theoretical analysis shows that a single pairwise comparison suffices to maximize social welfare, while either two pairwise comparisons or one cardinal rating enables recovery of second-order moments or even the full distribution, thereby supporting inequality-sensitive objectives. Leveraging a linear social choice model combined with a low-communication querying mechanism, the proposed approach achieves welfare-optimal outcomes with minimal communication overhead and facilitates fairness-aware decisions based on the dispersion and representativeness of the underlying utility distribution.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Machine Learning: Learning Preferences or Rankings
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Most social choice rules assume access to full rankings, while current alignment practice -- despite aiming for diversity -- typically treats voters as anonymous and comparisons as independent, effectively extracting only about one bit per voter. Motivated by this gap, we study social choice under an extreme communication budget in the linear social choice model, where each voter's utility is the inner product between a latent voter type and the embedding of the context and candidate. The candidate and voter spaces may be very large or even infinite. Our core idea is to model the electorate as an unknown distribution over voter types and to recover its moments as informative summary statistics for candidate selection. We show that one pairwise comparison per voter already suffices to select a candidate that maximizes social welfare, but this elicitation cannot identify the second moment and therefore cannot support objectives that account for inequality. We prove that two pairwise comparisons per voter, or alternatively a single graded comparison, identify the second moment; moreover, these richer queries suffice to identify all moments, and hence the entire voter-type distribution. These results enable principled solutions to a range of social choice objectives including inequality-aware welfare criteria such as taking into account the spread of voter utilities and choosing a representative subset.

Problem

• social choice
• communication budget
• voter utility
• inequality
• preference elicitation

Innovation

• moment-based social choice
• low-query elicitation
• linear utility model
• inequality-aware welfare
• voter-type distribution