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 language | English |
|---|---|
| Pages (from-to) | 195-217 |
| Number of pages | 23 |
| Journal | New Mathematics and Natural Computation |
| Volume | 8 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jul 2012 |
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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 journal › Article
}
TY - JOUR
T1 - Fuzzy Black'S Median Voter Theorem
T2 - Examining the structure of fuzzy rules and strict preference
AU - Gibilisco, Michael B.
AU - Mordeson, John N.
AU - Clark, Terry D.
PY - 2012/7
Y1 - 2012/7
N2 - 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.
AB - 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.
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U2 - 10.1142/S179300571240011X
DO - 10.1142/S179300571240011X
M3 - Article
AN - SCOPUS:84864194707
VL - 8
SP - 195
EP - 217
JO - New Mathematics and Natural Computation
JF - New Mathematics and Natural Computation
SN - 1793-0057
IS - 2
ER -