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Arrow's theorem and max-star transitivity

  • Conal Duddy
  • Juan Perote-Pena
  • Asjley Piggins

    (Department of Economics, National University of Ireland, Galway)

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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Paper provided by National University of Ireland Galway, Department of Economics in its series Working Papers with number 0140.

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Length: 12 pages
Date of creation: 2009
Date of revision: 2009
Handle: RePEc:nig:wpaper:0140
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  1. Perote-Pena, Juan & Piggins, Ashley, 2007. "Strategy-proof fuzzy aggregation rules," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 564-580, June.
  2. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
  3. 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.
  4. 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.
  5. Basu, Kaushik, 1984. "Fuzzy revealed preference theory," Journal of Economic Theory, Elsevier, vol. 32(2), pages 212-227, April.
  6. Barrett, C. & Pattanaik, P.K. & Salles, M., 1990. "Rationality and Aggregation of Preferences in an Ordinally Fuzzy Framework," Papers 9006, Dijon - Institut des Mathematiques Economiques.
  7. Rajat Deb & Manabendra Dasgupta, 1996. "Transitivity and fuzzy preferences," Social Choice and Welfare, Springer, vol. 13(3), pages 305-318.
  8. Dutta, Bhaskan, 1987. "Fuzzy preferences and social choice," Mathematical Social Sciences, Elsevier, vol. 13(3), pages 215-229, June.
  9. 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.
  10. 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.
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