# Optimized Distortion in Linear Social Choice

arXiv: https://arxiv.org/abs/2510.20020 · HTML: https://mlsanity.com/paper/2510.20020/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 22 references that are in the map.
- First posted on arXiv 22 Oct 2025.

## Builds on (most cited first, 6 of 6)

- [Axioms for AI Alignment from Human Feedback](https://mlsanity.com/paper/2405.14758/) (2024)
- [Distortion of AI Alignment: Does Preference Optimization Optimize for Preferences?](https://mlsanity.com/paper/2505.23749/) (2025)
- [Optimized Distortion and Proportional Fairness in Voting](https://mlsanity.com/paper/2205.15760/) (2022)
- [Group Fairness in Committee Selection](https://mlsanity.com/paper/1905.04438/) (2019)
- [Justifications of Welfare Guarantees under Normalized Utilities](https://mlsanity.com/paper/1905.10774/) (2019)
- [From Independence of Clones to Composition Consistency: A Hierarchy of Barriers to Strategic Nomination](https://mlsanity.com/paper/2502.16973/) (2025)

## Built on by (most cited first, 2 of 2)

- [AI Alignment From Social Choice Perspectives](https://mlsanity.com/paper/2606.21550/) (2026)
- [Linear Social Choice with Few Queries: A Moment-Based Approach](https://mlsanity.com/paper/2603.19510/) (2026)

## Abstract (arXiv)

Social choice theory offers a wealth of approaches for selecting a candidate on behalf of voters based on their reported preference rankings over options. When voters have underlying utilities for these options, however, using preference rankings may lead to suboptimal outcomes vis-`a-vis utilitarian social welfare. Distortion is a measure of this suboptimality, and provides a worst-case approach for developing and analyzing voting rules when utilities have minimal structure. However in many settings, such as common paradigms for value alignment, alternatives admit a vector representation, and it is natural to suppose that utilities are parametric functions thereof. We undertake the first study of distortion for linear utility functions. Specifically, we investigate the distortion of linear social choice for deterministic and randomized voting rules. We obtain bounds that depend only on the dimension of the candidate embedding, and are independent of the numbers of candidates or voters. Additionally, we introduce poly-time instance-optimal algorithms for minimizing distortion given a collection of candidates and votes. We empirically evaluate these in two real-world domains: recommendation systems using collaborative filtering embeddings, and opinion surveys utilizing language model embeddings, benchmarking several standard rules against our instance-optimal algorithms.