Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

Armajac Raventós-Pujol, María J. Campión and Esteban Induráin
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Armajac Raventós-Pujol: Institute for Advanced Research in Business and Economics and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
María J. Campión: Institute for Advanced Research in Business and Economics and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
Esteban Induráin: Institute for Advanced Materials and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
Authors registered in the RePEc Author Service: Armajac Raventós Pujol

Mathematics, 2020, vol. 8, issue 3, 1-18

Abstract: We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.

Keywords: Arrow’s impossibility theorems; mathematical social choice; fuzzy preferences; decomposition of preferences; aggregation of individual profiles; social rules; Arrovian models; Paretian property; independence of irrelevant alternatives; dictatorship (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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