Mandy Rice-Davies and the Non-diagnostic Evidence

Mandy Rice-Davies, who died yesterday aged 71, is known primarily for her pithy contribution to popular information theory literature. When told in court that Lord Astor had denied having an affair with her, she replied simply: "He would, wouldn't he?"

The point is that if the conditional likelihood of any piece of evidence (Lord Astor's denial of having met Mandy) is the same (100%) under a given hypothesis (Lord Astor met Mandy) as under its negation (Lord Astor did not meet Mandy), this evidence will be non-diagnostic with respect to the hypothesis, as a straightforward implication of Bayes' Theorem. Mandy Rice-Davies' formulation is of course superior in brevity.