INDEPENDENCE OF IRRELEVANT ALTERNATIVES AND FUZZY ARROW'S THEOREM

John N. Mordeson (), Michael B. Gibilisco () and Terry D. Clark ()
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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

New Mathematics and Natural Computation (NMNC), 2012, vol. 08, issue 02, 219-237

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.

Keywords: Arrow's theorem; independence of irrelevant alternatives; fuzzy preference profiles; fuzzy aggregation rules; nondictatorship (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S1793005712400121

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