Distortion of Metric Voting with Bounded Randomness

TL;DR

This paper introduces a new voting rule that uses bounded randomness to achieve a distortion less than 3, improving over deterministic rules while maintaining transparency.

Contribution

It demonstrates that bounded randomness can break the distortion barrier of 3, providing a voting rule with lower distortion and a simple, transparent winner selection process.

Findings

Achieves distortion of at most 3 - ε for some constant ε > 0

Selects winner uniformly from a constant-sized list

Builds on new structural results for Maximal and Stable Lotteries

Abstract

We study the design of voting rules in the metric distortion framework. It is known that any deterministic rule suffers distortion of at least $3$, and that randomized rules can achieve distortion strictly less than $3$, often at the cost of reduced transparency and interpretability. In this work, we explore the trade-off between these paradigms by asking whether it is possible to break the distortion barrier of $3$ using only "bounded" randomness. We answer in the affirmative by presenting a voting rule that (1) achieves distortion of at most $3 - \varepsilon$ for some absolute constant $\varepsilon > 0$, and (2) selects a winner uniformly at random from a deterministically identified list of constant size. Our analysis builds on new structural results for the distortion and approximation of Maximal Lotteries and Stable Lotteries.