Optimal Combined Districts in the House of Councilors

Abstract

Using the optimization model developed and used by Hotta (2015) to produce combined multi-member districts for prefectural assemblies, we identified optimal combined districts for the House of Councilors and evaluated the effects of the combined districts. For the object function of the optimization model, we used the maximum ratio of population per representative and α-divergence, which is an index used to measure the quasi-distance between one distribution and another; it is employed as an evaluation index founded on individual reductionism by Wada (2012, 2016). We loosened the limit of the number of combined districts and revealed the maximum ratio of the population per representative and distribution of the districts, which allowed us to verify possible combined districts. If we allow three combined districts, the maximum ratio is less than three, and if we allow eight combined districts, the maximum ratio is less than two.