Minimal winning coalitions and orders of criticality

Michele Aleandri (), Marco Dall’Aglio (), Vito Fragnelli () and Stefano Moretti ()
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Michele Aleandri: Luiss University
Marco Dall’Aglio: Luiss University
Vito Fragnelli: University of Eastern Piedmont
Stefano Moretti: Université PSL

Annals of Operations Research, 2022, vol. 318, issue 2, No 4, 787-803

Abstract: Abstract In this paper, we analyze the order of criticality in simple games, under the light of minimal winning coalitions. The order of criticality of a player in a simple game is based on the minimal number of other players that have to leave so that the player in question becomes pivotal. We show that this definition can be formulated referring to the cardinality of the minimal blocking coalitions or minimal hitting sets for the family of minimal winning coalitions; moreover, the blocking coalitions are related to the winning coalitions of the dual game. Finally, we propose to rank all the players lexicographically accounting the number of coalitions for which they are critical of each order, and we characterize this ranking using four independent axioms.

Keywords: Order of criticality; Hitting set; Dual game; Axiomatic approach (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-021-04199-6

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