13 January 2015, Computational Social Choice Seminar, Svetlana Obraztsova
The game-theoretic model for Plurality voting is among the most widely-used voting rules. Yet, its rigorous studies have shown it to be riddled by the common malady of many standard game-theoretic approaches. Specifically, a multitude of Nash equilibria, many of which are counter-intuitive and unlikely to appear in reality. Luckily, a remedy was recently introduced to limit the set of possible equilibria -- voting bias.
In this talk we will concentrate on two such biases. The "truth bias", wherein voters are incentivised to be truthful when their vote is not pivotal; and the "lazy bias", wherein voters are incentivised to abstain from the voting process all together, if their vote is not pivotal. These biases have been shown to be very 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 these biased voting models under Plurality. For pure Nash equilibria we provide (partial) characterizations based on understanding some crucial properties about the structure of equilibrium profiles. These properties demonstrate how the model leads to filtering out of undesirable equilibria. We also investigate the complexity of determining the existence of an equilibrium with a certain winning candidate, and compare different biases in that respect. Finally, we will touch upon the possibility of introducing bias into games with strategic candidates, rather than voters.