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Deegan-Packel & Johnston spatial power indices and characterizations

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  • Arnold Cédrick SOH VOUTSA

    (Université de Cergy-Pontoise, THEMA)

Abstract

In this paper, we propose two spatial power indices in political games, taking into account ideological preferences of players. To do this, we develop an explanatory spatial model linked to the asymmetry Deegan-Pakel index introduced by Rapoport & Golan [Rapoport, A., Golan, E., 1985. Assessment of political power in the israeli knesset. American Political Science Review 79 (3), 673-692], which is the original Deegan-Packel index readjusted for measuring power according to the spatial preferences of players in real political games. In addition to extending such a readjustment for the original John- ston index | transforming it concomitantly into the Johnston spatial power index | this paper presents both the general versions of these two spatial indices, and their axiomatic characterizations through new axioms such as the vetoer property and others mainly in- spired from Lorenzo-Freire et al. [Lorenzo-Freire, S., Alonso-Meijide, J. M., Casas-Mendez, B., Fiestras-Janeiro, M. G., 2007. Characterizations of the Deegan-Packel and johnston power indices. European Journal of Operational Research 177 (1), 431-444].

Suggested Citation

  • 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.
    • Handle: RePEc:ema:worpap:2020-16
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    File URL: http://thema.u-cergy.fr/IMG/pdf/2020-16.pdf
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    References listed on IDEAS

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    1. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Fiestras-Janeiro, M.G., 2007. "Characterizations of the Deegan-Packel and Johnston power indices," European Journal of Operational Research, Elsevier, vol. 177(1), pages 431-444, February.
    2. Owen, G & Shapley, L S, 1989. "Optimal Location of Candidates in Ideological Space," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 339-356.
    3. R J Johnston, 1978. "On the Measurement of Power: Some Reactions to Laver," Environment and Planning A, , vol. 10(8), pages 907-914, August.
    4. Enelow,James M. & Hinich,Melvin J., 1984. "The Spatial Theory of Voting," Cambridge Books, Cambridge University Press, number 9780521275156, January.
    5. 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.
    6. Dominique Lepelley & N. Andjiga & F. Chantreuil, 2003. "La mesure du pouvoir de vote," Post-Print halshs-00069255, HAL.
    7. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    8. Francesco Passarelli & Jason Barr, 2007. "Preferences, the Agenda Setter, and the Distribution of Power in the EU," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 41-60, January.
    9. Rapoport, Amnon & Golan, Esther, 1985. "Assessment of Political Power in the Israeli Knesset," American Political Science Review, Cambridge University Press, vol. 79(3), pages 673-692, September.
    10. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    11. 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.
    12. Shenoy, Prakash P., 1982. "The Banzhaf power index for political games," Mathematical Social Sciences, Elsevier, vol. 2(3), pages 299-315, April.
    13. 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.
    14. 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.
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    More about this item

    Keywords

    Game theory; Spatial voting games; Deegan-Packel spatial power index; Johnston spatial power index; Axiomatic characterizations; Political games.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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