2008): “Symmetry of Evidence without Evidence of Symmetry

The de Finetti Theorem is a cornerstone of the Bayesian approach. Bernardo [4, p. 5] writes that its message is very clear: if a sequence of observations is judged to be exchangeable, then any subset of them must be regarded as a random sample from some model, and there exists a prior distribution on the parameter of such model, hence requiring a Bayesian approach.We argue that while exchangeability, interpreted as symmetry of evidence, is a weak assumption, when combined with subjective expected utility theory, it implies also complete con\u85dence that experi-ments are identical. When evidence is sparse, and there is little evidence of symme-try, this implication of de Finettis hypotheses is not intuitive. This motivates our adoption of multiple-priors utility as the benchmark model of preference. We pro-vide two alternative generalizations of the de Finetti Theorem for this framework. A model of updating is also provided