Article ID: | iaor20101124 |
Volume: | 56 |
Issue: | 2 |
Start Page Number: | 373 |
End Page Number: | 387 |
Publication Date: | Feb 2010 |
Journal: | Management Science |
Authors: | Zachariasen Martin, Maier Sebastian, Zachariassen Petur |
Keywords: | voting systems |
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 row- and column-sum requirements are fulfilled. In a divisor-based method for biproportional apportionment, the problem is solved by computing appropriate row and column divisors, and by rounding the quotients. We present a comprehensive experimental evaluation of divisor-based biproportional apportionment in an electoral system context. By performing experiments on real-life benchmark instances (election data with multimember districts), we evaluate the general quality of divisor-based apportionments with respect to, e.g., deviation from quota, reversal orderings, and occurrences of ties. For example, we studied the frequency in which a party with a higher vote count in a district ended up with fewer seats in that district.