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

2024-05-07

arXiv.org

AI Summary

This paper studies the “sequential election” problem in metric spaces: given $n$ voters, $k$ candidates, and $ell$ positions, jointly select and assign candidates to positions to minimize total cost—comprising voter–candidate distances and candidate–position distances. Unlike classical single-winner elections, we establish the first unified metric distortion framework for this joint selection-and-allocation problem. Under information constraints—such as access only to ordinal preferences or partial coordinate information—we design mechanisms based on greedy selection, bipartite matching, and rank aggregation. We prove tight constant-factor distortion bounds (e.g., 2, 3, or 4), significantly improving over naive baselines. Our key contribution is breaking the single-winner modeling paradigm: we extend metric distortion theory to multi-position assignment for the first time, and provide optimality guarantees under multiple weak-information settings.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We provide mechanisms and new metric distortion bounds for line-up elections. In such elections, a set of $n$ voters, $k$ 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.

Problem

• minimize voter cost
• assign candidates to positions
• achieve low metric distortion

Innovation

• metric distortion bounds
• line-up elections
• ordinal preferences information