Soc Choice Welf https://doi.org/10.1007/s00355-018-1134-4 ORIGINAL PAPER On some oligarchy results when social preference is fuzzy 1 1 Conal Duddy · Ashley Piggins Received: 21 March 2017 / Accepted: 26 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We consider a model in which individual preferences are orderings of social states, but the social preference relation is fuzzy. We motivate interest in the model by presenting a version of the strong Pareto rule that is suited to the setting of a fuzzy social preference. We prove a general oligarchy theorem under the assumption that this fuzzy relation is quasi-transitive. The framework allows us to make a distinction between a “strong” and a “weak” oligarchy, and our theorem identiﬁes when the oligarchy must be strong and when it can be weak. Weak oligarchy need not be undesirable. 1 Introduction A social welfare function is a mapping from proﬁles of individual preference order- ings (reﬂexive, transitive and complete binary relations) into a social ordering of the alternatives (Sen 1970, pp. 8–9). Arrow’s (1963) impossibility theorem demonstrates that the only social welfare functions that satisfy unrestricted domain, independence We are grateful to participants at the 13th Meeting of the
Social Choice and Welfare – Springer Journals
Published: Jun 4, 2018
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