Publication detail

Apportionment in Proportional Electoral Systems Based on Integer Programming

Author(s): Pavel Doležel ,
Type: Submissions
Year: 2011
Number: 0
Published in: European Journal of Operational Research
Publishing place:
Keywords: Integer Programming, Uni-proportional, Bi-proportional, Apportionment, Electoral system, Constituency
JEL codes: D71, D72
Suggested Citation:
Grants: GACR 402/09/1066: Political Economy of Voting Behavior: Rational Voter Theory and Models of Strategic Voting
Abstract: In this work we introduce two apportionment methods for proportional electoral systems with constituencies based on integer programming. The reason for their introduction we see in the fact, that the commonly used apportionment methods often lead to substantial deviations from perfect proportionality, beyond the scope given by the elections threshold. There are generally three different sources of disproportionality-rounding, division of elections into constituencies and application of elections threshold. Our apportionment methods are designed so as to minimize the first two sources while keeping a positive elections threshold which prevents excessive fragmentation of the representation and hence avoids low efficiency. Each of the two introduced methods corresponds to one of two disproportionality measures. The first is based on Gallagher index and the second on Loosemore-Hanby index. We prove that our methods always find an optimal solution to uni-proportional allocation of seats to political parties, or to constituencies and that they also find an optimal solution to bi-proportional allocation of seats to political parties and constituencies jointly, when the marginal totals are given by the two uni-proportional allocations.


Česká Spořitelna


Patria Finance