Skip to main content
SpringerLink
Log in

Fuzzy preferences and Arrow-type problems in social choice

  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arrow KJ (1963) Social choice and individual values, 2nd edn. Wiley, New York

    Google Scholar 

  • Barrett CR, Pattanaik PK, Salles M (1986) On the structure of fuzzy social welfare functions. Fuzzy Sets Syst 19: 1–10

    Google Scholar 

  • Basu K (1984) Fuzzy revealed preference theory. J Econ Theory 32: 212–227

    Google Scholar 

  • Dutta B (1987) Fuzzy preferences and social choice. Math Soc Scie 13: 215–229

    Google Scholar 

  • Gibbard A (1969) Intransitive social indifference and the Arrow dilemma. Mimeographed

  • Obchinnikov SO (1981) Structure of fuzzy binary relations. Fuzzy Sets Syst 6: 169–195

    Google Scholar 

  • Sen AK (1985) Social choice theory. In: Arrow KJ, Intrilligator MJ (eds) Handbook of mathematical economics, vol. 3. North-Holland, Amsterdam

    Google Scholar 

  • Yager RR (1980) On a general class of fuzzy connectives. Fuzzy Sets Syst 3: 235–242

    Google Scholar 

  • Zimmermann HJ (1985) Fuzzy set Theory and its applications. Kluwer-Nijhoff, Hingham MA

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, Calcutta University, 56A, B.T.Road, 700050, Calcutta, India

    Asis Banerjee

Authors
  1. Asis Banerjee
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

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.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Banerjee, A. Fuzzy preferences and Arrow-type problems in social choice. Soc Choice Welfare 11, 121–130 (1994). https://doi.org/10.1007/BF00179208

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00179208

Keywords

Search

Navigation