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A Characterization of Consistent Collective Choice Rules

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  • BOSSERT, Walter
  • SUZUMURA, Kotaro

Abstract

We characterize a class of collective choice rules such that collective preference relations are consistent. Consistency is a weakening of transitivity and a strengthening of acyclicity requiring that there be no cycles with at least one strict preference. The properties used in our characterization are unrestricted domain, strong Pareto, anonymity and neutrality. If there are at most as many individuals as there are alternatives, the axioms provide an alternative characterization of the Pareto rule. If there are more individuals than alternatives, however, further rules become available.

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Bibliographic Info

Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 09-2006.

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Length: 12 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:mtl:montec:09-2006

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Keywords: Collective Choice Rules; Consistency; Pareto Rule;

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References

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  1. BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Consistent Rationalizability," Cahiers de recherche 2002-12, Universite de Montreal, Departement de sciences economiques.
  2. Sen, Amartya K, 1979. "Personal Utilities and Public Judgements: Or What's Wrong with Welfare Economics?," Economic Journal, Royal Economic Society, vol. 89(355), pages 537-58, September.
  3. 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.
  4. Sen, Amartya K, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 381-93, July.
  5. John Weymark, 1984. "Arrow's theorem with social quasi-orderings," Public Choice, Springer, vol. 42(3), pages 235-246, January.
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Cited by:
  1. 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.
  2. BOSSERT, Walter & SUZUMURA, Kotaro, 2009. "Decisive coalitions and coherence properties," Cahiers de recherche 2009-04, Universite de Montreal, Departement de sciences economiques.
  3. BOSSERT, Walter & SUZUMURA, Kotaro, 2009. "Quasi-transitive and Suzumura consistent relations," Cahiers de recherche 2009-05, Universite de Montreal, Departement de sciences economiques.
  4. Asheim, Geir B. & Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2006. "Infinite-horizon choice functions," Memorandum 17/2006, Oslo University, Department of Economics.
  5. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.
  6. Roberto Serrano & Allan M. Feldman, 2007. "Arrow’S Impossibility Theorem: Preference Diversity In A Single-Profile World," Working Papers wp2007_0710, CEMFI.
  7. Susumu Cato, 2013. "Social choice, the strong Pareto principle, and conditional decisiveness," Theory and Decision, Springer, vol. 75(4), pages 563-579, October.
  8. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer, vol. 41(1), pages 169-202, June.
  9. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer, vol. 39(4), pages 869-889, October.
  10. Susumu Cato, 2011. "Pareto principles, positive responsiveness, and majority decisions," Theory and Decision, Springer, vol. 71(4), pages 503-518, October.

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