# Favorite-Candidate Voting for Eliminating the Least Popular Candidate in Metric Spaces

arXiv: https://arxiv.org/abs/1911.12109 · HTML: https://mlsanity.com/paper/1911.12109/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2019.

## Built on by (most cited first, 1 of 1)

- [Plurality Veto: A Simple Voting Rule Achieving Optimal Metric Distortion](https://mlsanity.com/paper/2206.07098/) (2022)

## Abstract (arXiv)

We study single-candidate voting embedded in a metric space, where both voters and candidates are points in the space, and the distances between voters and candidates specify the voters' preferences over candidates. In the voting, each voter is asked to submit her favorite candidate. Given the collection of favorite candidates, a mechanism for eliminating the least popular candidate finds a committee containing all candidates but the one to be eliminated. Each committee is associated with a social value that is the sum of the costs (utilities) it imposes (provides) to the voters. We design mechanisms for finding a committee to optimize the social value. We measure the quality of a mechanism by its distortion, defined as the worst-case ratio between the social value of the committee found by the mechanism and the optimal one. We establish new upper and lower bounds on the distortion of mechanisms in this single-candidate voting, for both general metrics and well-motivated special cases.