Small One-Dimensional Euclidean Preference Profiles
Computer Science and Game Theory
2018-10-17 v2
Abstract
We characterize one-dimensional Euclidean preference profiles with a small number of alternatives and voters. In particular, we show the following. 1. Every preference profile with up to two voters is one-dimensional Euclidean if and only if it is single-peaked. 2. Every preference profile with up to five alternatives is one-dimensional Euclidean if and only if it is single-peaked and single-crossing. By [12], we thus obtain that the smallest single-peaked and single-crossing preference profiles that are not one-dimensional Euclidean consist of three voters and six alternatives.
Cite
@article{arxiv.1810.06461,
title = {Small One-Dimensional Euclidean Preference Profiles},
author = {Jiehua Chen and Sven Grottke},
journal= {arXiv preprint arXiv:1810.06461},
year = {2018}
}