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

The constitutional process in a democratic society is examined by analysing the role of decisive 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.