Additive representation of separable preferences on infinite products (original) (raw)
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This paper studies the nature of social welfare orders (SWO) on infinite utility streams, satisfying the efficiency principle known as monotonicity and the consequentialist equity principle known as strong equity. It provides a complete characterization of domain sets for which there exists such a SWO which is in addition representable by a real valued function. It then shows that for those domain sets for which there is no such SWO which is representable, the existence of such a SWO necessarily entails the existence of a non-Ramsey set, a non-constructive object.
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An Excess-Voting Function relative to a pro®le p assigns to each pair of alternatives xY y, the number of voters who prefer x to y minus the number of voters who prefer y to x. It is shown that any non-binary separable Excess-Voting Function can be achieved from a preferences pro®le when individuals are endowed with separable preferences. This result is an extension of Hollard and Le Breton (1996). Soc Choice Welfare (1999) 16: 159±167 Many thanks are due to Jean-FrancË ois Laslier and to two referees for their valuable remarks to improve this paper. I would like to thank Basudeb Chaudhuri for his careful reading.
Arrovian impossibilities in aggregating preferences over non-resolute outcomes
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Given a society confronting a set of alternatives A, we consider the aggregation of individual preferences over the power set A of A into a social preference over A. In case we allow individuals to have any complete and transitive preference over A, Arrow's impossibility theorem naturally applies. However, the Arrovian impossibility prevails, even when the set of admissible preferences over A is severely restricted by strong axioms that relate preferences over A to preferences over A. In fact, we identify a very narrow domain of lexicographic orderings over A which exhibits the Arrovian impossibility in all of its superdomains. As the lexicographic extension we use is compatible with almost all standard extension axioms, we interpret our results as the strong prevalence of Arrow's impossibility theorem in aggregating preferences over sets.
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Let + be an interval order on a topological space (X, r), and let x < L y if and only if [y<z~x+z], and x+2' y if and only if [z <x * z + y]. Then <t and <t" are complete preorders. In the particular case when 4 is a semiorder, let x <t!. y if and only if x.<* _ ~1 and x<"* y. Then 4% is a complete preorder, too. We present sufficient conditions for the existence of continuous utility functions representing < t , -X 2 * and <'1 , by using the notion of strong separability of a preference relation, which was introduced by Chateauneuf (Journal of Mathemarical Economics, 1987, 16, 139-146). Finally, we discuss the existence of a pair of continuous functions u, u representing a strongly separable interval order + on a measurable topological space (X, T, CL, A).
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Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019), 2019
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