Hyper-Stable Social Welfare Functions

Jean Lainé (1) , Ali Ihsan Ozkes (1, 2) , Remzi Sanver (1)

1 Department of Economics, Bilgi University
2 X-DEP-ECO - Département d'Économie de l'École Polytechnique

We introduce a new consistency condition for neutral social welfare functions, called hyperstability. A social welfare function a selects a complete weak order from a profile PN of linear orders over any finite set of alternatives, given N individuals. Each linear order P in PN generates a linear order over orders of alternatives,called hyper-preference, by means of a preference extension. Hence each profile PN generates a hyper-profile ˙PN. We assume that all preference extensions are separable: the hyper-preference of some order P ranks order Q above order Q0 if the set of alternative pairs P and Q agree on contains the one P and Q0 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 a is hyper-stable (resp. Kemeny-stable) if at any profile PN, at least one linearization of a(PN) is ranked first by a( ˙PN), where ˙PN is any separable (resp. Kemeny) hyper-profile induced from PN. We show that no scoring rule is hyper-stable, and that no unanimous scoring rule is Kemeny-stable, while there exists a hyper-stable Condorcet social welfare function.

Mots clés: Hyperpreferences; Kemeny distance; Social Welfare Functions; Stability

Domaines: Economies et finances

Jean Lainé, Ali Ihsan Ozkes, Remzi Sanver. Hyper-Stable Social Welfare Functions. 2014. ⟨hal-00871312v2⟩