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Single-peakedness Based on the Net Preference Matrix: Characterization and Algorithms

Abstract : In this paper, we propose a new relaxation of the single-peaked property by constraining the net preference matrix instead of the preference profile. More precisely, this new domain restriction holds for a given profile P if there exists a single-peaked profile P' with the same net preference matrix as P. We provide a characterization of net preference matrices that can be “implemented” by a single-peaked profile, and propose a polynomial time algorithm to recognize these matrices. In cases where preferences are not net single-peaked, we recall a dynamic programming approach for obtaining an axis over candidates such that the net preference matrix respects as much as possible (in some sense) our net single-peakedness condition. We also formulate an integer linear program for partial net single-peakedness. Finally we present the results of numerical tests on real election data.
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https://hal.archives-ouvertes.fr/hal-01518068
Contributor : Olivier Spanjaard <>
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  • HAL Id : hal-01518068, version 1

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Olivier Spanjaard, Paul Weng. Single-peakedness Based on the Net Preference Matrix: Characterization and Algorithms. 6th International Workshop on Computational Social Choice (COMSOC-2016), Jun 2016, Toulouse, France. ⟨hal-01518068⟩

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