The Banzhaf power index for ternary bicooperative games

Authors:
J. M. Bilbao;J. R. Fernández;N. Jiménez;J. J. López
Affiliations:
Applied Mathematics II, University of Seville, Spain;Applied Mathematics II, University of Seville, Spain;Applied Mathematics II, University of Seville, Spain;Applied Mathematics II, University of Seville, Spain
Venue:
Discrete Applied Mathematics
Year:
2010

Citing 4
Cited 0

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Abstract

In this paper we analyze ternary bicooperative games, which are a refinement of the concept of a ternary voting game introduced by Felsenthal and Machover. Furthermore, majority voting rules based on the difference of votes are simple bicooperative games. First, we define the concepts of the defender and detractor swings for a player. Next, we introduce the Banzhaf power index and the normalized Banzhaf power index. The main result of the paper is an axiomatization of the Banzhaf power index for the class of ternary bicooperative games. Moreover, we study ternary bicooperative games with two lists of weights and compute the Banzhaf power index using generating functions.