Fuzzy Black'S Median Voter Theorem

Examining the structure of fuzzy rules and strict preference

Michael B. Gibilisco, John N. Mordeson, Terry D. Clark

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)195-217
Number of pages23
JournalNew Mathematics and Natural Computation
Volume8
Issue number2
DOIs
StatePublished - Jul 2012

Fingerprint

Fuzzy rules
Vote
Fuzzy sets
Fuzzy Rules
Agglomeration
Voting
Theorem
Fuzzy Preference Relation
Preference Relation
Aggregation
Subset

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Computational Mathematics
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Human-Computer Interaction

Cite this

Fuzzy Black'S Median Voter Theorem : Examining the structure of fuzzy rules and strict preference. / Gibilisco, Michael B.; Mordeson, John N.; Clark, Terry D.

In: New Mathematics and Natural Computation, Vol. 8, No. 2, 07.2012, p. 195-217.

Research output: Contribution to journalArticle

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