Multiple vote electoral systems: a remedy for political polarization

We examine the mechanical effect of a multiple vote, proportional representation electoral system on party vote share in n dimensions. In one dimension, Cox (1990) has proven that such a system is centripetal: it drives parties to the center of the political spectrum. However, as populism has swept across Western Europe and the United States, the importance of multiple policy dimensions has grown considerably. We use simulations to examine how a multiple vote system could alter electoral outcomes in all possible parliamentary systems. We find that multiple vote systems act centripetally in multiple dimensions too, though weakly in extreme cases where parties are sorted into ideological clusters at opposite corners of the ideological space. Even in these cases, though, we find that a slight disturbance of the conditions (by introducing an additional party- even if it is very small) strengthens the centripetal properties of the multiple vote system.