A Bayesian assessment of the probability that the defendant in a criminal trial is guilty depends on the presumed base rate for guilt and the estimated likelihoods of the evidence. This article explores how the base rate shall be determined. Bayesian scholars have recommended a base rate of 1/N, where N is the number of ‘possible perpetrators’, but it is unclear how the reference class of possible perpetrators shall be defined. Several solutions are explored, and it is demonstrated that each solution leads to serious sacrifices in some fundamental principle of criminal justice. Some solutions lead to arbitrary assessments, or assessments that deviate from the facts. Other solutions fail to uphold an acceptable ratio between wrongful acquittals and wrongful convictions.
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