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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.

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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2010-11.

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Length: 19 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:mtl:montde:2010-11

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Keywords: Product Filters; Decisiveness; Acyclicity; Suzumura Consistency.;

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  1. Truchon, M., 1993. "Acyclicity and Decisiveness Structures," Papers 9316, Laval - Recherche en Politique Economique.
  2. KIRMAN, Alan P. & SONDERMANN, Dieter, . "Arrow's theorem, many agents, and indivisible dictators," CORE Discussion Papers RP -118, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  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. 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.
  5. Sen, Amartya K, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 381-93, July.
  6. Sen, Amartya K, 1976. "Liberty, Unanimity and Rights," Economica, London School of Economics and Political Science, vol. 43(171), pages 217-45, August.
  7. Bossert, Walter & Suzumura, Kotaro, 2010. "Consistency, Choice, and Rationality," Economics Books, Harvard University Press, number 9780674052994.
  8. Blair, Douglas H & Pollak, Robert A, 1982. "Acyclic Collective Choice Rules," Econometrica, Econometric Society, vol. 50(4), pages 931-43, July.
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