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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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File URL: http://hdl.handle.net/1866/2149
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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2006-12.

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

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Keywords: Collective Choice Rules; Consistency; Pareto Rule;

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References

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  1. WEYMARK, John, . "Arrow's theorem with social quasi-orderings," CORE Discussion Papers RP -609, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Sen, Amartya K, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 381-93, July.
  3. 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.
  4. 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.
  5. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2002. "Consistent Rationalizability," Discussion Paper 82, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
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Cited by:
  1. Allan M Feldman & Roberto Serrano, 2007. "Arrow's Impossibility Theorem: Preference Diversity in a Single-Profile World," Working Papers 2007-12, Brown University, Department of Economics.
  2. Susumu Cato, 2011. "Pareto principles, positive responsiveness, and majority decisions," Theory and Decision, Springer, vol. 71(4), pages 503-518, October.
  3. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer, vol. 39(4), pages 869-889, October.
  4. BOSSERT, Walter & SUZUMURA, Kotaro, 2009. "Decisive Coalitions and Coherence Properties," Cahiers de recherche 05-2009, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Geir Asheim & Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2010. "Infinite-horizon choice functions," Economic Theory, Springer, vol. 43(1), pages 1-21, April.
  6. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer, vol. 41(1), pages 169-202, June.
  7. Walter Bossert & Kotaro Suzumura, 2012. "Quasi-transitive and Suzumura consistent relations," Social Choice and Welfare, Springer, vol. 39(2), pages 323-334, July.
  8. Susumu Cato, 2013. "Social choice, the strong Pareto principle, and conditional decisiveness," Theory and Decision, Springer, vol. 75(4), pages 563-579, October.
  9. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.
  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.

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