Incomplete Preferences in Single-Peaked Electorates
Abstract
Incomplete preferences are likely to arise in real-world preference aggregation scenarios. This paper deals with determining whether an incomplete preference profile is single-peaked. This is valuable information since many intractable voting problems become tractable given single-peaked preferences. We prove that the problem of recognizing single-peakedness is \NP-complete for incomplete profiles consisting of partial orders. Despite this intractability result, we find several polynomial-time algorithms for reasonably restricted settings. In particular, we give polynomial-time recognition algorithms for weak orders, which can be viewed as preferences with indifference.
Cite
@article{arxiv.1907.00752,
title = {Incomplete Preferences in Single-Peaked Electorates},
author = {Zack Fitzsimmons and Martin Lackner},
journal= {arXiv preprint arXiv:1907.00752},
year = {2020}
}
Comments
This work is based on a conference paper by Martin Lackner (AAAI 2014) and a follow-up conference paper by Zack Fitzsimmons (TARK 2015)