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Success and decisiveness on proper symmetric games

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  • Josep Freixas
  • Montserrat Pons

Abstract

This paper provides a complete study for the possible rankings of success and decisiveness for individuals in symmetric voting systems, assuming anonymous and independent probability distributions. It is proved that for any pair of symmetric voting systems it is always possible to rank success and decisiveness in opposite order whenever the common probability of voting for “acceptance” is big enough. On the contrary, for probability values lower than one-half it is not possible to reverse the ranking of these two measures. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Josep Freixas & Montserrat Pons, 2015. "Success and decisiveness on proper symmetric games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 779-794, December.
    • Handle: RePEc:spr:cejnor:v:23:y:2015:i:4:p:779-794
    DOI: 10.1007/s10100-013-0332-5
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    1. 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.
    2. Josep Freixas, 2010. "On ordinal equivalence of the Shapley and Banzhaf values for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 513-527, October.
    3. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, September.
    4. Federico Valenciano & Annick Laruelle & Ricardo Martínez, 2004. "Success Versus Decisiveness: Conceptual Discussion And Case Study," Working Papers. Serie AD 2004-30, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    5. František Turnovec & Jacek W. Mercik & Mariusz Mazurkiewicz, 2008. "Power Indices Methodology: Decisiveness, Pivots, and Swings," Springer Books, in: Matthew Braham & Frank Steffen (ed.), Power, Freedom, and Voting, chapter 2, pages 23-37, Springer.
    6. Freixas, Josep & Marciniak, Dorota & Pons, Montserrat, 2012. "On the ordinal equivalence of the Johnston, Banzhaf and Shapley power indices," European Journal of Operational Research, Elsevier, vol. 216(2), pages 367-375.
    7. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    8. Carreras, Francesc & Freixas, Josep, 2008. "On ordinal equivalence of power measures given by regular semivalues," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 221-234, March.
    9. 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.
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    1. Josep Freixas & Montserrat Pons, 2017. "Using the Multilinear Extension to Study Some Probabilistic Power Indices," Group Decision and Negotiation, Springer, vol. 26(3), pages 437-452, May.
    2. Ibarzabal, Nora & Laruelle, Annick, 2018. "Ghost seats in parliaments," European Journal of Operational Research, Elsevier, vol. 264(1), pages 354-363.
    3. Josefa Mula & Marija Bogataj, 2021. "OR in the industrial engineering of Industry 4.0: experiences from the Iberian Peninsula mirrored in CJOR," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(4), pages 1163-1184, December.

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