The Distortion of Binomial Voting Defies Expectation

TL;DR

This paper introduces binomial voting, a new voting rule that guarantees low expected distortion and high welfare across various voter utility distributions, advancing the understanding of voting rule performance beyond worst-case scenarios.

Contribution

The paper proposes and analyzes binomial voting, a novel rule that offers distribution-independent guarantees on expected distortion and welfare in social choice.

Findings

Binomial voting achieves low expected distortion.

It provides strong welfare guarantees.

The rule performs well across different utility distributions.

Abstract

In computational social choice, the distortion of a voting rule quantifies the degree to which the rule overcomes limited preference information to select a socially desirable outcome. This concept has been investigated extensively, but only through a worst-case lens. Instead, we study the expected distortion of voting rules with respect to an underlying distribution over voter utilities. Our main contribution is the design and analysis of a novel and intuitive rule, binomial voting, which provides strong distribution-independent guarantees for both expected distortion and expected welfare.