Decisive sets,majority voting and the existence of a group preference function

Summary The constitutional process in a democratic society is examined by analysing the role ofdecisive sets in determining the preferences of the entire population. Firstly we consider the properties of sets which emerge from a group preference function satisfying the four conditions set by Arrow. Secondly we reverse the analysis and define first a set of desirable properties of the decisive sets. We then prove that under these fairly general conditions a group preference function exists for which all four of Arrow's conditions are simultaneously satisfied.I wish to thank Peter Newman, an anonymous referee and the editor of this Journal for helpful comments.