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Strategy-proof fuzzy aggregation rules

  • Juan Perote Pena
  • Ashley Piggins

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

We investigate the structure of fuzzy aggregation rules which, for every permissible profile of fuzzy individual preferences, specify a fuzzy social preference. We show that all fuzzy aggregation rules which are strategyproof and satisfy a minimal range condition are dictatorial. In other words, there is an individual whose fuzzy preferences determine the entire fuzzy social ranking at every profile in the domain of the aggregation rule. To prove this theorem, we show that all fuzzy aggregation rules which are strategyproof and satisfy the minimal range condition must also satisfy counterparts of independence of irrelevant alternatives and the Pareto criterion. There has been hardly any treatment of the manipulability problem in the literature on social choice with fuzzy preferences.

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Paper provided by National University of Ireland Galway, Department of Economics in its series Working Papers with number 0098.

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Date of creation: 2005
Date of revision: 2005
Handle: RePEc:nig:wpaper:0098
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  1. Basu, Kaushik, 1984. "Fuzzy revealed preference theory," Journal of Economic Theory, Elsevier, vol. 32(2), pages 212-227, April.
  2. Leclerc, B., 1984. "Efficient and binary consensus functions on transitively valued relations," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 45-61, August.
  3. Garcia-Lapresta, Jose Luis & Llamazares, Bonifacio, 2001. "Majority decisions based on difference of votes," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 463-481, June.
  4. Barrett, C Richard & Pattanaik, Prasanta K, 1989. "Fuzzy Sets, Preference and Choice: Some Conceptual Issues," Bulletin of Economic Research, Wiley Blackwell, vol. 41(4), pages 229-53, October.
  5. Dutta, Bhaskan, 1987. "Fuzzy preferences and social choice," Mathematical Social Sciences, Elsevier, vol. 13(3), pages 215-229, June.
  6. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  7. D'ASPREMONT, Claude & GEVERS, Louis, . "Social welfare functionals and interpersonal comparability," CORE Discussion Papers RP -1564, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Gregory Richardson, 1998. "The structure of fuzzy preferences: Social choice implications," Social Choice and Welfare, Springer, vol. 15(3), pages 359-369.
  9. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  10. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
  11. 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.
  12. Tang, Fang-Fang, 1994. "Fuzzy Preferences and Social Choice," Bulletin of Economic Research, Wiley Blackwell, vol. 46(3), pages 263-69, July.
  13. 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.
  14. Blackorby, Charles, 1975. "Degrees of Cardinality and Aggregate Partial Orderings," Econometrica, Econometric Society, vol. 43(5-6), pages 845-52, Sept.-Nov.
  15. Rajat Deb & Manabendra Dasgupta, 1996. "Transitivity and fuzzy preferences," Social Choice and Welfare, Springer, vol. 13(3), pages 305-318.
  16. Barbera, Salvador, 1983. "Strategy-Proofness and Pivotal Voters: A Direct Proof of the Gibbard-Satterthwaite Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 413-17, June.
  17. Pattanaik, Prasanta K., 1973. "On the stability of sincere voting situations," Journal of Economic Theory, Elsevier, vol. 6(6), pages 558-574, December.
  18. Salvador Barberà, 2001. "An introduction to strategy-proof social choice functions," Social Choice and Welfare, Springer, vol. 18(4), pages 619-653.
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