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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 the assumption that the social relation is reflexive and complete. This leads to a new set-theoretic concept applied to product spaces.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 64 (2012)
Issue (Month): 3 ()
Pages: 258-262

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Handle: RePEc:eee:matsoc:v:64:y:2012:i:3:p:258-262

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Web page: http://www.elsevier.com/locate/inca/505565

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  1. Sen, Amartya K, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 381-93, July.
  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. 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. Sen, Amartya K, 1976. "Liberty, Unanimity and Rights," Economica, London School of Economics and Political Science, vol. 43(171), pages 217-45, August.
  5. Bossert, Walter & Suzumura, Kotaro, 2009. "Consistency, Choice and Rationality," PIE/CIS Discussion Paper 428, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  6. Truchon, M., 1993. "Acyclicity and Decisiveness Structures," Papers 9316, Laval - Recherche en Politique Economique.
  7. 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.
  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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