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Probabilistic spatial power indexes

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  • Stefano Benati
  • Giuseppe Vittucci Marzetti

Abstract

In this study, we present a generalization of spatial power indexes able to overcome their main limitations, namely (i) the excessive concentration of power measures; (ii) the too high sensitivity to players’ location in the ideological space. Voters’ propensity to support an issue is modeled via a random utility function with two additive terms: the deterministic term accounts for voters’ preference-driven/predictable behavior; the random one is a catch-all term that accounts for all the idiosyncratic/unpredictable factors. The relative strength of the two terms gives rise to a continuum of cases ranging from the Shapley value, where all aggregation patterns are equally probable, to a standard spatial value, like the Owen–Shapley index, where instead the conditional order is fully deterministic. As an illustrative application, we analyze the distribution of power in the Council of Ministers under three different scenarios: (i) EU15 Pre-Nice; (ii) EU27 Nice Treaty; (iii) EU27 Lisbon Treaty. Copyright Springer-Verlag 2013

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  • Stefano Benati & Giuseppe Vittucci Marzetti, 2013. "Probabilistic spatial power indexes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 391-410, February.
    • Handle: RePEc:spr:sochwe:v:40:y:2013:i:2:p:391-410
    DOI: 10.1007/s00355-011-0608-4
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    Cited by:

    1. Di Giannatale, Paolo & Passarelli, Francesco, 2013. "Voting chances instead of voting weights," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 164-173.
    2. Tom Blockmans & Marie-Anne Guerry, 2015. "Probabilistic Spatial Power Indexes: The Impact of Issue Saliences and Distance Selection," Group Decision and Negotiation, Springer, vol. 24(4), pages 675-697, July.
    3. Martin, Mathieu & Nganmeni, Zephirin & Tchantcho, Bertrand, 2017. "The Owen and Shapley spatial power indices: A comparison and a generalization," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 10-19.
    4. Arnold Cédrick SOH VOUTSA, 2020. "Deegan-Packel & Johnston spatial power indices and characterizations," THEMA Working Papers 2020-16, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    5. Stefano Benati & Giuseppe Vittucci Marzetti, 2021. "Voting power on a graph connected political space with an application to decision-making in the Council of the European Union," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 733-761, November.
    6. Hans Peters & José M. Zarzuelo, 2017. "An axiomatic characterization of the Owen–Shapley spatial power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 525-545, May.
    7. Arnold Cédrick SOH VOUTSA, 2021. "The Public Good spatial power index in political games," THEMA Working Papers 2021-01, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    8. Diego Varela & Javier Prado-Dominguez, 2012. "Negotiating the Lisbon Treaty: Redistribution, Efficiency and Power Indices," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 6(2), pages 107-124, July.
    9. Philip D. Grech, 2021. "Power in the Council of the EU: organizing theory, a new index, and Brexit," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 223-258, February.
    10. Qianqian Kong & Hans Peters, 2021. "An issue based power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 23-38, March.
    11. Albizuri, M.J. & Goikoetxea, A., 2022. "Probabilistic Owen-Shapley spatial power indices," Games and Economic Behavior, Elsevier, vol. 136(C), pages 524-541.
    12. Benati, Stefano & Rizzi, Romeo & Tovey, Craig, 2015. "The complexity of power indexes with graph restricted coalitions," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 53-63.
    13. M. J. Albizuri & A. Goikoetxea, 2021. "The Owen–Shapley Spatial Power Index in Three-Dimensional Space," Group Decision and Negotiation, Springer, vol. 30(5), pages 1027-1055, October.

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