The Arrow general possibility theorem

Democratic voting as meaningless First, irrationalism claims that voting is arbitrary. Second, irrationalism claims that voting is meaningless: even if a voting method survives the first claim as fair, it is yet meaningless, because: (a) the outcome of voting is manipulable; and (b) we cannot know that manipulation occurred since again there is not enough information available from the data of voting to know the preferences underlying choices expressed in voting. The second claim of meaninglessness presents and interprets results of social choice theory. We have already treated (in Chapter 2) the crucial premise that preferences cannot be known from choices. Now, we will begin examination of the premise that voting is manipulable. The premise of manipulability is derived from the possibility of majority cycling as shown by Arrow (1963/1951), the possibility of strategic voting as shown by Gibbard (1973) and Satterthwaite (1975), the possibility of agenda control as shown by McKelvey (1976) and Schofield (1978), and finally the strategic introduction of new issues and dimensions (Riker 1982). Over the next three chapters, we discuss the Arrow theorem. In this chapter, we review the origins of the Arrow theorem in the ordinalist revolution in economics, and distinguish social choice as welfare economics from social choice as voting theory. Next, we present the contents of the Arrow theorem, followed by discussion of claims of its empirical relevance by Arrow and Riker.