The importance of being conservative: Some reflections on human Bayesian behaviour

The phenomenon of conservatism in human Bayesian probability revision is examined for possible adaptive advantages. It is proved that violation of the assumption of conditional independence of data that are not taken into account is likely to result in posterior odds which are too extreme. In addition, any uncertainty in the reliability of the data implies that a Bayesian processor acting on the assumption that the data are reliable will overestimate posterior odds. It is argued that violations of either of the assumptions of conditional independence and reliability of the data are very common. Because of the nature of most inference situations, the existence or magnitude of such violations is often unknown to the processor. Hence conservatism may be interpreted as a desirable mechanism that compensates for the overconfidence inherent in the inference situation. Finally, it is shown that several findings in the Bayesian paradigm may be regarded as outcomes of a process that behaves optimally in view of the violation of these two assumptions.