Invoking 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 theoretic framework and to examine if new possibility results to Gibbard’s and Sen’s paradoxes can be developed thanks to it. According to us, Cartesian product structure is a pertinent way to describe individual rights in social choice theory since it discriminates the personal features comprised in each social state. Consequently, the concept of personal protected sphere is clarified. 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 with other solutions used in the literature for both impossibility theorems.