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Arrow’s theorem and max-star transitivity

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  • Conal Duddy
  • Juan Perote-Peña
  • Ashley Piggins

Abstract

In the literature on social choice and fuzzy preferences, a central question is how to represent the transitivity of a fuzzy binary relation. Arguably the most general way of doing this is to assume a form of transitivity called max-star transitivity. The star operator in this formulation is commonly taken to be a triangular norm. The familiar max-min transitivity condition is a member of this family, but there are infinitely many others. Restricting attention to fuzzy aggregation rules that satisfy counterparts of unanimity and independence of irrelevant alternatives, we characterise the set of max-star transitive relations that permit preference aggregation to be non-dictatorial. This set contains all and only those triangular norms that contain a zero divisor.
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  • Conal Duddy & Juan Perote-Peña & Ashley Piggins, 2011. "Arrow’s theorem and max-star transitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(1), pages 25-34, January.
    • Handle: RePEc:spr:sochwe:v:36:y:2011:i:1:p:25-34
    DOI: 10.1007/s00355-010-0461-x
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    References listed on IDEAS

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    Cited by:

    1. Armajac Raventós-Pujol & María J. Campión & Esteban Induráin, 2020. "Decomposition and Arrow-Like Aggregation of Fuzzy Preferences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    2. Piggins, Ashley & Duddy, Conal, 2016. "Oligarchy and soft incompleteness," MPRA Paper 72392, University Library of Munich, Germany.
    3. Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, vol. 148(2), pages 793-805.

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    JEL classification:

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

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