Fuzzy Black'S Median Voter Theorem: Examining the structure of fuzzy rules and strict preference

作者: MICHAEL B. GIBILISCO , JOHN N. MORDESON , TERRY D. CLARK

DOI: 10.1142/S179300571240011X

关键词: Fuzzy classificationCardinal voting systemsArtificial intelligenceType-2 fuzzy sets and systemsMachine learningMedian voter theoremDefuzzificationVotingMathematical economicsFuzzy numberMathematicsPreference

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

参考文章(26)
Antoine Billot, Economic Theory of Fuzzy Equilibria Springer Berlin Heidelberg. ,(1995) , 10.1007/978-3-642-79949-5
Heinz J. Skala, Arrow’s Impossibility Theorem: Some New Aspects Springer Netherlands. pp. 215- 225 ,(1978) , 10.1007/978-94-009-9838-4_11
Gregory Richardson, The structure of fuzzy preferences: Social choice implications Social Choice and Welfare. ,vol. 15, pp. 359- 369 ,(1998) , 10.1007/S003550050111
Asis Banerjee, Fuzzy preferences and Arrow-type problems in social choice Social Choice and Welfare. ,vol. 11, pp. 121- 130 ,(1994) , 10.1007/BF00179208
Jeffrey S. Banks, Singularity theory and core existence in the spatial model Journal of Mathematical Economics. ,vol. 24, pp. 523- 536 ,(1995) , 10.1016/0304-4068(94)00704-E
F.J. Montero, J. Tejada, A necessary and sufficient condition for the existence of Orlovsky's choice set Fuzzy Sets and Systems. ,vol. 26, pp. 121- 125 ,(1988) , 10.1016/0165-0114(88)90010-3
M. Dasgupta, R. Deb, Fuzzy choice functions Social Choice and Welfare. ,vol. 8, pp. 171- 182 ,(1991) , 10.1007/BF00187373
Fouad Ben Abdelaziz, José Rui Figueira, Olfa Meddeb, On the manipulability of the fuzzy social choice functions Fuzzy Sets and Systems. ,vol. 159, pp. 177- 184 ,(2008) , 10.1016/J.FSS.2007.06.015
C.R. Barrett, Prasanta K. Pattanaik, Maurice Salles, On the structure of fuzzy social welfare functions Fuzzy Sets and Systems. ,vol. 19, pp. 1- 10 ,(1986) , 10.1016/S0165-0114(86)80072-0
Richard D. McKelvey, Norman Schofield, Structural instability of the core Journal of Mathematical Economics. ,vol. 15, pp. 179- 198 ,(1986) , 10.1016/0304-4068(86)90009-1