Strategic Voting and the Logic of Knowledge

We propose a general framework for strategic voting when a voter may lack knowledge about other votes or about other voters' knowledge about her own vote. In this setting we define notions of manipulation and equilibrium. We also model action changing knowledge about votes, such as a voter revealing its preference or as a central authority performing a voting poll. Some forms of manipulation are preserved under such updates and others not. Another form of knowledge dynamics is the effect of a voter declaring its vote. We envisage Stackelberg games for uncertain profiles. The purpose of this investigation is to provide the epistemic background for the analysis and design of voting rules that incorporate uncertainty.