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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.

Suggested Citation

  • BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "A Characterization of Consistent Collective Choice Rules," Cahiers de recherche 09-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:09-2006
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    References listed on IDEAS

    as
    1. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    2. John Weymark, 1984. "Arrow's theorem with social quasi-orderings," Public Choice, Springer, vol. 42(3), pages 235-246, January.
    3. repec:bla:econom:v:72:y:2005:i:286:p:185-200 is not listed on IDEAS
    4. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro & 鈴村, 興太郎, 2002. "Consistent Rationalizability," Discussion Paper 82, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    5. 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 537-558, September.
    6. repec:bla:econom:v:43:y:1976:i:172:p:381-90 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Bossert, Walter & Suzumura, Kotaro, 2012. "Product filters, acyclicity and Suzumura consistency," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 258-262.
    2. Geir Asheim & Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2010. "Infinite-horizon choice functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 1-21, April.
    3. BOSSERT, Walter & SUZUMURA, Kotaro, 2009. "Decisive coalitions and coherence properties," Cahiers de recherche 2009-04, Universite de Montreal, Departement de sciences economiques.
    4. Walter Bossert & Kotaro Suzumura, 2012. "Quasi-transitive and Suzumura consistent relations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 323-334, July.
    5. Piggins, Ashley & Duddy, Conal, 2016. "Oligarchy and soft incompleteness," MPRA Paper 72392, University Library of Munich, Germany.
    6. Conal Duddy & Ashley Piggins, 2018. "On some oligarchy results when social preference is fuzzy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 717-735, December.
    7. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.
    8. Bossert, Walter & Cato, Susumu, 2021. "Superset-robust collective choice rules," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 126-136.
    9. Bossert, Walter & Cato, Susumu, 2020. "Acyclicity, anonymity, and prefilters," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 134-141.
    10. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    11. 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.
    12. Susumu Cato, 2015. "Conditions on social-preference cycles," Theory and Decision, Springer, vol. 79(1), pages 1-13, July.
    13. Susumu Cato & Daisuke Hirata, 2010. "Collective choice rules and collective rationality: a unified method of characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 611-630, April.
    14. Susumu Cato, 2013. "Social choice, the strong Pareto principle, and conditional decisiveness," Theory and Decision, Springer, vol. 75(4), pages 563-579, October.
    15. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 869-889, October.
    16. Cato, Susumu, 2018. "Incomplete decision-making and Arrow’s impossibility theorem," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 58-64.
    17. Kotaro Suzumura, 2020. "Reflections on Arrow’s research program of social choice theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 219-235, March.
    18. Duddy, Conal & Piggins, Ashley, 2022. "Collective choice rules with social maximality," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    19. 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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    More about this item

    Keywords

    Collective Choice Rules; Consistency; Pareto Rule;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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