Tight Distortion Bounds for Distributed Single-Winner Metric Voting on a Line

TL;DR

This paper introduces distributed voting mechanisms for single-winner metric voting on a line, achieving optimal distortion bounds for decentralized decision-making with agents partitioned into districts.

Contribution

The paper presents simple distributed mechanisms that attain the optimal distortion bounds for specific social cost objectives in a line metric setting.

Findings

Achieves distortion at most 2+√5 for average-of-max and max-of-average objectives.

Mechanisms match previously known lower bounds, demonstrating optimality.

Applicable to decentralized voting with agents partitioned into districts.

Abstract

We consider the distributed single-winner metric voting problem on a line, where agents and alternative are represented by points on the line of real numbers, the agents are partitioned into disjoint districts, and the goal is to choose a single winning alternative in a decentralized manner. In particular, the choice is done by a distributed voting mechanism which first selects a representative alternative for each district of agents and then chooses one of these representatives as the winner. In this paper, we design simple distributed mechanisms that achieve distortion at most $2+\sqrt{5}$ for the average-of-max and the max-of-average social cost objectives, matching the corresponding lower bound shown in previous work for these objectives.