Arrow’s Theorem

The basic results of social choice, Condorcet’s Paradox and Arrow’s Theorem, show that the Condorcet criterion is not sufficient, and that, more generally, all methods of collective choice are bound to violate some plausible-looking conditions. In this chapter all the conditions used in the proof of Arrow’s Theorem are discussed one by one. I review the criticisms and proposals put forth in the literature on the Theorem, and try to show that in the context of democratic decision-making, the conditions are, indeed, prima facie plausible. The Independence condition is the least transparent and most misunderstood of all the Arrovian conditions. I show that many authors, including Arrow himself, have partly misunderstood the nature of the condition. These misunderstandings are behind the widespread belief that, according to the social choice theory, we have to face a tragic choice between “dictatorship and democratic chaos”. Various forms of strategic behavior are discussed. Although such behavior cannot always be characterized as dishonest, the possibility of strategic voting constitutes a potential problem of normative political theory.