現在、衆議院議員の議員定数465名のうち、289名が小選挙区制で選出されている。これら289議席は、茨城県に7議席、北海道に12議席、東京に30議席といった具合に、人口に応じて各都道府県に配分されている。既存研究では、一票の重みの格差の是正を主な目的として、各都道府県での選挙区割の改善案が示されてきた。本研究では、行政圏と生活圏の不調和と少子高齢化に伴うシルバー民主主義の問題に焦点を当て、これらの解決に向けた選挙区割の数理最適化モデルを開発し、その有用性を実データに基づく数値実験によって示す。

"One Person, One Vote: One Vote, One Value" is one of the fundamental principles of representative democracy. In order to measure the extent to which this principle is attained, two indexes are mainly employed. Mass media and judiciaries use the ratio of the largest to the smallest districts and academic researchers utilize Samuels and Snyder's (2001) MAL, the sum of the absolute difference between the seat share and the population share in each district. However, these indexes have several limitations. Therefore, we cannot accurately and precisely capture the historical transition of malapportionment in Japan. In this study, we employ a new index based on a-divergence, introduced to this field by Wada and Kamahara (2016) . This index has two valuable properties. First, by changing the parameter a, we obtain several variants of the index that conform with philosophies of seat distribution. Second, the index decomposes the overall degree of malapportionment into two factors of malapportionment: apportionment and districting. This study aims to comprehensively show the historical transition of malapportionment in Japan's House of Representatives by using this index.

　Although existing studies often find a distributive bias for overrepresented areas, they fail to explain when such a bias becomes salient. The bottleneck is partially the result of their assumption that targeting overrepresented areas is a cost-efficient strategy. However, this is not always the case, because voters in such areas do not necessarily respond to money. This study argues that risk-averse parties invest in overrepresented areas only when they can avoid the risk of freeriding by opposition supporters. Specifically, hegemonic parties are supposedly risk-averse, because their survival depends on the credibility in rewarding supporters and punishing opponents. Through a systematic analysis of the Malaysian ruling party (BN), this study demonstrates that the BN targets overrepresented areas only with a risk-immune item. This holds true even after controlling the latent endogeneity of malapportionment.

一票の最大格差を最小とする最適区割やその列挙によって，多くの選挙区割候補を提示することができるようになったが，どの区割が良い区割であるのかを明示する指標が格差以外になく，選択が困難であった．また，最高裁は，