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Minimal-axiom characterizations of the Coleman and Banzhaf indices of voting power

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  • Barua, Rana
  • Chakravarty, Satya R.
  • Sarkar, Palash

Abstract

Coleman [Coleman, J.S., 1971. Control of collectives and the power of a collectivity to act. In: Lieberman, B. (Ed.), Social Choice. Gordon and Breach, New York, pp. 269-298] suggested two indices of voting power, power to prevent an action and power to initiate an action. This paper develops two-axiom (and hence, minimal) characterizations of both the indices. We also show that similar characterizations can be done for other indices.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 58 (2009)
Issue (Month): 3 (November)
Pages: 367-375

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Handle: RePEc:eee:matsoc:v:58:y:2009:i:3:p:367-375

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Web page: http://www.elsevier.com/locate/inca/505565

Related research

Keywords: Voting game Voting power The Coleman indices The Banzhaf index Axioms Characterization;

References

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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. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer, vol. 15(4), pages 567-582.
  3. Leech, Dennis, 2002. " Designing the Voting System for the Council of the European Union," Public Choice, Springer, vol. 113(3-4), pages 437-64, December.
  4. Barua, Rana & Chakravarty, Satya R. & Roy, Sonali & Sarka, Palash, 2007. "A Characterization and Some Properties of the Banzhaf-Coleman-Dubey-Shapley Sensitivity Index," Staff General Research Papers 12807, Iowa State University, Department of Economics.
  5. R J Johnston, 1978. "On the measurement of power: some reactions to Laver," Environment and Planning A, Pion Ltd, London, vol. 10(8), pages 907-914, August.
  6. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
  7. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer, vol. 23(3), pages 261-81.
  8. Gerard van der Laan & René van den Brink, 1998. "Axiomatization of a class of share functions for n-person games," Theory and Decision, Springer, vol. 44(2), pages 117-148, April.
  9. Federico Valenciano & Annick Laruelle, 2002. "Assessment Of Voting Situations: The Probabilistic Foundations," Working Papers. Serie AD 2002-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  10. Andrzej S. Nowak & Tadeusz Radzik, 2000. "note: An alternative characterization of the weighted Banzhaf value," International Journal of Game Theory, Springer, vol. 29(1), pages 127-132.
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