FUZZY BLACK'S MEDIAN VOTER THEOREM: EXAMINING THE STRUCTURE OF FUZZY RULES AND STRICT PREFERENCE

Michael B. Gibilisco (), John N. Mordeson () and Terry D. Clark ()
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Michael B. Gibilisco: Department of Political Science, Creighton University, Omaha, NE 68178, USA
John N. Mordeson: Department of Mathematics, Creighton University, Omaha, NE 68178, USA
Terry D. Clark: Department of Political Science, Creighton University, Omaha, NE 68178, USA

New Mathematics and Natural Computation (NMNC), 2012, vol. 08, issue 02, 195-217

Abstract: Under certain aggregation rules, particular subsets of the voting population fully characterize the social preference relation, and the preferences of the remaining voters become irrelevant. In the traditional literature, these types of rules, i.e. voting and simple rules, have received considerable attention because they produce non-empty social maximal sets under single-peaked preference profiles but are particularly poorly behaved in multi-dimensional space. However, the effects of fuzzy preference relations on these types of rules is largely unexplored. This paper extends the analysis of voting and simple rules in the fuzzy framework. In doing so, we contribute to this literature by relaxing previous assumptions about strict preference and by illustrating that Black's Median Voter Theorem does not hold under all conceptualizations of the fuzzy maximal set.

Keywords: Black's Median Voter Theorem; fuzzy preferences; fuzzy maximal set; fuzzy aggregation rules; fuzzy simple rules; fuzzy voting rule (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S179300571240011X

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