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A Derivation of Probabilities of Correct and Wrongful Conviction in a Criminal Trial

This article derives key variables in the analysis of standards of proof in criminal law from basic conditional probabilities. The variables derived are the probability of correct and wrongful conviction, the expected sanction, and society's incarceration costs, while the basic conditional probabilities are the probability of observing (any given) evidence against individual i given that individual j committed the crime (for any j including j equal to i. The variables are derived from the conditional probabilities as a function of the standard of the proof using simple Bayesian updating.