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arXiv · 1907.00752

Incomplete Preferences in Single-Peaked Electorates

Zack Fitzsimmons·Martin Lackner
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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.

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Zack Fitzsimmons, Martin Lackner. 2019-07-01. Incomplete Preferences in Single-Peaked Electorates. https://doi.org/10.1613/jair.1.11577

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