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

Sebastian Maier (), Petur Zachariassen () and Martin Zachariasen ()
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Sebastian Maier: Institute of Mathematics, University of Augsburg, D-86135 Augsburg, Germany
Petur Zachariassen: University of the Faroe Islands, FO-100 Tórshavn, Faroe Islands
Martin Zachariasen: Department of Computer Science, University of Copenhagen, DK-2100 Copenhagen, Denmark

Management Science, 2010, vol. 56, issue 2, 373-387

Abstract: 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.

Keywords: electoral systems; divisor-based biproportional apportionment; computer simulation (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (10)

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