Abstract
Since 1994 the House of Representatives election in Japan has included 300 single-member districts. In view of the principle of “one man, one vote” it is ideal that the population disparity ratio between districts be as close to 1 to 1 as possible, and it is desirable that the ratio be less than 1 to 2. However, the current ratio remains 1 to 2.064 in spite of redistricting in 2002. Nemoto and Hotta (2005a) made a numerical study of the cause of this large population disparity, and showed the main factor is not apportionment method or redistricting. In this paper, we explore another factor by using the mathematical optimization technique. If we change the number of single-member districts to between 280 and 320, the limit of reduction in the disparity ratio is 1 to 1.977. Furthermore, even if the apportionment method is revised, it is 1 to 1.747. These results mean that the difference in the weight of one vote in Japan cannot be improved significantly, even if the apportionment method and number of single-member districts are modified simultaneously.
