Social choice and Lukasiewicz logic

Abstract

An approach to the social choice problem based on multiple valued logic is suggested. It is assumed that individual preference are classical binary relations, whereas the social preference is a valued binary relation. The role of Lukasiewicz logic in modelling valued transitive relations is discussed. We argue that this logic is a natural choice for contructing valued social preference. The paper is concerned with 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 binary relations 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 Unrestrict Domain, Anomymity, Neutrality, and Positive Responsiveness.