The Distortion of Distributed Metric Social Choice

TL;DR

This paper analyzes how distributing decision-making in metric social choice impacts efficiency, providing bounds on the distortion introduced by such distributed mechanisms for various objectives.

Contribution

It introduces bounds on the distortion of distributed social choice mechanisms for multiple objectives, including new objectives tailored for distributed settings.

Findings

Bounds on distortion for total cost and maximum cost objectives

Analysis of distributed mechanisms' efficiency loss

Introduction of new objectives suited for distributed decision-making

Abstract

We consider a social choice setting with agents that are partitioned into disjoint groups, and have metric preferences over a set of alternatives. Our goal is to choose a single alternative aiming to optimize various objectives that are functions of the distances between agents and alternatives in the metric space, under the constraint that this choice must be made in a distributed way: The preferences of the agents within each group are first aggregated into a representative alternative for the group, and then these group representatives are aggregated into the final winner. Deciding the winner in such a way naturally leads to loss of efficiency, even when complete information about the metric space is available. We provide a series of (mostly tight) bounds on the distortion of distributed mechanisms for variations of well-known objectives, such as the (average) total cost and the maximum cost, and also for new objectives that are particularly appropriate for this distributed setting and have not been studied before.