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Independence Of Irrelevant Alternatives And Fuzzy Arrow'S Theorem

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  • JOHN N. MORDESON

    ()
    (Department of Mathematics, Creighton University, Omaha, Nebraska 68178, USA)

  • MICHAEL B. GIBILISCO

    ()
    (Department of Political Science, Creighton University, Omaha, Nebraska 68178, USA)

  • TERRY D. CLARK

    ()
    (Department of Political Science, Creighton University, Omaha, Nebraska 68178, USA)

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    Abstract

    The literature involving fuzzy Arrow results uses the same independence of irrelevant alternatives condition. We introduce three other types of independence of irrelevant alternative conditions and show that they can be profitably used in the examination of Arrow's theorem. We also generalize some known nondictatorship results. One known fuzzy aggregation rule that is nondictatorial is the average of the individual preferences. We show that a weighted average is also nondictatorial. Moreover, it is not an automorphic image of the ordinary average, which demonstrates that we have proposed a framework unique from the present known results.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 08 (2012)
    Issue (Month): 02 ()
    Pages: 219-237

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    Handle: RePEc:wsi:nmncxx:v:08:y:2012:i:02:p:219-237

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    Related research

    Keywords: Arrow's theorem; independence of irrelevant alternatives; fuzzy preference profiles; fuzzy aggregation rules; nondictatorship;

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