Beyond the Turnout Paradox by Luis Fernando Medina Sierra

Author:Luis Fernando Medina Sierra
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

2.4 Characterizing the Equilibria of Voting Games

The time has come to put together the ideas of the preceding analysis into a model that we can use to develop comparative statics results on aggregate turnout. To that end I will consider a highly general model of voting and will later introduce constraints that will make it easy to analyze.

The most important sense in which the model in this section generalizes the ones above is in its equilibrium concept. While up to this point I have described the Nash equilibria of voting games, now I will extend the analysis to cover correlated equilibria as well. The reason for this has nothing to do with the description of the equilibria themselves. None of the results in this section will overturn what we have already learned because every Nash equilibrium is also a correlated equilibrium. But for reasons that will become clear soon, especially in the next chapter, we will need to take our analysis beyond the equilibria themselves and consider the properties of their stability sets. When it comes to that, in games with arbitrarily large numbers of players the correlated equilibria generate results that are more useful than the ones that can be obtained by focusing only on the Nash equilibria. In due course I will elaborate this point.

Momentarily let’s return to the case considered in the previous chapter (Sect. 1.​2). A correlated equilibrium is a probabilistic measure μ defined over the game’s strategy space such that no player benefits from a unilateral deviation. So, μ is a correlated equilibrium if:

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