Two impossibility results in public choice theory

In this paper we deal with some problems of public choice theory. We start with exposition of Arrow's impossibility result which was the starting point in constitution of a whole problematic: the impossibility of existence of a social welfare function. We will mention one solution to the paradox, proposed by Duncan Black, namely, the existence of single-peaked structure of preferences. Then we will pass to another impossibility result that of impossibility of aggregation of judgments over multiple interconnected propositions. We will introduce the idea that this problem represents a larger frame in which the problem of aggregating preferences can be embedded. We will expose one solution to that paradox as well - the existence of unidimensional alignment in the structure of individuals. The main question then is by what means do we achieve this kind of a structure? We will propose a skecth for a future study in which a belief revision theory play important role in finding a solution to these problems.