The shield that never was: societies with single-peaked preferences are more open to manipulation and control

Authors:
Piotr Faliszewski;Edith Hemaspaandra;Lane A. Hemaspaandra;Jörg Rothe
Affiliations:
AGH Univ. of Sci. & Techn., Krakóów, Poland;Rochester Inst. of Technology, Rochester, NY;University of Rochester, Rochester, NY;Universität Düsseldorf, Düsseldorf, Germany
Venue:
Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge
Year:
2009

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Abstract

Much work has been devoted, during the past twenty years, to using complexity to protect elections from manipulation and control. Many results have been obtained showing NP-hardness shields, and recently there has been much focus on whether such worst-case hardness protections can be bypassed by frequently correct heuristics or by approximations. This paper takes a very different approach: We argue that when electorates follow the canonical political science model of societal preferences the complexity shield never existed in the first place. In particular, we show that for electorates having single-peaked preferences, many existing NP-hardness results on manipulation and control evaporate.