Abstract
There are alternative ways of decomposing a given fuzzy weak preference relation into its antisymmetric and symmetric components. In this paper I have provided support to one among these alternative specifications. It is shown that on this specification the fuzzy analogue of the General Possibility Theorem is valid even when the transitivity restrictions on the individual and the social preference relations are relatively weak. In the special case where the individual preference relations are exact but the social preference relation is permitted to be fuzzy it is possible to distinguish between different degrees of power of the dictator. This power increases with the strength of the transitivity requirement.
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For comments on an earlier version of the paper I am indebted to an anonymous referee, an anonymous member of the Board of Editors and to participants in the 1991 Annual Conference of the Indian Econometric Society at North Bengal University, India. However, I retain sole responsibility for any error(s) that the paper may contain.
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Banerjee, A. Fuzzy preferences and Arrow-type problems in social choice. Soc Choice Welfare 11, 121–130 (1994). https://doi.org/10.1007/BF00179208
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DOI: https://doi.org/10.1007/BF00179208