basic problem in voting theory is that all the strategy profiles in which nobody is pivotal are Nash equilibria. We study elections where voters decide simultaneously on several binary issues. We extend the concept of conditional sincerity introduced by Alesina and Rosenthal (Econometrica 64(6):1311–1341, 1996) and propose an intuitive and simple criterion to refine equilibria in which players are not pivotal. This is shown to have a foundation in a refinement of perfection that takes into account the material voting procedure. We prove that in large elections the proposed solution is characterized through a weaker definition of Condorcet winner and always survives sophisticated voting.
A concept of sincerity for combinatorial voting
De Sinopoli, Francesco;Meroni, Claudia
2018-01-01
Abstract
basic problem in voting theory is that all the strategy profiles in which nobody is pivotal are Nash equilibria. We study elections where voters decide simultaneously on several binary issues. We extend the concept of conditional sincerity introduced by Alesina and Rosenthal (Econometrica 64(6):1311–1341, 1996) and propose an intuitive and simple criterion to refine equilibria in which players are not pivotal. This is shown to have a foundation in a refinement of perfection that takes into account the material voting procedure. We prove that in large elections the proposed solution is characterized through a weaker definition of Condorcet winner and always survives sophisticated voting.
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