On the H-Manipulability of Fuzzy Social Choice Functions

In voting theory the well-known Gibbard-Satterthwaite theorem is about the manipulability of aggregators which consists of the aggregation of individual preferences expressed as a complete ordering over the set of alternatives. This paper deals with the generalization of such a theorem in a context where each individual expresses a fuzzy preference (weak) ordering. This extension is called H-manipulability. The concept of fuzzy game form as the generalization of Gibbard’s concept game form is also introduced here in a fuzzy framework. The proof of the Hmanipulability theorem is relied on the connection of fuzzy social choice functions with fuzzy aggregation rules. In particular, the dictatorship of fuzzy aggregation rules corresponds to the H-dictatorship fuzzy social choice.