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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 2010-11, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:2010-11
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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.
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    Cited by:

    1. Cato, Susumu, 2018. "Incomplete decision-making and Arrow’s impossibility theorem," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 58-64.

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    More about this item

    Keywords

    Product Filters; Decisiveness; Acyclicity; Suzumura Consistency.;
    All these keywords.

    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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