Generalized Roll-Call Model for the Shapley-Shubik Index
18 Pages Posted: 13 Feb 2016
Date Written: February 13, 2016
In 1996 D. Felsenthal and M. Machover considered the following model. An assembly consisting of n voters exercises roll-call. All n! possible orders in which the voters may be called are assumed to be equiprobable. The votes of each voter are independent with expectation 0
whose vote finally decides the aggregated outcome. It turned out that the probability to be pivotal is equivalent to the Shapley-Shubik index. Here we give an easy combinatorial proof of this coincidence, further weaken the assumptions of the underlying model, and study generalizations to the case of more than two alternatives.
Keywords: simple games, influence, Shapley-Shubik index, several levels of approval
JEL Classification: C71, D72
Suggested Citation: Suggested Citation