Representative Proxy Voting

TL;DR

This paper models proxy voting on a line, demonstrating how to efficiently select proxies that accurately represent voters' preferences and ensure outcomes close to direct voting results.

Contribution

It introduces a polynomial-time method to find optimal proxy arrangements and establishes bounds on the number of proxies needed for effective representation.

Findings

Optimal proxy arrangements can be computed in polynomial time.

A small number of proxies suffices for accurate representation.

Proxy voting outcomes closely match direct voting results under certain rules.

Abstract

We study a model of proxy voting where the candidates, voters, and proxies are all located on the real line, and instead of voting directly, each voter delegates its vote to the closest proxy. The goal is to find a set of proxies that is $\theta$-representative, which entails that for any voter located anywhere on the line, its favorite candidate is within a distance $\theta$ of the favorite candidate of its closest proxy. This property guarantees a strong form of representation as the set of voters is not required to be fixed in advance, or even be finite. We show that for candidates located on a line, an optimal proxy arrangement can be computed in polynomial time. Moreover, we provide upper and lower bounds on the number of proxies required to form a $\theta$-representative set, thus showing that a relatively small number of proxies is enough to capture the preferences of any set of voters. An additional beneficial property of a $\theta$-representative proxy arrangement is that for strict-Condorcet voting rules, the outcome of proxy voting is similarly close to the outcome of direct voting.