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Fuzzy Black’s Median Voter Theorem: Examining the Structure of Fuzzy Rules and Strict Preference

Gibilisco, Michael B. and Mordeson, John N. and Clark, Terry D. (2012) Fuzzy Black’s Median Voter Theorem: Examining the Structure of Fuzzy Rules and Strict Preference. New Mathematics and Natural Computation, 08 (02). pp. 195-217. ISSN 1793-0057. doi:10.1142/S179300571240011X. https://resolver.caltech.edu/CaltechAUTHORS:20180116-090802358

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1142/S179300571240011XDOIArticle
http://www.worldscientific.com/doi/abs/10.1142/S179300571240011XPublisherArticle
Additional Information:© 2012 World Scientific Publishing Co Pte Ltd.
Subject Keywords:Black's Median Voter Theorem; fuzzy preferences; fuzzy maximal set; fuzzy aggregation rules; fuzzy simple rules; fuzzy voting rule
Issue or Number:02
DOI:10.1142/S179300571240011X
Record Number:CaltechAUTHORS:20180116-090802358
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180116-090802358
Official Citation: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 New Mathematics and Natural Computation 2012 08:02, 195-217
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84328
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Jan 2018 18:09
Last Modified:15 Nov 2021 20:18

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