Optimized Distortion in Linear Social Choice

2025-10-22

AI Summary

This paper studies distortion optimization in linear social choice: minimizing the worst-case distortion of voting rules under utilitarian social welfare, where candidates are represented as vectors and voter utilities are parameterized linear functions. It introduces distortion analysis systematically into the linear utility framework, deriving a tight upper bound on distortion that depends solely on the embedding dimension of candidates—not on the number of voters or candidates. Based on this bound, the paper designs the first instance-optimal, polynomial-time solvable voting algorithm. The method integrates deterministic and randomized mechanisms and is compatible with embedding representations generated by collaborative filtering or large language models. Empirical evaluation on real-world datasets from recommendation systems and opinion surveys demonstrates that the proposed algorithm significantly reduces distortion and improves social welfare compared to classical voting rules.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Machine Learning: Learning Preferences or Rankings
• Humans and AI: Voting

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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-à-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.

Problem

• Analyzing distortion in linear utility social choice
• Developing dimension-dependent bounds for voting rules
• Introducing poly-time algorithms for minimizing distortion

Innovation

• Studied distortion for linear utility functions
• Introduced poly-time instance-optimal algorithms
• Empirically evaluated algorithms using embeddings