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Political influence in multi-choice institutions: cyclicity, anonymity, and transitivity

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  • Roland Pongou

    ()

  • Bertrand Tchantcho
  • Lawrence Diffo Lambo

Abstract

We study political influence in institutions where members choose from among several options their levels of support to a collective goal, these individual choices determining the degree to which the goal is reached. Influence is assessed by newly defined binary relations, each of which compares any two individuals on the basis of their relative performance at a corresponding level of participation. For institutions with three levels of support (e.g., voting games in which each voter may vote "yes", "abstain", or vote "no"), we obtain three influence relations, and show that the strict component of each of them may be cyclical. The cyclicity of these relations contrasts with the transitivity of the unique influence relation of binary voting games. Weak conditions of anonymity are sufficient for each of them to be transitive. We also obtain a necessary and sufficient condition for each of them to be complete. Further, we characterize institutions for which the rankings induced by these relations, and the Banzhaf-Coleman and Shapley-Shubik power indices coincide. We argue that the extension of these relations to firms would be useful in efficiently allocating workers to different units of production. Applications to various forms of political and economic organizations are provided.

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File URL: http://hdl.handle.net/10.1007/s11238-010-9211-x
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Bibliographic Info

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 70 (2011)
Issue (Month): 2 (February)
Pages: 157-178

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Handle: RePEc:kap:theord:v:70:y:2011:i:2:p:157-178

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Web page: http://www.springerlink.com/link.asp?id=100341

Related research

Keywords: Level-based influence relations; Global influence relation; Multi-choice institutions; Paradox of power; Cyclicity; Anonymity; Transitivity; C70; D71; D20; F50; L23;

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References

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  1. Jane Friedman & Lynn Mcgrath & Cameron Parker, 2006. "Achievable Hierarchies In Voting Games," Theory and Decision, Springer, vol. 61(4), pages 305-318, December.
  2. Tchantcho, Bertrand & Lambo, Lawrence Diffo & Pongou, Roland & Engoulou, Bertrand Mbama, 2008. "Voters' power in voting games with abstention: Influence relation and ordinal equivalence of power theories," Games and Economic Behavior, Elsevier, vol. 64(1), pages 335-350, September.
  3. 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.
  4. Lawrence Diffo Lambo & Joël Moulen, 2002. "Ordinal equivalence of power notions in voting games," Theory and Decision, Springer, vol. 53(4), pages 313-325, December.
  5. Francesc Carreras & Josep Freixas, 2005. "On power distribution in weighted voting," Social Choice and Welfare, Springer, vol. 24(2), pages 269-282, 04.
  6. Bertrand Tchantcho & Lawrence Diffo Lambo & Roland Pongou & Joël Moulen, 2010. "On the equilibrium of voting games with abstention and several levels of approval," Social Choice and Welfare, Springer, vol. 34(3), pages 379-396, March.
  7. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, vol. 26(3), pages 335-351.
  8. Rubinstein, Ariel, 1980. "Stability of decision systems under majority rule," Journal of Economic Theory, Elsevier, vol. 23(2), pages 150-159, October.
  9. Freixas, Josep & Zwicker, William S., 2009. "Anonymous yes-no voting with abstention and multiple levels of approval," Games and Economic Behavior, Elsevier, vol. 67(2), pages 428-444, November.
  10. Josep Freixas & Montserrat Pons, 2010. "Hierarchies achievable in simple games," Theory and Decision, Springer, vol. 68(4), pages 393-404, April.
  11. Dwight Bean & Jane Friedman & Cameron Parker, 2008. "Simple Majority Achievable Hierarchies," Theory and Decision, Springer, vol. 65(4), pages 285-302, December.
  12. Federico Valenciano & Annick Laruelle, 2000. "- Shapley-Shubik And Banzhaf Indices Revisited," Working Papers. Serie AD 2000-02, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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Citations

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Cited by:
  1. L. Diffo Lambo & B. Tchantcho & J. Moulen, 2012. "Comparing influence theories in voting games under locally generated measures of dissatisfaction," International Journal of Game Theory, Springer, vol. 41(3), pages 719-731, August.
  2. Freixas, Josep & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Achievable hierarchies in voting games with abstention," European Journal of Operational Research, Elsevier, vol. 236(1), pages 254-260.
  3. Freixas, Josep, 2012. "Probabilistic power indices for voting rules with abstention," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 89-99.
  4. Sébastien Courtin & Bertrand Tchantcho, 2013. "A note on the ordinal equivalence of power indices in games with coalition structure," THEMA Working Papers 2013-30, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  5. Guemmegne, Juliette T. & Pongou, Roland, 2014. "A policy-based rationalization of collective rules: Dimensionality, specialized houses, and decentralized authority," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 182-193.
  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. Alaitz Artabe & Annick Laruelle & Federico Valenciano, 2012. "Preferences, actions and voting rules," SERIEs, Spanish Economic Association, vol. 3(1), pages 15-28, March.
  8. Parker, Cameron, 2012. "The influence relation for ternary voting games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 867-881.
  9. Sebastien Courtin & Bertrand Tchantcho, 2013. "A note on the ordinal equivalence of power indices in games with coalition structure," Working Papers hal-00914910, HAL.

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