Characteristics of Strategy-Proof Fuzzy Choice
This paper considers the strategic manipulation of fuzzy choice functions where both individuals and groups can choose alternatives to various degrees. Past efforts to model fuzzy choice and strategic manipulation have allowed individual preferences to be fuzzy but still required groups to select only one alternative (e.g. Abdelaziz, Jose and Meddeb ; Corte-Real ). Under this new framework, I find, with very minimal assumptions on fuzzy preferences, strategy-proof fuzzy choice functions satisfy fuzzy versions of peak-only, weak Paretianism and monotonicity. In addition, the only type of strategy-proof fuzzy choice function corresponds to the traditional augmented median rule. Further, I illustrate the implications this framework in the spatial model. These results are relevant to the manipulation literature, which remains divided as to whether choice functions can be both non-manipulable and non-dictatorial when restricting individual preferences to a single-peaked domain (e.g. Mackie ; Penn, Patty and Gailmard ). In this context, the paper suggests that social choice can be both strategy-proof and non-dictatorial if alternatives are chosen to various degrees.