Apportionment in Theory and Practice
Mark Beumer

Abstract:
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.