By Michael B. Gibilisco, Annie M. Gowen, Karen E. Albert, John N. Mordeson, Mark J. Wierman, Terry D. Clark (auth.)
This publication bargains a accomplished research of the social selection literature and exhibits, by means of using fuzzy units, how using fuzzy personal tastes, instead of that of strict ones, may perhaps have an effect on the social selection theorems. to do that, the ebook explores the presupposition of rationality in the fuzzy framework and exhibits that the 2 stipulations for rationality, completeness and transitivity, do exist with fuzzy personal tastes. particularly, this publication examines: the stipulations lower than which a maximal set exists; the Arrow’s theorem; the Gibbard-Satterthwaite theorem and the median voter theorem. After displaying non-empty maximal set does exists for fuzzy choice kin, this e-book is going directly to demonstrating the lifestyles of a fuzzy aggregation rule gratifying all 5 Arrowian stipulations, together with non-dictatorship. whereas the Gibbard-Satterthwaite theorem merely considers person fuzzy personal tastes, this paintings indicates that either members and teams can pick out choices to varied levels, leading to a social selection that may be either strategy-proof and non-dictatorial. furthermore, the median voter theorem is proven to carry lower than strict fuzzy personal tastes yet now not lower than vulnerable fuzzy personal tastes. by means of offering a typical version of fuzzy social selection and via drawing the mandatory connections among the foremost theorems, this e-book fills an incredible hole within the present literature and encourages destiny empirical examine within the field.
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Extra resources for Fuzzy Social Choice Theory
Finally, ρ3 is complete but not strongly connected and not connected. Connectedness places more restrictions on FWPRs than completeness. Under connectedness, if ρ (x, y) = 0, then it must be true that ρ (y, x) = 1. The fuzzy completeness condition represents the strongest break away from traditional social choice approach, with minimal requirements on fuzzy preferences. 24 3 Rationality of Fuzzy Preferences Throughout the subsequent sections, we will make use of all three definitions to better detail the structure of fuzzy preferences.
2. [reflexive] An FWPR ρ is reflexive if for all x ∈ X, ρ (x, x) = 1. 2 Of course, significant exceptions exist (see Billot (1992) and Ponsard (1990) for the most prominent examples). However, in these cases ρ (x, y) refers to the preference for x over y, and ρ (x, x) refers to the intrinsic value of x and varies between 0 and 1. This interpretation makes it quite difficult to dissemble ρ into indifference and strict preference relations. 1 The Structure of Fuzzy Preference Relations 23 Reflexivity of ρ allows us to say that every alternative is definitely equally as good as itself.
In this case there is no best choice. : Social Choice and Individual Values. : Positive Political Theory I: Collective Preference. : Positive Political Theory II: Strategy and Structure. : Acyclic collective choice rules. : A direct proof of Arrow’s theorem. : Arrow’s general (im)possibility theorem. Tech. : An impossibility theorem for spatial models. : The possibility-impossibility boundary in social choice. , Suzumura, K. ) Social Choice Re-examined (Proceedings of the 1994 International Economic Association Conference at Schloss Hernstein, Austria), pp.