Condorcet's Principle and the Preference Reversal Paradox
Copyright policy )Condorcet's Principle and the Preference Reversal Paradox
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 Proceedings TARK 2017, arXiv:1707.08250. 15 pages
- Department of Computer Science University of Oxford United Kingdom
- THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD United Kingdom
- University of Oxford United Kingdom
FOS: Computer and information sciences, Computer Science - Computer Science and Game Theory, Electronic computers. Computer science, QA1-939, QA75.5-76.95, Mathematics, Computer Science and Game Theory (cs.GT)
FOS: Computer and information sciences, Computer Science - Computer Science and Game Theory, Electronic computers. Computer science, QA1-939, QA75.5-76.95, Mathematics, Computer Science and Game Theory (cs.GT)
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