A Characterization of the Totally Critical Raw Banzhaf Power Index on Dichotomous Voting Games with Several Levels of Approval in Input

Bertrand Mbama Engoulou (), Pierre Wambo and Lawrence Diffo Lambo
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Bertrand Mbama Engoulou: The University of Douala
Pierre Wambo: Ecole Normale Superieure
Lawrence Diffo Lambo: Ecole Normale Superieure

Group Decision and Negotiation, 2023, vol. 32, issue 4, No 5, 888 pages

Abstract: Abstract In this paper, we propose an axiomatization of the totally critical raw Banzhaf index (TCRBI). In the literature, the TCRBI was introduced as a generalization of the Banzhaf power index on the class of yes–no voting games with several ordered levels of approval in input ((j, 2)-simple games). Its principal strength, compared to earlier generalizations of the Banzhaf power index, is the fact that it preserves the desirability relation regardless of the number of input levels of approval. Our main result is that, up to a multiplicative positive real number, the TCRBI is the only power index on the class of (j, 2)-simple games, satisfying the following set of axioms : Equal treatment, Positivity, Null Player, and Linear Transfer.

Keywords: Game theory; (j; k)-simple games; Banzhaf power index; Desirability relation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10726-023-09831-3

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