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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Alonso-Meijide, J.M., Bowles, C., Holler, M.J. et al. Monotonicity of power in games with a priori unions. Theory Decis 66, 17–37 (2009). https://doi.org/10.1007/s11238-008-9114-2
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DOI: https://doi.org/10.1007/s11238-008-9114-2