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Shapley-Shubik and Banzhaf Indices Revisited

Departamento de Fundamentos del Análisis Económico, Universidad de Alicante, Campus San Vicente, 03071 Alicante, Spain
Departamento de Economía Aplicada IV, Universidad del País Vasco, Avenida L. Aguirre, 83, 48015 Bilbao, Spain

We provide a new axiomatization of the Shapley-Shubik and the Banzhaf power indices in the domain of simple superadditive games by means of transparent axioms. Only anonymity is shared with the former characterizations in the literature. The rest of the axioms are substituted by more transparent ones in terms of power in collective decision-making procedures. In particular, a clear restatement and a weaker alternative for the transfer axiom are proposed. Only one axiom differentiates the characterization of either index, and these differentiating axioms provide a new point of comparison. In a first step both indices are characterized up to a zero and a unit of scale. Then both indices are singled out by simple normalizing axioms.

Key Words: Power indices; voting power; collective decision-making; simple games; axiomatization
History: Received: November 24, 1999; revision received: May 17, 2000;revision received: August 7, 2000;

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