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Arrow’s theorem and max-star transitivity

  • Conal Duddy

    ()

  • Juan Perote-Peña

    ()

  • Ashley Piggins

    ()

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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File URL: http://hdl.handle.net/10.1007/s00355-010-0461-x
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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 36 (2011)
Issue (Month): 1 (January)
Pages: 25-34

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Handle: RePEc:spr:sochwe:v:36:y:2011:i:1:p:25-34
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  1. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
  2. Basu, Kaushik, 1984. "Fuzzy revealed preference theory," Journal of Economic Theory, Elsevier, vol. 32(2), pages 212-227, April.
  3. Richard Barrett & Maurice Salles, 2006. "Social Choice With Fuzzy Preferences," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200615, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
  4. Dutta, Bhaskan, 1987. "Fuzzy preferences and social choice," Mathematical Social Sciences, Elsevier, vol. 13(3), pages 215-229, June.
  5. Conal Duddy & Juan Perote-Peña & Ashley Piggins, 2010. "Manipulating an aggregation rule under ordinally fuzzy preferences," Social Choice and Welfare, Springer, vol. 34(3), pages 411-428, March.
  6. Perote-Pena, Juan & Piggins, Ashley, 2007. "Strategy-proof fuzzy aggregation rules," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 564-580, June.
  7. Barrett, C.R. & Pattanaik, P.K. & Salles, M., 1990. "Rationality and Aggregation of Preferences in an Ordinally Fuzzy Framework," Institut des Mathématiques Economiques – Document de travail de l’I.M.E. (1974-1993) 9006, Institut des Mathématiques Economiques. LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS, Université de Bourgogne.
  8. Dutta, Bhaskar & Panda, Santosh C. & Pattanaik, Prasanta K., 1986. "Exact choice and fuzzy preferences," Mathematical Social Sciences, Elsevier, vol. 11(1), pages 53-68, February.
  9. Rajat Deb & Manabendra Dasgupta, 1996. "Transitivity and fuzzy preferences," Social Choice and Welfare, Springer, vol. 13(3), pages 305-318.
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