Voting power in an ideological spectrum: The Markov-Pólya index

Power distributions of voting games in which only certain coalitions are allowed, due to the fact that the players are spread across an ideological spectrum, are considered. The paper extends Edelman’s model [Edelman, P., 1997. A note on voting. Math. Soc. Sci. 34, 37–50] concerning ́ allowable coalitions. The Markov-Polya index is introduced as a parametrized family of power indices which has Edelman’s extension of the Shapley-Shubik index as a special case. Unlike the extended Shapley-Shubik index, it puts different weights on the allowable coalitions. For particular parameter values, simple explicit power formulas are derived.  2000 Elsevier Science B.V. All rights reserved. ́