Metric Distortion of Line-up Elections: The Right Person for the Right Job

TL;DR

This paper introduces mechanisms for line-up elections that achieve low metric distortion using limited information, effectively approximating optimal outcomes in complex voter-candidate-position scenarios.

Contribution

It provides new metric distortion bounds and mechanisms for line-up elections under various informational settings, advancing the understanding of efficient election design.

Findings

Constant distortion bounds achieved with limited information

Mechanisms work with ordinal preferences and partial location data

Outcomes closely approximate the optimal with minimal data

Abstract

We provide mechanisms and new metric distortion bounds for line-up elections. In such elections, a set of $n$ voters, $m$ candidates, and $\ell$ positions are all located in a metric space. The goal is to choose a set of candidates and assign them to different positions, so as to minimize the total cost of the voters. The cost of each voter consists of the distances from itself to the chosen candidates (measuring how much the voter likes the chosen candidates, or how similar it is to them), as well as the distances from the candidates to the positions they are assigned to (measuring the fitness of the candidates for their positions). Our mechanisms, however, do not know the exact distances, and instead produce good outcomes while only using a smaller amount of information, resulting in small distortion. We consider several different types of information: ordinal voter preferences, ordinal position preferences, and knowing the exact locations of candidates and positions, but not those of voters. In each of these cases, we provide constant distortion bounds, thus showing that only a small amount of information is enough to form outcomes close to optimum in line-up elections.