4 - Justifying Bayesianism

Summary

What reasons do we have for accepting or rejecting Bayesian decision theory? Empirical theories stand or fall on the basis of their ability to handle the facts; above all, by the quality of their explanations and the accuracy of their predictions. As an empirical theory of judgement and decision making, subjective expected utility theory has endured a good deal of criticism in the last 30 years or so, with a range of experimental results suggesting that it is a poor predictor of people's behaviour. On the other hand, none of the main rival empirical theories seem to do much better when confronted with data other than that used to generate them; according to some studies they do worse.1 So, while there is every reason to be cautious about the theory's predictive abilities in a wide range of cases, there is as yet no good reason to abandon it entirely.

It is as a normative theory, however, that we are interested in the problem of justifying acceptance of Bayesian decision theory. Although normative theories cannot be refuted by direct appeal to the facts, the general principles of a normative theory can be assessed in a similar way to an empirical one. A scientific theory will have its laws assessed by deriving predictions about concrete cases and then testing to see whether the predictions turn out to be true or not. A normative theory doesn't make predictions, but it will have implications for concrete situations which can be compared with our judgements about what is correct in those cases. A theory of valid inference, for instance, can be tested against concrete instances of inferences that we are inclined (or otherwise) to make: a theory of grammar against sentences that competent speakers find acceptable; and so on.

The fundamental lesson of the Quine–Duhem problem – that the falsity of a scientific hypothesis can rarely be deduced from a set of observations – applies equally to normative theories. When general normative principles clash with our judgements regarding a concrete case, all that follows is that we cannot coherently hold onto both.