Monotonicity of power in games with a priori unions |
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| Authors: | J M Alonso-Meijide C Bowles M J Holler S Napel |
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| Institution: | (1) Department of Statistics and Operations Research, University of Santiago de Compostela, Santiago, Spain;(2) Economics Department, European University Institute, Florence, Italy;(3) Department of Economics, University of Hamburg, Hamburg, Germany;(4) Department of Economics, University of Bayreuth, Bayreuth, Germany |
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| Abstract: | Power indices are commonly required to assign at least as much power to a player endowed with some given voting weight as
to any player of the same game with smaller weight. This local monotonicity and a related global property however are frequently
and for good reasons violated when indices take account of a priori unions amongst subsets of players (reflecting, e.g., ideological
proximity). This paper introduces adaptations of the conventional monotonicity notions that are suitable for voting games
with an exogenous coalition structure. A taxonomy of old and new monotonicity concepts is provided, and different coalitional
versions of the Banzhaf and Shapley–Shubik power indices are compared accordingly.
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| Keywords: | Monotonicity Voting power Coalitional values Coalition structures A priori unions |
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