ABSTRACT
Sections 9.1-9.3 are based on the work of Abdelaziz, Figueria, and Meddeb [1]. In social decision-making contexts, a manipulator often has incentive to change the social choice in his/her favor by strategically misrepresenting his/her preference. The Gibbard-Satterthwaite theorem [19, 26] states that a social choice function over three or more alternatives that does not provide incentive to individuals to misrepresent their sincere preferences must be dictatorial. This chapter extends their result to the case of fuzzy weak preference relations. Here we use the approach given in [1] by defining the best alternative set in three ways and thus provide three generalizations of the Gibbard-Satterthwaite theorem in the fuzzy context.
