Bounding reasonable doubt: implications for plea bargaining

A bound for reasonable doubt is offered based on the cost of type I and type II errors. The bound increases with the punishment, hence its use as a conviction threshold may leave too many offenders of severe crimes at large. Plea bargaining addresses this limitation but introduces strategic interaction between concerned parties. Considering strategic interaction between defendants and judge/jury, it is shown that to any plea offer there corresponds a unique equilibrium. Moreover, all equilibria share the same conviction threshold, given by the reasonable doubt bound. The latter property ensures that the plea bargaining procedure is consistent with the ‘equality before the law’ principle. The former property (that to any plea offer there corresponds a unique equilibrium) bears implications for the design of plea bargain schemes.