Hyper-Stable Social Welfare Functions
AbstractWe introduce a new consistency condition for neutral social welfare functions, called hyperstability. A social welfare function ! selects a complete weak order from a profile P of linear orders over any finite set of alternatives. Each linear order p in P generates a linear order over orders of alternatives, called hyper-preference, by means of a preference extension. Hence each profile P generates an hyper-profile ˙P . We assume that all preference extensions are separable: 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 separable extensions contains all Kemeny extensions, which build hyper-preferences by using the Kemeny distance criterion. A social welfare function ! is hyper stable (resp. Kemeny stable) if at any profile P, at least one linearization of !(P) is ranked first by !( ˙P ), where ˙P is any separable (resp. Kemeny) hyper-profile induced from P. We show that no scoring rule is hyper stable, and that no unanimous scoring rule is Kemeny stable, while there exists an hyper stable Condorcet social welfare function.
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Date of creation: 09 Oct 2013
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Hyperpreferences - Kemeny distance - Social Welfare Functions - Stability;
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