Apportionment in Theory and Practice

Apportionment is the problem of translating an election outcome to a number of seats in fixed-size political house. Mathematically, the problem consists of translating a sequence of reals to a sequence of integers, while ensuring that the sum of the sequence sums to a pre-determined number. The problem arises because seats are indivisible, whereas an election outcome generally gives rise to fractional remainders. This thesis approaches the problem of apportionment from both a theoretical and a practical side. The theoretical part discusses all known apportionment methods and the problems these methods encounter; e.g., the Alabama paradox and quota violations. In the second, practical part this thesis investigates the apportionment system in the Netherlands. I answer the question to what extent the Dutch system suffers from the problems encountered with apportionment. This leads to the question whether alternative apportionment methods are more appropriate in the Dutch case.