Indices of criticality in simple games

Marco Dall'Aglio (1) , Vito Fragnelli (2) , Stefano Moretti (3)

1 Department of Economics and Finance
2 University of eastern piedmont of Novara
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

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.

Mots clés: Simple games; power indices; criticality; weighted majority games; monotonicity

Domaines: Informatique [cs]; Mathématiques [math]

Marco Dall'Aglio, Vito Fragnelli, Stefano Moretti. Indices of criticality in simple games. International Game Theory Review, 2019, 21 (1), ⟨10.1142/S0219198919400036⟩. ⟨hal-02302286⟩