A computational approach to unbiased districting

Authors:
Clemens Puppe;Attila TasnáDi
Affiliations:
Department of Economics, University of Karlsruhe, D-76128 Karlsruhe, Germany;Department of Mathematics, Corvinus University of Budapest, H-1093 Budapest, Fvám tér 8, Hungary
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

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Abstract

In the context of discrete districting problems with geographical constraints, we demonstrate that determining an (ex post) unbiased districting, which requires that the number of representatives of a party should be proportional to its share of votes, turns out to be a computationally intractable (NP-complete) problem. This raises doubts as to whether an independent jury will be able to come up with a ''fair'' redistricting plan in case of a large population; that is, there is no guarantee for finding an unbiased districting (even if such exists). We also show that, in the absence of geographical constraints, an unbiased districting can be implemented by a simple alternating-move game among the two parties.