We consider binary voting systems in which a probability distribution
over coalitions is known. In this broader context decisiveness is
an extension of the Penrose-Banzhaf index and success an extension of the Rae index for simple games. Although decisiveness and success are conceptually different we analyze their numerical behavior. The main result provides necessary and sufficient conditions for the ordinal equivalence of them. Indeed, under anonymous probability distributions they become ordinally equivalent. Moreover, it is proved that for these distributions, decisiveness and success respect the strength of the seats, whereas luckiness reverses the order.
CitationFreixas, J.; Pons, M. Similarities and differences between success and decisiveness. A: Workshop on Cooperative Games in Multiagent Systems. "The Fifth Workshop on Cooperative Games in Multiagent Systems". Paris: AA Publications, 2014, p. 1-15.
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