Metric Distortion of Obnoxious Distributed Voting

TL;DR

This paper analyzes how well distributed voting mechanisms perform in selecting the most socially optimal alternative in a metric space, considering limited information scenarios and establishing tight bounds on their distortion.

Contribution

It introduces and evaluates bounds on the distortion of distributed voting mechanisms with varying information access, focusing on full-information and ordinal methods.

Findings

Tight bounds on the distortion for different mechanisms.

Analysis of the impact of information availability on mechanism performance.

Comparison between full-information and ordinal mechanisms.

Abstract

We consider a distributed voting problem with a set of agents that are partitioned into disjoint groups and a set of obnoxious alternatives. Agents and alternatives are represented by points in a metric space. The goal is to compute the alternative that maximizes the total distance from all agents using a two-step mechanism which, given some information about the distances between agents and alternatives, first chooses a representative alternative for each group of agents, and then declares one of them as the overall winner. Due to the restricted nature of the mechanism and the potentially limited information it has to make its decision, it might not be always possible to choose the optimal alternative. We show tight bounds on the distortion of different mechanisms depending on the amount of the information they have access to; in particular, we study full-information and ordinal mechanisms.