Stable Voting Rules on the Edge of Optimal Metric Distortion

2026-09-08

AI Summary

本文提出了一种基于零和博弈的随机投票规则，其度量失真不超过2.13713，接近最优下界2.11264，并为稳定k-彩票提供了精确的失真界限。

Abstract

We prove the existence of a randomized voting rule with metric distortion at most $2.13713$, within $0.025$ of the lower bound of $2.11264$. Our rule comes from a generalization of stable $k$-lotteries developed in the context of committee selection. In contrast to prior work, our rule samples from a single distribution derived from a zero-sum game, without mixing between voting rules. Our result also gives sharp distortion bounds for stable $k$-lotteries, and in particular shows that stable $2$-lotteries have distortion $7/3$, despite only relying on aggregate preferences over triples of candidates.

Problem

• voting rule
• metric distortion
• randomized

Innovation

• randomized voting rule
• metric distortion
• zero-sum game
• stable k-lotteries