Abstract
An approach to the social choice problem based on multiple valued logic is suggested. It is assumed that individual preferences are classical binary relations, whereas the social preference is a fuzzy binary relation. The role of Lukasiewicz logic in modelling fuzzy transitive relations is discussed. We argue that this logic is a natural choice for constructing fuzzy social preferences. The paper is concerned with the Arrow’s theory of social welfare functions. Standard conditions of Unrestricted Domain, Pareto, Independence of Irrelevant Alternatives, and Nondictatorship are employed. We show that certain means in fuzzy binary relation spaces are social welfare functions satisfying conditions of the classical Arrow’s Possibility Theorem. It is also shown that collective choice rules given by means are completely characterized by the conditions of Unrestricted Domain, Anonymity, Neutrality, and Positive Responsiveness.
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