Abstract
The ordinal equivalence of the Shapley-Shubik and Banzhaf-Coleman power indices in a simple game would be important to many applications, where consideration of “how much” more power one member has than another is irrelevant. The reason is that if the ordinal equivalence holds, then another question of which index to use goes out. To the ordinal equivalence problem, this paper gives the following answers. The ordinal equivalence holds true either in the weighted majority games as a subclass of simple games or in the five- or less-member simple games. However, it does not necessarily hold true in the six- or more-member simple games.
