Condorcet's Principle and the Preference Reversal Paradox

Dominik Peters
(University of Oxford)

We prove that every Condorcet-consistent voting rule can be manipulated by a voter who completely reverses their preference ranking, assuming that there are at least 4 alternatives. This corrects an error and improves a result of [Sanver, M. R. and Zwicker, W. S. (2009). One-way monotonicity as a form of strategy-proofness. Int J Game Theory 38(4), 553-574.] For the case of precisely 4 alternatives, we exactly characterise the number of voters for which this impossibility result can be proven. We also show analogues of our result for irresolute voting rules. We then leverage our result to state a strong form of the Gibbard-Satterthwaite Theorem.

In Jérôme Lang: Proceedings Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2017), Liverpool, UK, 24-26 July 2017, Electronic Proceedings in Theoretical Computer Science 251, pp. 455–469.
15 pages.
Published: 25th July 2017.

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