Power indices in simple games measure the relevance of a player through her ability in being critical, i.e. essential for a coalition to win. We introduce new indices that measure the power of a player in being decisive through the collaboration of other players. We study the behavior of these criticality indices to compare the power of different players within a single voting situation, and that of the same player with varying weight across different voting situations. In both cases we establish monotonicity results in line with those of Turnovec [1998]. Finally, we examine which properties characterizing the indices of Shapley–Shubik and Banzhaf are shared by these new indices.

Indices of Criticality in Simple Games / Dall'Aglio, Marco; Fragnelli, Vito; Moretti, Stefano. - (2019), pp. 583-603. [10.1142/9789811202018_0028]

Indices of Criticality in Simple Games

Marco Dall'Aglio
;
2019

Abstract

Power indices in simple games measure the relevance of a player through her ability in being critical, i.e. essential for a coalition to win. We introduce new indices that measure the power of a player in being decisive through the collaboration of other players. We study the behavior of these criticality indices to compare the power of different players within a single voting situation, and that of the same player with varying weight across different voting situations. In both cases we establish monotonicity results in line with those of Turnovec [1998]. Finally, we examine which properties characterizing the indices of Shapley–Shubik and Banzhaf are shared by these new indices.
978-981-120-201-8
978-981-120-200-1
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/191088
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