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 0whose 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.
['Sascha Kurz']
Generalized roll-call model for the Shapley-Shubik index