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More Democracy Through Mathematics

For democratic elections to be honest, pick districts should have similar sizes. once populations shift, districts ought to be decentralised – a posh and, in several countries, arguable task once political parties conceive to influence redistricting. Mathematicians at the Technical University of metropolis (TUM) have currently developed a way that permits the economical calculation of optimally sized pick districts.

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When constituents solid their vote for a candidate, they assume it carries a similar weight as that of the others. pick districts ought to so be sized equally in step with population. once populations amendment, boundaries ought to be redrawn.



For example, 34 political districts were redrawn for the upcoming parliamentary election in Germany — a complex task. In other countries, this process often results in major controversy. Political parties often engage in gerrymandering, to create districts with a disproportionately large number of own constituents. In the United States, for example, state governments frequently exert questionable influence when redrawing the boundaries of congressional districts.

“An effective and neutral method for political district zoning, which sounds like an administrative problem, is actually of great significance from the perspective of democratic theory,” emphasizes Stefan Wurster, Professor of Policy Analysis at the Bavarian School of Public Policy at TUM. “The acceptance of democratic elections is in danger whenever parties or individuals gain an advantage out of the gate. The problem becomes particularly relevant when the allocation of parliamentary seats is determined by the number of direct mandates won. This is the case in majority election systems like in USA, Great Britain and France.”

Test case: German parliamentary election

Prof. Peter Gritzmann, head of the Chair of Applied pure mathematics and separate arithmetic at stomach, together along with his employee Fabian Klemm and his colleague Andreas Brieden, prof of statistics at the University of the German Federal military, has developed a technique that permits the optimum distribution of electoral district boundaries to be calculated in associate degree economical and, of course, politically neutral manner.

The mathematicians tested their methodology mistreatment electoral districts of the German parliament. in step with the German Federal Electoral Act, the amount of constituents in an exceedingly district mustn't deviate quite fifteen % from the common. In cases wherever the deviation exceeds twenty five %, electoral district borders should be redrawn. during this case, the relevant committee should adhere to varied provisions: for instance, districts should be contiguous and not cross state, county or municipal boundaries. The electoral districts square measure divided into precincts with one spot every.

Better than needed by law

“There square measure a lot of ways in which to consolidate communities to electoral districts than there square measure atoms within the legendary universe,” says Peter Gritzmann. “But, mistreatment our model, we are able to still realize economical solutions during which all districts have roughly equal numbers of constituents – which in an exceedingly ‘minimally invasive’ manner that needs no citizen to modify precincts.”

Deviations of zero.3 to 8.7 % from the common size of electoral districts can't be avoided based mostly only on the various variety of voters in individual states. however the new methodology achieves this optimum. “Our method comes near the theoretical limit in each state, and that we find yourself way below the fifteen % deviation allowed by law,” says Gritzmann.

Deployment attainable in several countries

The researchers used a mathematical model developed within the unit to calculate the electoral districts: “Geometric clustering” teams the communities to clusters, the optimized electoral districts. The target definition for calculations will be randomly changed, creating the methodology applicable to several countries with totally different election laws.

The methodology is additionally applicable to different sorts of problems: for instance, in voluntary lease and utilization exchanges in agriculture, to work out adequate tariff teams for insurers or to model hybrid materials. “However, drawing electoral district boundaries could be a terribly special application, as a result of here arithmetic will facilitate strengthen democracies,” sums up Gritzmann.

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