I think Bayesian justice would result in a larger percentage of defendants being found guilty at trial, because instead of "guilty beyond a reasonable doubt", the prosecution would only have to prove "expected value of conviction > expected value of no conviction".

EDIT: On the other hand, if someone committed an awful crime, but can convince you that they won't do it again; or if they might, but they pay a lot of taxes; let them go.

If the standard used is value to society, then if the defendant is judged to have no value to society, and executions are cheap, then convict and execute if p(defendent will commit more crime) > 0. If the defendant has a net cost to society, execute regardless.

If government functions via redistribution of taxation, then most people have a negative value to society, since most of the government's income comes from the top 10% or so. Therefore, execute the bottom 90%. Tax, and redistribute among the survivors. Again, the bottom 90% has negative value. Execute. Repeat. You eventually converge on a single citizen, whose expected contribution to society (minus his cost to society) is zero by some measures. At that point, flip a coin.