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Product Filters, Acyclicity and Suzumura Consistency

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  • BOSSERT, Walter
  • SUZUMURA, Kotaro

Abstract

In a seminal contribution, Hansson (1976) demonstrates that the collection of decisive coalitions associated with an Arrovian social welfare function forms an ultrafilter. 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 notion of decisiveness with acyclical or Suzumura consistent social preferences and without assuming that the social relation is complete. This leads to a new set-theoretic concept applied to product spaces.

Suggested Citation

  • BOSSERT, Walter & SUZUMURA, Kotaro, 2010. "Product Filters, Acyclicity and Suzumura Consistency," Cahiers de recherche 20-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  • Handle: RePEc:mtl:montec:20-2010
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    References listed on IDEAS

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    1. Sen, Amartya K, 1976. "Liberty, Unanimity and Rights," Economica, London School of Economics and Political Science, vol. 43(171), pages 217-245, August.
    2. John Weymark, 1984. "Arrow's theorem with social quasi-orderings," Public Choice, Springer, vol. 42(3), pages 235-246, January.
    3. Ferejohn, John A. & Fishburn, Peter C., 1979. "Representations of binary decision rules by generalized decisiveness structures," Journal of Economic Theory, Elsevier, vol. 21(1), pages 28-45, August.
    4. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
    5. Truchon, Michel, 1996. "Acyclicity and Decisiveness Structures," Journal of Economic Theory, Elsevier, vol. 69(2), pages 447-469, May.
    6. 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.
    7. Bossert, Walter & Suzumura, Kotaro, 2010. "Consistency, Choice, and Rationality," Economics Books, Harvard University Press, number 9780674052994, December.
    8. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
    9. John Ferejohn & Talbot Page, 1978. "On the Foundations of Intertemporal Choice," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 60(2), pages 269-275.
    10. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 381-393.
    11. Edward Packel, 1980. "Impossibility results in the axiomatic theory of intertemporal choice," Public Choice, Springer, vol. 35(2), pages 219-227, January.
    12. Kotaro Suzumura, 2000. "Presidential Address: Welfare Economics Beyond Welfarist-Consequentialism," The Japanese Economic Review, Japanese Economic Association, vol. 51(1), pages 1-32, March.
    13. repec:spr:stchwe:978-3-540-79832-3 is not listed on IDEAS
    14. Blair, Douglas H & Pollak, Robert A, 1982. "Acyclic Collective Choice Rules," Econometrica, Econometric Society, vol. 50(4), pages 931-943, July.
    15. Bengt Hansson, 1976. "The existence of group preference functions," Public Choice, Springer, vol. 28(1), pages 89-98, December.
    16. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-390, November.
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    More about this item

    Keywords

    product filters; decisiveness; acyclicity; Suzumura consistency;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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