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Aggregation of preferences: The fuzzy case

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Abstract

The basic purpose of this paper is to link both theorems of impossibility and existence by introducing fuzzy relations of preference and an exogeneous requirement, the planner's one, and then proving the fundamental part played by the extremist agents, leximin and leximax. In other words, to bring out the link between the planner's requirement and the difficulty of the transition from individual to collective, as well as the theoric relation between this requirement and the extremist agents, we define a fuzzy behavior of preference which allows us to build up two determinant fuzzy coalitions. These coalitions will be the base of the planner's requirement and the link between pessimistic results (Arrow's impossibility) and optimistic ones (May's theorem of majority choice).

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Billot, A. Aggregation of preferences: The fuzzy case. Theor Decis 30, 51–93 (1991). https://doi.org/10.1007/BF00134636

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