Revisiting the Distortion of Distributed Voting

TL;DR

This paper analyzes the limits of deterministic and randomized distributed voting mechanisms in terms of distortion, providing tight bounds and empirical comparisons using synthetic and real data.

Contribution

It establishes asymptotically tight bounds on the distortion of all deterministic mechanisms and explores the distortion bounds of randomized mechanisms under various informational assumptions.

Findings

Tight bounds on deterministic mechanism distortion established.

Randomized mechanisms can achieve lower distortion under certain informational assumptions.

Empirical analysis compares multiple mechanisms on synthetic and real-world data.

Abstract

We consider a setting with agents that have preferences over alternatives and are partitioned into disjoint districts. The goal is to choose one alternative as the winner using a mechanism which first decides a representative alternative for each district based on a local election with the agents therein as participants, and then chooses one of the district representatives as the winner. Previous work showed bounds on the distortion of a specific class of deterministic plurality-based mechanisms depending on the available information about the preferences of the agents in the districts. In this paper, we first consider the whole class of deterministic mechanisms and show asymptotically tight bounds on their distortion. We then initiate the study of the distortion of randomized mechanisms in distributed voting and show bounds based on several informational assumptions, which in many cases turn out to be tight. Finally, we also experimentally compare the distortion of many different mechanisms of interest using synthetic and real-world data.