Alternative forms of the Shapley value and the Shapley-Shubik index

✍ Scribed by Dan S. Felsenthal; Moshé Machover

• Publisher: Springer US
• Year: 1996
• Tongue: English
• Weight: 217 KB
• Volume: 87
• Category: Article
• ISSN: 0048-5829
• DOI: 10.1007/bf00118651

✦ Synopsis

We prove the validity of an alternative representation of the Shapley-Shubik (1954) index of voting power, based on the following model. Voting in an assembly consisting of n voters is conducted by roll-call. Every voter is assumed to vote "yea" or "nay" with equal probability, and all n! possible orders in which the voters may be called are also assumed to be equiprobable. Thus there are altogether 2 '~ n! distinct roll-call patterns. Given a simple voting * The authors wish to thank Robert Aumann, Ken Binmore, Emmanuel Farjoun and Amnon Rapoport for their helpful comments.