人口に比例して議員定数を配分することは一見簡単な問題と思えるが,実は意外と難しい.この問題はアメリカ合衆国憲法に記載されているが,200年以上にわたり議論が続いており,解くことのできない問題ともいわれている.しかしながら,現時点では,この問題はヒル方式かウェブスター方式で解かれると考えられている.両方式間の最大の争点は,大州と小州間の配分議席数による偏りである.どちらの配分方式がより小さな偏りを与えるのか.本論文では,従来の考え方の矛盾点を明らかにし,新しい考え方により,ヒル方式だけでなくウェブスター方式も絶対的に小州に有利なこと,さらに,従来の定説どおり,ヒル方式がウェブスター方式より相対的に小州に有利なことを示し,ウェブスター方式の優位性を与えた.The problem of assigning seats in the U.S. House of Representatives based proportionally on the population of states is seemingly simple but to solve it is not. The U.S. Constitution poses this apportionment problem and the issues of which is the best method have been debated for more than 200 years. In fact, it might be considered to be unsolvable. However, at least at this moment, only one of Hill's and Webster's methods is believed to solve the apportionment problem. First it is shown that both methods favor the small states in our model, which appears to disagree with an established opinion. Since Hill's method favors the small states more than Webster's also in our model, the author's conclusion is that Webster's method is the best, which is outwardly the same as Balinski and Young's assertion.