Optimal Apportionment

Abstract

This paper provides a theoretical foundation that supports the degressive proportionality principle in apportionment problems, such as the allocation of seats in a federal parliament. The utility assigned by an individual to a constitutional rule is a function of the frequency with which each collective decision matches the individual’s own will. The core of the argument is that, if the function is concave, then classical utilitarianism at the social level recommends decision rules that exhibit degressive proportionality with respect to the population size.