  This paper studies whether Bayesian simultaneous three-way hypothesis tests
can be logically coherent. Two types of results are obtained. First, under the
standard error-wise constant loss, only for a limited set of models can a Bayes
simultaneous test be logically coherent. Second, if more general loss functions
are used, then it is possible to obtain Bayes simultaneous tests that are
always logically coherent. An explicit example of such a loss function is
provided.
