WHEN SEVERAL BAYESIANS AGREE THAT THERE WILL BE NO REASONING TO A FORGONE CONCLUSION

When can a Bayesian investigator select an hypothesis H and design an experiment (or a sequence of experiments) to make certain that, given the experimental outcome(s), the posterior probability of It will be l ower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a fore gone conclusion cannot occur. Through an example, we discuss how this result extends to the perspective of an onlooker who agrees with the i nvestigator about the statistical model for the data but who holds a d ifferent prior probability for the statistical parameters of that mode l. We consider, specifically, one-sided and two-sided statistical hypo theses involving i.i.d. Normal data with conjugate priors. In a conclu ding section, using an ''improper'' prior, we illustrate how the prece ding results depend upon the assumption that probability is countably additive.