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Decisive coalitions and coherence properties

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  • Bossert, Walter
  • Suzumura, Kotaro

Abstract

In a seminal contribution, Hansson has demonstrated that the family of decisive coalitions associated with an Arrovian social welfare function forms an ultrafilter. If the population under consideration is infinite, his result implies the existence of nondictatorial social welfare functions. He goes on to show that if transitivity is weakened to quasi-transitivity as the coherence property imposed on a social relation, the set of decisive coalitions is a filter. We examine the structure of decisive coalitions and analogous concepts with alternative coherence properties, namely, acyclicity and Suzumura consistency, and without assuming that the social relation is complete.

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Bibliographic Info

Paper provided by Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University in its series PIE/CIS Discussion Paper with number 427.

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Length: 21 p.
Date of creation: Mar 2009
Date of revision:
Handle: RePEc:hit:piecis:427

Note: This version: March 12, 2009
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Keywords: Infinite-Population Social Choice; Decisiveness; Suzumura Consistency;

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References

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  1. Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
  2. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-90, November.
  3. BOSSERT, Walter & SUZUMURA, Kotaro, 2008. "Multi-Profile Intergenerational Social Choice," Cahiers de recherche 2008-08, Universite de Montreal, Departement de sciences economiques.
  4. Edward Packel, 1980. "Impossibility results in the axiomatic theory of intertemporal choice," Public Choice, Springer, vol. 35(2), pages 219-227, January.
  5. Samuelson, Paul A, 1977. "Reaffirming the Existence of "Reasonable" Bergson-Samuelson Social Welfare Functions," Economica, London School of Economics and Political Science, vol. 44(173), pages 81-88, February.
  6. Blair, Douglas H & Pollak, Robert A, 1982. "Acyclic Collective Choice Rules," Econometrica, Econometric Society, vol. 50(4), pages 931-43, July.
  7. Kotaro Suzumura, 1999. "Welfare Economics Beyond Welfarist-Consequentialism," Discussion Paper Series a382, Institute of Economic Research, Hitotsubashi University.
  8. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "A Characterization of Consistent Collective Choice Rules," Cahiers de recherche 2006-12, Universite de Montreal, Departement de sciences economiques.
  9. Parks, Robert P, 1976. "An Impossibility Theorem for Fixed Preferences: A Dictatorial Bergson-Samuelson Welfare Function," Review of Economic Studies, Wiley Blackwell, vol. 43(3), pages 447-50, October.
  10. Susumu Cato & Daisuke Hirata, 2010. "Collective choice rules and collective rationality: a unified method of characterizations," Social Choice and Welfare, Springer, vol. 34(4), pages 611-630, April.
  11. Kemp, Murray C & Ng, Yew-Kwang, 1976. "On the Existence of Social Welfare Functions, Social Orderings and Social Decision Functions," Economica, London School of Economics and Political Science, vol. 43(169), pages 59-66, February.
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Cited by:
  1. BOSSERT, Walter & SUZUMURA, Kotaro, 2009. "Quasi-transitive and Suzumura consistent relations," Cahiers de recherche 2009-05, Universite de Montreal, Departement de sciences economiques.
  2. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.
  3. Susumu Cato & Daisuke Hirata, 2010. "Collective choice rules and collective rationality: a unified method of characterizations," Social Choice and Welfare, Springer, vol. 34(4), pages 611-630, April.

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