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Alonso-Meijide, José Maria ; Bowles, Carlos ; Holler, Manfred J. ; Napel, Stefan:
Monotonicity of Power in Games with A Priori Unions.
In: Theory and Decision.
Bd. 66
(2009)
Heft 1
.
- S. 17-37.
ISSN 1573-7187
DOI: https://doi.org/10.1007/s11238-008-9114-2
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 mono- tonicity 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.