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

Sebastian Maier, Petur Zachariasen, Martin Zachariasen

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)373-387
Number of pages15
JournalManagement Science
Issue number2
Publication statusPublished - 2010


  • Electoral system
  • divisor-based biproportional apportionment
  • computer simulation


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