Nicolas Gabriel Andjiga

Metric rationalization of social welfare functions

Metric rationalization of social decision rules has been intensively investigated when the social outcome is a nonempty subset of alternatives. The present paper proposes a similar framework for social welfare functions (SWFs)—that is when each social outcome is a ranking of alternatives. A metric rationalizable SWF reports as an approximation of the unanimity consensus the relative ranking of any pair of alternatives as in the closest profile where individuals all agree on those alternatives, the closeness being measured with respect to a metric on profiles. Two notions of unanimity are in consideration: top unanimity on an alternative holds when individuals all agree that it is top ranked while pairwise unanimity on a pair occurs when individuals all prefer an alternative to another. Without strong requirements on metrics, characterizations provided in both cases show that metric rationalizations of SWFs are essentially equivalent to the Pareto principle for SWFs. Furthermore, two interesting classes of metric rationalizable SWFs–multi-valued scoring SWFs and pairwise scoring SWFs–are each uniquely identified by means of some appropriate and appealing properties on metrics among which decomposability, neutrality and monotonicity are known.

Binary games in constitutional form and collective choice

Abstract In this paper, we define the notion of binary game in constitutional form. For this game, we define a core and give a necessary and sufficient condition for a game to be stable. We define a representation of a collective choice rule by a binary game in constitutional form and characterize those collective choice rules which are representable. We finally introduce the notion of c -social decision function and characterize, as an application of our theorem on stability of binary constitutional games, the collective choice rules which are c -social decision functions. Our representation of a collective choice rule by a binary game in constitutional form is an obvious improvement of the classical representation by a simple game.

A note on the core of voting games

Abstract In this paper, we give a definition of the dominance relation which is slightly different from the usual dominance relation, in order to explicitly take into consideration the possibility for a voting game (a simple game) to be non-monotonic. In this context, we obtain a characterization of core stable voting games which is a generalization of Nakamuras theorem.

Generalized Binary Constitutions and the Whole Set of Arrovian Social Welfare Functions

Arrows theorem [1963] states that a social welfare function (SWF) that simultaneously satis.es completeness, transitivity, independence of irrelevant alternatives (IIA) and Pareto principle is necessarily dictatorial in the sense that the social decision on any pair of candidates coincides with the strict preference of a fixed individual, the Arrows dictator. When individual preferences are weak orders, no further description is provided on the social outcome as soon as the Arrows dictator is indifferent on a pair of candidates. We provide in the present paper another proof of the Arrows theorem using generalized binary constitutions. Moreover we completely characterize the set of Arrovian SWFs, those are complete and transitive SWFs that satisfy IIA and the Pareto principle.