Voting power in an ideological spectrum. The Markov-Pólya index (Q1590147)

The author considers a weighted majority game with \(n\) players. He supposes that only certain coalitions in such a game can be formed, due to ideological constraints. In particular, it is supposed that the players are arrayed on a line, and only convex sets of players can be formed. The paper develops an extended Shapley-Shubik index for such a game, which it calls the Markov-Polya index, since the probabilities of pivoting turn out to be given by the Markov-Polya distribution. This result nicely extends that of \textit{P. H. Edelman} [ibid. 34, 37-50 (1997; Zbl 0917.90078)].