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Hyper-stable social welfare functions

Abstract : We define a new consistency condition for neutral social welfare functions, called hyper-stability. A social welfare function (SWF) selects a weak order from a profile of linear orders over any finite set of alternatives. Each profile induces a profile of hyper-preferences, defined as linear orders over linear orders, in accordance with the betweenness criterion: the hyper-preference of some order P ranks order Q above order Q’ if the set of alternative pairs P and Q agree on contains the one P and Q’ agree on. A special sub-class of hyper-preferences satisfying betweenness is defined by using the Kemeny distance criterion. A neutral SWF is hyper-stable (resp. Kemeny-stable) if given any profile leading to the weak order R, at least one linear extension of R is ranked first when the SWF is applied to any hyper-preference profile induced by means of the betweenness (resp. Kemeny) criterion. We show that no scoring rule is hyper-stable, unless we restrict attention to the case of three alternatives. Moreover, no unanimous scoring rule is Kemeny-stable, while the transitive closure of the majority relation is hyper-stable. Copyright Springer-Verlag Berlin Heidelberg 2016
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Submitted on : Tuesday, April 11, 2017 - 6:22:18 PM
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Jean Lainé, Ali Ihsan Ozkes, Remzi Sanver. Hyper-stable social welfare functions. Social Choice and Welfare, Springer Verlag, 2016, 46 (1), pp.157-182. ⟨10.1007/s00355-015-0908-1⟩. ⟨hal-01505809⟩



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