In general diagnostic problems multiple disorders can occur simultaneously. AI systems have traditionally handled the potential combinatorial explosion of possible hypotheses in such problems by focusing attention on a few "most plausible" ones. This raises the issue of establishing what makes one hypothesis more plausible than others. Typically a hypothesis (a set of disorders) must not only account for the given manifestations, but it must also satisfy some notion of simplicity (or coherency, or parsimony, etc) to be considered. While various criteria for simplicity have been proposed in the past, these have been based on intuitive and subjective grounds. In this paper, we address the issue of if and when several previously-proposed criteria of parsimony are reasonable in the sense that they are guaranteed to at least identify the most probable hypothesis. Hypothesis likelihood is calculated using a recent extension of Bayesian classification theory for multimembership classification in causal diagnostic domains. The significance of this result is that it is now possible to decide objectively a priori the appropriateness of different criteria for simplicity in developing an inference method for certain classes of general diagnostic problems.