580

**Reasoning to a Foregone Conclusion**

**J.B. Kadane, M.J. Schervish, and T. Seidenfeld**

### Abstract:

*When can a Bayesian 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 H will be
greater than its prior probability? We discuss an elementary result
which establishes sufficient conditions under which this cannot
occur. We illustrate how, when the sufficient conditions fail, because
probability is finitely but not countably additive, it may be that a
Bayesian can design an experiment to lead his/her posterior
probability into a foregone conclusion. The problem has a decision
theoretic version, which we discuss from several perspectives. Also we
relate this issue in Bayesian hypothesis testing to various concerns
about ``optimal stopping.''
**
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