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The Hoede–Bakker Index Modified to the Shapley–Shubik and Holler–Packel Indices

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  • Agnieszka Rusinowska

    (GATE, CNRS, Université Lumière Lyon 2)

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.

Suggested Citation

  • Agnieszka Rusinowska, 2010. "The Hoede–Bakker Index Modified to the Shapley–Shubik and Holler–Packel Indices," Group Decision and Negotiation, Springer, vol. 19(6), pages 543-569, November.
  • Handle: RePEc:spr:grdene:v:19:y:2010:i:6:d:10.1007_s10726-009-9157-y
    DOI: 10.1007/s10726-009-9157-y
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    1. Garrett, Geoffrey & Tsebelis, George, 1996. "An institutional critique of intergovernmentalism," International Organization, Cambridge University Press, vol. 50(2), pages 269-299, April.
    2. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 171-197, January.
    3. Mika Widgrén & Stefan Napel, 2001. "Inferior players in simple games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 209-220.
    4. 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.
    5. Mika WidgrÚn & Stefan Napel, 2002. "The Power of a Spatially Inferior Player," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 327-343.
    6. Matthew Braham & Manfred J. Holler, 2005. "The Impossibility of a Preference-Based Power Index," Journal of Theoretical Politics, , vol. 17(1), pages 137-157, January.
    7. Stefan Napel & Mika Widgren, 2004. "Power Measurement as Sensitivity Analysis," Journal of Theoretical Politics, , vol. 16(4), pages 517-538, October.
    8. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    9. Stefan Napel & Mika Widgrén, 2005. "The Possibility of a Preference-Based Power Index," Journal of Theoretical Politics, , vol. 17(3), pages 377-387, July.
    10. Geoffrey Garrett & George Tsebelis, 2001. "Even More Reasons to Resist the Temptation of Power Indices in the EU," Journal of Theoretical Politics, , vol. 13(1), pages 99-105, January.
    11. Bernard Steunenberg & Dieter Schmidtchen & Christian Koboldt, 1999. "Strategic Power in the European Union," Journal of Theoretical Politics, , vol. 11(3), pages 339-366, July.
    12. Garrett, Geoffrey & Tsebelis, George, 1996. "An institutional critique of intergovernmentalism: erratum," International Organization, Cambridge University Press, vol. 50(3), pages 539-539, July.
    13. Geoffrey Garrett & George Tsebelis, 1999. "More Reasons to Resist the Temptation of Power Indices in the European Union," Journal of Theoretical Politics, , vol. 11(3), pages 331-338, July.
    14. Rae, Douglas W., 1969. "Decision-Rules and Individual Values in Constitutional Choice," American Political Science Review, Cambridge University Press, vol. 63(1), pages 40-56, March.
    15. Geoffrey Garrett & George Tsebelis, 1999. "Why Resist the Temptation to Apply Power Indices to the European Union?," Journal of Theoretical Politics, , vol. 11(3), pages 291-308, July.
    16. Harrie de Swart & Agnieszka Rusinowska, 2007. "On some properties of the Hoede-Bakker index," Post-Print halshs-00201414, HAL.
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