Recognizing majority-rule equilibrium in spatial voting games

Abstract

It is provably dicult (NP-complete) to determine whether a given point can be defeated in a majority-rule spatial voting game. Nevertheless, one can easily generate a point with the property that if any point cannot be defeated, then this point cannot be defeated. Our results suggest that majority-rule equilibrium can exist as a purely practical matter: when the number of voters and the dimension of the policy space are both large, it can be too dicult to find an alternative to defeat the status quo. It is also computationally dicult to determine the radius of the yolk or the Nakamura number of a weighted voting game.