Incomplete Preferences in Single-Peaked Electorates

Zack Fitzsimmons, Martin Lackner
2020 The Journal of Artificial Intelligence Research  
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 singlepeaked 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
more » ... orithms for reasonably restricted settings. In particular, we give polynomial-time recognition algorithms for weak orders, which can be viewed as preferences with indifference.
doi:10.1613/jair.1.11577 fatcat:rou3kgcejrb7bccoha6tmtiq2e