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

arXiv: https://arxiv.org/abs/2603.19510 · HTML: https://mlsanity.com/paper/2603.19510/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 58 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 23 of 23)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [BeaverTails: Towards Improved Safety Alignment of LLM via a Human-Preference Dataset](https://mlsanity.com/paper/2307.04657/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [A Roadmap to Pluralistic Alignment](https://mlsanity.com/paper/2402.05070/) (2024)
- [Distributional Preference Learning: Understanding and Accounting for Hidden Context in RLHF](https://mlsanity.com/paper/2312.08358/) (2023)
- [A Voting-Based System for Ethical Decision Making](https://mlsanity.com/paper/1709.06692/) (2017)
- [Axioms for AI Alignment from Human Feedback](https://mlsanity.com/paper/2405.14758/) (2024)
- [Learning general Gaussian mixtures with efficient score matching](https://mlsanity.com/paper/2404.18893/) (2024)
- [Distributional Preference Alignment of LLMs via Optimal Transport](https://mlsanity.com/paper/2406.05882/) (2024)
- [Direct Preference Optimization With Unobserved Preference Heterogeneity: The Necessity of Ternary Preferences](https://mlsanity.com/paper/2405.15065/) (2024)
- [Direct Alignment with Heterogeneous Preferences](https://mlsanity.com/paper/2502.16320/) (2025)
- [Representation with Incomplete Votes](https://mlsanity.com/paper/2211.15608/) (2022)
- [Towards Reward Fairness in RLHF: From a Resource Allocation Perspective](https://mlsanity.com/paper/2505.23349/) (2025)
- [Learning Linear Utility Functions From Pairwise Comparison Queries](https://mlsanity.com/paper/2405.02612/) (2024)
- [Peeking Behind the Ordinal Curtain: Improving Distortion via Cardinal Queries](https://mlsanity.com/paper/1907.08165/) (2019)
- [Computing Voting Rules with Elicited Incomplete Votes](https://mlsanity.com/paper/2402.11104/) (2024)
- [Judging with Confidence: Calibrating Autoraters to Preference Distributions](https://mlsanity.com/paper/2510.00263/) (2025)
- [Learning Correlated Reward Models: Statistical Barriers and Opportunities](https://mlsanity.com/paper/2510.15839/) (2025)
- [Optimized Distortion in Linear Social Choice](https://mlsanity.com/paper/2510.20020/) (2025)

## Built on by (most cited first, 1 of 1)

- [AI Alignment From Social Choice Perspectives](https://mlsanity.com/paper/2606.21550/) (2026)

## Abstract (arXiv)

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.