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2020•Iranian journal of fuzzy systemsRequires access

Arrow theorems in the fuzzy setting

Armajac Raventós-Pujol, María Jesús Campión, Esteban Induráin

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Abstract

Throughout this paper, our  main idea is to analyze the Arrovian approach in a fuzzy context, paying attention to different extensions of the classical Arrow's model arising in mathematical Social Choice to aggregate preferences that the agents define on a set of alternatives. There is a wide set of extensions. Some of them give rise to an impossibility theorem as in the Arrovian classical  model. But others lead to possibility results. We explore the main grounds that lead to impossibility or possibility. In this analysis,   representative examples arise. One of them corresponds to an impossibility result, and the other ones allow the aggregation  of fuzzy individual preferences to an individual one. We introduce new techniques for the proofs, specially for the one that leads to impossibility.

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What this paper is about

Throughout this paper, our  main idea is to analyze the Arrovian approach in a fuzzy context, paying attention to different extensions of the classical Arrow's model arising in mathematical Social Choice to aggregate preferences that the agents define on a set of alternatives. There is a wide set of extensions. Some of them give rise to an impossibility theorem as in the Arrovian classical  model. But others lead to possibility results. We explore the main grounds that lead to impossibility or possibility. In this analysis,   representative examples arise. One of them corresponds to an impossibility result, and the other ones allow the aggregation  of fuzzy individual preferences to an individual one. We introduce new techniques for the proofs, specially for the one that leads to impossibility.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Throughout this paper, our  main idea is to analyze the Arrovian approach in a fuzzy context, paying attention to different extensions of the classical Arrow's model arising in mathematical Social Choice to aggregate preferences that the agents define on a set of alternatives. There is a wide set of extensions. Some of them give rise to an impossibility theorem as in the Arrovian classical  model. But others lead to possibility results. We explore the main grounds that lead to impossibility or possibility. In this analysis,   representative examples arise. One of them corresponds to an impossibility result, and the other ones allow the aggregation  of fuzzy individual preferences to an individual one. We introduce new techniques for the proofs, specially for the one that leads to impossibility.

Key concepts: Impossibility, Arrow's impossibility theorem, Arrow, Social choice theory, Mathematical economics, Mathematical proof, Context (archaeology), Set (abstract data type)

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