Yes-No look at the Shapley-Shubik index: Two new power indices from the Felsenthal and Machover bargaining model

Une analyse de l’indice de Shapley-Shubik lors des appels nominaux: Deux nouveaux indices de pouvoir issus du modèle de négociation de Felsenthal et Machover

Nicolas Andjiga, Hélène Ferrer (), Issofa Moyouwou and Fabrice Valognes ()
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Nicolas Andjiga: University of Yaoundé 1 = Université de Yaoundé I
Hélène Ferrer: CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique
Issofa Moyouwou: University of Yaoundé 1 = Université de Yaoundé I
Fabrice Valognes: CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique

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Abstract: A comprehensive analysis of the Shapley-Shubik[13] index of voting power is provided through a detailed investigation of voters' pivotality in all possible rollcalls, as described in Felsenthal and Machover [4]. In a simple voting game, a pivotal voter in a roll-call is the one whose vote completely determines the final outcome, regardless of the votes of their successors. The present paper sheds new light on the Shapley-Shubik index of voting power by distinguishing between positive pivotality (for adoption) and negative pivotality (for rejection) which considerably strengthens their original result. This distinction has been first proposed by Hu [6] for the Shapley-Shubik power index and the Banzhaf index [1] to the case of "blocking". We go deeper into the analysis and show that the Shapley-Shubik index is a convex combination of two new indices we provide namely the positive pivotality index and the negative pivotality index. Finally, we present an axiomatic characterization for each of these two new indices by using two weighted versions of the classical transfer axiom developed by Dubey [3].

Keywords: Simple games; Shapley-Shubik index; roll call model; voting power; bargaining procedures; Jeux simples; indice de Shapley-Shubik; modèle d’appel nominal; pouvoir de vote; modèle de négociation (search for similar items in EconPapers)
Date: 2025
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-04948243v1
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Published in Revue d'économie politique, 2025, 2025 (1), pp.55-73. ⟨10.3917/redp.351.0055⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-04948243

DOI: 10.3917/redp.351.0055

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