Of course. However, such reasoning can and should be applied differently. Ideally, a scientist is not attached to a hypothesis, but rather regards those as provisionally true which have a certain probability. If the opposite hypothesis had the same probability, he would have the same confidence in it. In a legal situation, as a matter of principle on the hypothesis “defendant is guilty” can be proved at all (with some level of confidence); “defendant is innocent” cannot be proved, but rather is assumed if “defendant is guilty” has a low probability, where “low” here is actually quite high, since it is generally regarded that it is worse to punish an innocent defendant wrongly rather than let a guilty defendant go.

Of course, these are just general remarks and have no direct bearing on the case discussed.

]]>I actually have no opinion about whether the judge’s ruling was right or wrong, not having studied the merits of the particular case. What I do say is that the stated logical basis for the ruling is incoherent. The final conclusion may be right for other reasons.

]]>First, it might be reasonable to consider an additional catch-all hypothesis for the “unknown unknowns.” If the argument is that A is probably true because, even though it is unlikely, the alternatives are less likely, I would want considerable assurance that I had exhausted the alternatives.

Secondly, we should not stop after computing the posterior probabilities, but also consider the asymmetric costs of wrongful conviction relative to failure to convict.

Maybe the judge’s requirement to consider the likelihood of A in absolute terms, without considering the likelihood of B and C, is a heuristic that at least approximates a Bayesian decision-making process that considers “unknown unknowns” and asymmetric costs.

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