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arXiv · 1810.06461

Small One-Dimensional Euclidean Preference Profiles

Jiehua Chen·Sven Grottke
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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.

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Jiehua Chen, Sven Grottke. 2018-10-15. Small One-Dimensional Euclidean Preference Profiles. https://arxiv.org/abs/1810.06461

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