Invoking Cartesian Product Structure on Social States : New Resolutions of Sen's and Gibbard's Impossibility theorems.
Résumé
The purpose of this article is to introduce a Cartesian product struc- ture into the social choice theoretical framework and to examine if new possibility results to Gibbard's and Sen's paradoxes can be de- veloped 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. Fi- nally we compare the advantages of our approach to other solutions proposed in the literature for both impossibility theorems.