Plurality Voting with Truth-Biased Agents

Abstract

We study a game-theoretic model for Plurality, one of the most well-studied and widely-used voting rules. It is well known that the most standard game-theoretic approaches can be problematic in the sense that they lead to a multitude of Nash equilibria, many of which are counter-intuitive. Instead, we focus on a model recently proposed to avoid such issues [2,6,11]. The main idea of the model is that voters have incentives to be truthful when their vote is not pivotal, i.e., when they cannot change the outcome by a unilateral deviation. This modification is quite powerful and recent simulations reveal that equilibria which survive this refinement tend to have nice properties.

We undertake a theoretical study of pure Nash and strong Nash equilibria of this model under Plurality. For pure Nash equilibria we provide characterizations based on understanding some crucial properties about the structure of equilibrium profiles. These properties demonstrate how the model leads to filtering out undesirable equilibria. We also prove that deciding the existence of an equilibrium with a certain candidate as a winner is NP-hard. We then move on to strong Nash equilibria, where we obtain analogous characterizations. Finally, we also observe some relations between strong Nash equilibria and Condorcet winners, which demonstrate that this notion forms an even better refinement of stable profiles.

Work supported by the project ALGONOW of the research funding program Thales (co-financed by the European Social Fund-ESF and Greek national funds), and also by a grant of the Russian government (FCP).