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Generalized Roll-Call Model for the Shapley-Shubik Index

18 Pages Posted: 13 Feb 2016  

Sascha Kurz

University of Bayreuth

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 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.

Keywords: simple games, influence, Shapley-Shubik index, several levels of approval

JEL Classification: C71, D72

Suggested Citation

Kurz, Sascha, Generalized Roll-Call Model for the Shapley-Shubik Index (February 13, 2016). Available at SSRN: or

Sascha Kurz (Contact Author)

University of Bayreuth ( email )

Universit├Ątsstr. 30
Lehrstuhl f├╝r Wirtschaftsmathematik
Bayreuth, Bavaria D-95440
+49 921 55 7353 (Phone)
+49 921 55 7352 (Fax)


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