Rational choice theory is the descendant of earlier philosophical political economy. Its core is the effort to explain and sometimes to justify collective results of individuals acting from their own individual motivations – usually their own self interest, but sometimes far more general concerns that can be included under the rubric of preferences. The resolute application of the assumption of self-interest to social actions and institutions began with Hobbes and Machiavelli, who are sometimes therefore seen as the figures who divide modern from early political philosophy. Machiavelli commended the assumption of self interest to the prince; Hobbes applied it to everyone. Their view of human motivation went on to remake economics through the work of Mandeville and Adam Smith. And it was plausibly a major factor in the decline of virtue theory, which had previously dominated ethics for many centuries.
Game theory was invented almost whole by the mathematician von Neumann and the economist Morgenstern during the Second World War. Their theory was less a theory that made predictions or gave explanations than a framework for viewing complex social interactions. It caught on with mathematicians and defence analysts almost immediately, with social psychologists much later, and with economists and philosophers later still. But it has now become almost necessary to state some problems game theoretically in order to keep them clear and to relate them to other analyses. The game-theory framework represents ranges of payoffs that players can get from their simultaneous or sequential moves in games in which they interact. Moves are essentially choices of strategies, and outcomes are the intersections of strategy choices. If you and I are in a game, both of us typically depend on our own and on the other’s choices of strategies for our payoffs.
The most striking advance in economics in the twentieth century is arguably the move from cardinal to ordinal value theory. The change had great advantages for resolving certain classes of problems but it also made many tasks more difficult. For example, the central task of aggregation from individual to collective preferences or utility could be done – at least in principle – as a matter of mere arithmetic in the cardinal system. In that system, Benthamite utilitarianism was the natural theory for welfare economics. In the ordinal system, however, there was no obvious way to aggregate from individual to collective preferences. We could do what Pareto said was all that could be done: we could optimize by making those (Pareto) improvements that made at least one person better off but no one worse off. But we could not maximize. In his impossibility theorem, Arrow (1951) showed that, under reasonable conditions, there is no general method for converting individual to collective orderings.
After game theory and the Arrow impossibility theorem, the next major contribution to rational choice theory was the economic theory of democracy of Downs (1957). Downs assumed that everyone involved in the democratic election system is primarily self interested. Candidates are interested in their own election; citizens are interested in getting policies adopted that benefit themselves. From this relatively simple assumption, however, he deduced two striking results that ran counter to standard views of democracy. In a two-party system, parties would rationally locate themselves at the centre of the voter distribution; and citizens typically have no interest in voting or in learning enough to vote in their interests even if they do vote.
The problem of the rational voter can be generalized. Suppose that I am a member of a group of many people who share an interest in having some good provided but that no one of us values its provision enough to justify paying for it all on our own. Suppose further that, if every one of us pays a proportionate share of the cost, we all benefit more than we pay. Unfortunately, however, my benefit from my contribution alone might be less than the value of my contribution. Hence, if our contributions are strictly voluntary, I may prefer not to contribute a share and merely to enjoy whatever follows from the contributions of others. I am then a free-rider. If we all rationally attempt to be free-riders, our group fails and none of us benefits.
A potentially disturbing implication of the game theoretic understanding of rationality in interactive choice contexts, of the Arrow impossibility theorem, of the economic theory of democracy and of the logic of collective action is that much of philosophical democratic theory, which is usually normative, is irrelevant to our possibilities. The things these theories often tell us we should be doing cannot be done.