Advanced Search
MyIDEAS: Login to save this article or follow this journal

The structure of fuzzy preferences: Social choice implications

Contents:

Author Info

  • Gregory Richardson

    (Shorter College, Box 393, Rome, GA 30165, USA)

Registered author(s):

    Abstract

    It has been shown that, with an alternative factorization of fuzzy weak preferences into symmetric and antisymmetric components, one can prove a fuzzy analogue of Arrow's Impossibility Theorem even when the transitivity requirements on individual and social preferences are very weak. It is demonstrated here that the use of this specification of strict preference, however, requires preferences to also be strongly connected. In the absence of strong connectedness, another factorization of fuzzy weak preferences is indicated, for which nondictatorial fuzzy aggregation rules satisfying the weak transitivity requirement can still be found. On the other hand, if strong connectedness is assumed, the fuzzy version of Arrow's Theorem still holds for a variety of weak preference factorizations, even if the transitivity condition is weakened to its absolute minimum. Since Arrow's Impossibility Theorem appeared nearly half a century ago, researchers have been attempting to avoid Arrow's negative result by relaxing various of his original assumptions. One approach has been to allow preferences - those of individuals and society or just those of society alone - to be "fuzzy." In particular, Dutta [4] has shown that, to a limited extent, one can avoid the impossibility result (or, more precisely, the dictatorship result) by using fuzzy preferences, employing a particularly weak version of transitivity among the many plausible (but still distinct) definitions of transitivity that are available for fuzzy preferences. Another aspect of exact preferences for which the extension to the more general realm of fuzzy preferences is ambiguous is the factorization of a weak preference relation into a symmetric component (indifference) and an antisymmetric component (strict preference). There are several ways to do this for fuzzy weak preferences, all of them equivalent to the traditional factorization in the special case when preferences are exact, but quite different from each other when preferences are fuzzy (see, for example, [3]). A recent paper in this journal [1], by A. Banerjee, argues that the choice of definitions for indifference and strict preference, given a fuzzy weak preference, can also have "Arrovian" implications. In particular, [1] claims that Dutta's version of strict preference presents certain intuitive difficulties and recommends a different version, with its own axiomatic derivation, for which the dictatorship results reappear even with Dutta's weak version of transitivity. However, the conditions used to derive [1]'s version of strict preference imply a restriction on how fuzzy the original weak preference can be, namely, that the fuzzy weak preference relation must be strongly connected. Without this restriction, I will show that the rest of [1]'s conditions imply yet a third version of strict preference, for which Dutta's possibility result under weak transitivity still holds. On the other hand, if one accepts the strong connectedness required in order for it to be valid, I show that [1]'s dictatorship theorem can in fact be strengthened to cover any version of transitivity for fuzzy preferences, no matter how weak, and further, that this dictatorship result holds for any "regular" formulation of strict preference, including the one originally used by Dutta.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://link.springer.de/link/service/journals/00355/papers/8015003/80150359.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted

    File URL: http://link.springer.de/link/service/journals/00355/papers/8015003/80150359.ps.gz
    Download Restriction: Access to the full text of the articles in this series is restricted

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Springer in its journal Social Choice and Welfare.

    Volume (Year): 15 (1998)
    Issue (Month): 3 ()
    Pages: 359-369

    as in new window
    Handle: RePEc:spr:sochwe:v:15:y:1998:i:3:p:359-369

    Note: Received: 13 May 1996 / Accepted: 13 January 1997
    Contact details of provider:
    Web page: http://link.springer.de/link/service/journals/00355/index.htm

    Order Information:
    Web: http://link.springer.de/orders.htm

    Related research

    Keywords:

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    Cited by:
    1. Juan Perote Pena & Ashley Piggins, 2005. "Strategy-proof fuzzy aggregation rules," Working Papers 0098, National University of Ireland Galway, Department of Economics, revised 2005.
    2. Louis Fono & Maurice Salles, 2011. "Continuity of utility functions representing fuzzy preferences," Social Choice and Welfare, Springer, vol. 37(4), pages 669-682, October.
    3. David E. A. Giles & Robert Draeseke, 2001. "Econometric Modelling based on Pattern recognition via the Fuzzy c-Means Clustering Algorithm," Econometrics Working Papers 0101, Department of Economics, University of Victoria.
    4. Dinko Dimitrov, 2001. "Fuzzy Preferences, Liberalism and Non-discrimination," Economic Thought journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 2, pages 63-76.
    5. Robert Draeseke & David E. A. Giles, 1999. "A Fuzzy Logic Approach to Modelling the Underground Economy," Econometrics Working Papers 9909, Department of Economics, University of Victoria.
    6. Peter Casey & Mark Wierman & Michael Gibilisco & John Mordeson & Terry Clark, 2012. "Assessing policy stability in Iraq: a fuzzy approach to modeling preferences," Public Choice, Springer, vol. 151(3), pages 409-423, June.
    7. Espin, Rafael & Fernandez, Eduardo & Mazcorro, Gustavo & Lecich, Maria Ines, 2007. "A fuzzy approach to cooperative n-person games," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1735-1751, February.
    8. Subramanian, S., 2009. "The Arrow paradox with fuzzy preferences," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 265-271, September.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:spr:sochwe:v:15:y:1998:i:3:p:359-369. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.