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## A Primer on Rational Decision Making

Introduction (Via Ken Binmore @ Princeton)

A rational number is the ratio of two whole numbers. The ancients thought that all numbers were rational, but Pythagoras’s theorem shows that the length of the diagonal of a square of unit area is irrational. Tradition holds that the genius who actually made this discovery was drowned, lest he shake the Pythagorean faith in the ineffable nature of number. But nowadays everybody knows that there is nothing irrational about the square root of two, even though we still call it an irrational number.

There is similarly nothing irrational about a philosopher who isn’t a rationalist. Rationalism in philosophy consists of arriving at substantive conclusions without appealing to any data. If you follow the scientific method, you are said to be an empiricist rather than a rationalist. But only creationists nowadays feel any urge to persecute scientists for being irrational.

What of rational decision theory? Here the controversy over what should count as rational is alive and kicking. Bayesianism.

Bayesianism is the doctrine that Bayesian decision theory is always rational. The doctrine entails, for example, that David Hume was wrong to argue that scientific induction can’t be justified on rational grounds. Dennis Lindley (1988) is one of many scholars who are convinced that Bayesian inference has been shown to be the only coherent form of inference.

The orthodoxy promoted by Lindley and others has become increasingly claustrophobic in economics, but Gilboa and Schmeidler (2001) have shown that it is still possible to consider alternatives without suffering the metaphorical fate of the Pythagorean heretic who discovered the irrationality of √2. Encouraged by their success, I follow their example by asking three questions:What is Bayesian decision theory? When should we count Bayesian decision theory as rational? What should we do when Bayesian decision theory isn’t rational?