When will party whips succeed? Evidence from almost symmetric voting games

Abstract

The true preferences of some members of parliament sometimes imply voting against the party line, but these members fear sanctions. In the mostly unique pure strategy equilibrium of such a voting game, voters always follow the party line, even if their true preferences are strong and (opportunity) costs from sanctions are arbitrarily small. I qualify this disturbing result by applying the equilibrium selection theory of Harsanyi and Selten (1988). Pure strategy equilibria are selected only for large deviation costs. Otherwise, mixed strategy equilibria are selected which support majorities in true preferences (true majorities), for negligible costs almost with certainty.