Abstract
The objective function of the optimization model for the apportionment problem is to minimize the maximum gap in the value of vote. The limit of the disparity ratio can be obtained by the optimal solution of the model. The limit of the maximum vote-value disparity is 1.598 to 1 by allocating 295 seats to 47 prefectures and 4.311 to 1 by 73 to 47. The main cause of the gap for the apportionment problem is to distribute the seats to each prefecture and just the number of the members of each House of the Diet. One way to improve the maximum difference of one vote is to straddling two or more prefectures, and the other is to change the number of the members. The purpose of the study is to clarify the effect of them by analyzing the solution of the optimization model.
