Theory and Decision 53 (4):313-325 (2002)

In this paper, we are concerned with the preorderings (SS) and (BC) induced in the set of players of a simple game by the Shapley–Shubik and the Banzhaf–Coleman's indices, respectively. Our main result is a generalization of Tomiyama's 1987 result on ordinal power equivalence in simple games; more precisely, we obtain a characterization of the simple games for which the (SS) and the (BC) preorderings coincide with the desirability preordering (T), a concept introduced by Isbell (1958), and recently reconsidered by Taylor (1995): this happens if and only if the game is swap robust, a concept introduced by Taylor and Zwicker (1993). Since any weighted majority game is swap robust, our result is therefore a generalization of Tomiyama's. Other results obtained in this paper say that the desirability relation keeps itself in all the veto-holder extensions of any simple game, and so does the (SS) preordering in all the veto-holder extensions of any swap robust simple game
Keywords Voting games  Power indices  Desirability relation  Veto-holder extension  Swap robust
Categories (categorize this paper)
DOI 10.1023/A:1024158301610
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 56,999
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Hierarchies Achievable in Simple Games.Josep Freixas & Montserrat Pons - 2010 - Theory and Decision 68 (4):393-404.

Add more citations

Similar books and articles


Added to PP index

Total views
45 ( #223,362 of 2,410,443 )

Recent downloads (6 months)
1 ( #540,320 of 2,410,443 )

How can I increase my downloads?


My notes