Svante Janson: Probabilistic studies of election methods

I describe a method to study election methods by probabilistic methods. The main idea is to consider the proportions of votes for the different parties as fixed, but let the total number of seats be random and tend to infinity. (This is in contrast to earlier studies, originating with Polya (1918), where the number of seats is fixed and the party sizes are random.)

In particular, I will study the (asymptotic) bias of several common election methods, including the odd-number method used in Sweden and d'Hondt's method; this is the expectation of the difference between the proportion of seats and the proportion of votes for a party.

I will also briefly mention a study (with Svante Linusson) of the Alabama paradox.