On the Likelihood of Single-Peaked Preferences
Abstract
This paper contains an extensive combinatorial analysis of the single-peaked domain restriction and investigates the likelihood that an election is single-peaked. We provide a very general upper bound result for domain restrictions that can be defined by certain forbidden configurations. This upper bound implies that many domain restrictions (including the single-peaked restriction) are very unlikely to appear in a random election chosen according to the Impartial Culture assumption. For single-peaked elections, this upper bound can be refined and complemented by a lower bound that is asymptotically tight. In addition, we provide exact results for elections with few voters or candidates. Moreover, we consider the P\'{o}lya urn model and the Mallows model and obtain lower bounds showing that single-peakedness is considerably more likely to appear for certain parameterizations.
Keywords
Cite
@article{arxiv.1505.05852,
title = {On the Likelihood of Single-Peaked Preferences},
author = {Marie-Louise Lackner and Martin Lackner},
journal= {arXiv preprint arXiv:1505.05852},
year = {2019}
}