Nathan Schachtman, Esq., PC* emailed me the following interesting query a while ago:
When I was working through some of the Bayesian in the law issues with my class, I raised the problem of priors of 0 and 1 being off “out of bounds” for a Bayesian analyst. I didn’t realize then that the problem had a name: Cromwell’s Rule.
My point was then, and more so now, what is the appropriate prior the jury should have when it is sworn? When it hears opening statements? Just before the first piece of evidence is received?
Do we tell the jury that the defendant is presumed innocent, which means that it’s ok to entertain a very, very small prior probability of guilt, say no more than 1/N, where N is the total population of people? This seems wrong as a matter of legal theory. But if the prior = 0, then no amount of evidence can move the jury off its prior.
*Schachtman’s legal practice focuses on the defense of product liability suits, with an emphasis on the scientific and medico-legal issues. He teaches a course in statistics in the law at the Columbia Law School, NYC. He also has a legal blog here.
Nathan: Notice too that a prior of .5 in innocence is rather informative–overly so, it seems to me. Bottom line: the jury should not start with a prior for guilt, but be open to a relevant and unbiased scrutiny of the evidence in accord with “innocent until proved guilty”*.
* Be it BARD or POE or other legal standard for the case (see comment to Corey)