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Independence Of Irrelevant Alternatives And Fuzzy Arrow'S Theorem

Author

Listed:
  • 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)

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.

Suggested Citation

  • John N. Mordeson & Michael B. Gibilisco & Terry D. Clark, 2012. "Independence Of Irrelevant Alternatives And Fuzzy Arrow'S Theorem," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 219-237.
    • Handle: RePEc:wsi:nmncxx:v:08:y:2012:i:02:n:s1793005712400121
    DOI: 10.1142/S1793005712400121
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