Indices of Criticality in Simple Games | Zendy

Marco Dall’Aglio | Zendy; Vito Fragnelli | Zendy; Stefano Moretti | Zendy

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Indices of Criticality in Simple Games

Author(s) -

Marco Dall’Aglio,

Vito Fragnelli,

Stefano Moretti

Publication year - 2019

Publication title -

international game theory review

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.216

H-Index - 23

eISSN - 1793-6675

pISSN - 0219-1989

DOI - 10.1142/s0219198919400036

Subject(s) - simple (philosophy) , measure (data warehouse) , criticality , mathematical economics , voting , relevance (law) , monotonic function , power index , weighted voting , computer science , power (physics) , econometrics , mathematics , data mining , mathematical analysis , philosophy , physics , epistemology , quantum mechanics , politics , nuclear physics , political science , law

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.

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