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The Hoede-Bakker index modified to the Shapley-Shubik and Holler-Packel indices

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Agnieszka Rusinowska () (GATE - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines)
Abstract

We present some modifications of the Hoede-Bakker index defined in a social network in which players may influence each other. Due to influences of the other actors, the final decision of a player may be different from his original inclination. The modifications presented in the paper are defined for an arbitrary probability distribution over all inclination vectors. In particular, they concern the situation in which the inclination vectors may be not equally probable. Furthermore, by assuming special probability distributions over all inclination vectors, we construct modifications of the Hoede-Bakker index that coincide with the Shapley- Shubik index and with the Holler-Packel index,respectively. We present a practical example in which the concepts in question are applied to Dutch parties, and a theoretical example in which we show how the modifications can be calculated.

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Paper provided by HAL in its series Post-Print with number halshs-00406430_v1.

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Date of creation: 2009
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Publication status: Published, Group Decision and Negotiation, 2009, forthcoming
Handle: RePEc:hal:journl:halshs-00406430_v1

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Keywords: Hoede-Bakker index; inclination vector; probability distribution; Shapley-Shubik index; Holler- Packel index;

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  1. Garrett, Geoffrey & Tsebelis, George, 1996. "An institutional critique of intergovernmentalism," International Organization, Cambridge University Press, vol. 50(02), pages 269-299, March. [Downloadable!]
  2. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer, vol. 24(1), pages 171-197, January. [Downloadable!] (restricted)
  3. Tsebelis, George & Garrett, Geoffrey, 1996. "Agenda setting power, power indices, and decision making in the European Union," International Review of Law and Economics, Elsevier, vol. 16(3), pages 345-361, September. [Downloadable!] (restricted)
  4. Mika Widgrén & Stefan Napel, 2002. "The Power of a Spatially Inferior Player," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 327-343.
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  5. Mika Widgrén & Stefan Napel, 2001. "Inferior players in simple games," International Journal of Game Theory, Springer, vol. 30(2), pages 209-220. [Downloadable!] (restricted)
  6. Harrie De Swart & Agnieszka Rusinowska, 2007. "On some properties of the Hoede-Bakker index," Post-Print halshs-00201414_v1, HAL. [Downloadable!]
  7. Garrett, Geoffrey & Tsebelis, George, 1996. "An Institutional Critique of Intergovernmentalism," International Organization, MIT Press, vol. 50(2), pages 269-99, Spring.
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