Characteristics of Strategy-Proof Fuzzy Social Choice

The Gibbard-Satterthwaite theorem, which states that a social choice function over three or more alternatives that does not incentivize individuals to misrepresent their sincere preferences must be dictatorial, under a fuzzy framework requires the specification of a fuzzy social choice function that selects some type of outcome. This chapter considers the strategic manipulation of fuzzy social choice functions where both individuals and groups can choose alternatives to various degrees and shows that with minimal assumptions on individual preferences, strategy proof fuzzy social choice functions satisfy fuzzy versions of peak-only, weak Paretianism, and monotonicity. Furthermore, strategy-proofness is necessary and sufficient for the augmented median voter rule which is considered in chapter 6.

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