Divisor-Based Biproportional Apportionment in Electoral Systems: A Real-Life Benchmark Study

Biproportional apportionment methods provide two-way proportionality in electoral systems where the electoral region is subdivided into electoral districts. The problem is to assign integral values to the elements of a matrix that are proportional to a given input matrix, and such that a set of rowand column-sum requirements are fulfilled. In a divisor-based method for biproportional apportionment the problem is solved by computing appropriate rowand column-divisors, and by rounding the quotients. We present a comprehensive experimental evaluation of divisor-based biproportional apportionment in an electoral system context. Firstly, we study the practical performance of a range of algorithms by performing experiments on real-life benchmark instances (election data with multi-member districts). Secondly, we evaluate the general quality of divisor-based apportionments with respect to, e.g., deviation from quota, reversal orderings and occurrences of ties.