Invoking a cartesian product structure on social states: new resolutions of Sen's and Gibbard's impossibility theorems

The purpose of this article is to introduce a Cartesian product structure into the social choice theoretical framework and to examine if new possibility results to Gibbard's and Sen's paradoxes can be developed thanks to it. We believe that a Cartesian product structure is a pertinent way to describe individual rights in the social choice theory since it discriminates the personal features comprised in each social state. First we define some conceptual and formal tools related to the Cartesian product structure. We then apply these notions to Gibbard's paradox and to Sen's impossibility of a Paretian liberal. Finally we compare the advantages of our approach to other solutions proposed in the literature for both impossibility theorems.

Smith and Rawls share a room

We consider one-to-one matching (roommate) problems in which agents (students) can either be matched as pairs or remain single. The aim of this paper is twofold. First, we review a key result for roommate problems (the ``lonely wolf'' theorem) for which we provide a concise and elementary proof. Second, and related to the title of this paper, we show how the often incompatible concepts of stability (represented by the political economist Adam Smith) and fairness (represented by the political philosopher John Rawls) can be reconciled for roommate problems.