A Brief Criminological Comment on Bill Cosby and Bill Clinton

Bayes’ Rule (a simple algebraic transformation of Bayes’ Theorem that converts probabilities into odds) supplies the appropriate guidance with respect to how recently announced evidence against Bill Cosby should update our belief with respect to his guilt or innocence. 

The Rule says that, broadly speaking, we should update our beliefs via a likelihood ratio that is formed by dividing the probability that X number of women (substitute for X however many women have testified against Cosby) wouldn't lie if Cosby is guilty by the probability that X number of women would lie if Cosby is innocent.

The language “broadly speaking” was included since the probabilities are clearly conditioned on many factors, such as the personality characteristics, the clustering in time of the accusations, and so on.  With respect to factors such as personality characteristics and assuming even minimal independence, the greater the number of women that accuse Cosby, the greater the likelihood that what any individual woman says is true.

Thus, strictly speaking, we are counseled to divide compound conditional probabilities.  Ceteris paribus, the wider the range of walks of life of women that accuse Cosby is, the greater the likelihood that Cosby is guilty becomes.

It will come as no surprise to honest people that at least with respect to the raw numbers and personality standards, Bill Clinton may well compare, under the nearly universally accepted Bayesian standard, quite unfavorably to even Bill Cosby in terms of the probability of guilt (see, for example, this Free Republic thread). 

Of course, Bill Cosby’s wife isn’t about to run for president, and Bill Clinton was a Democrat.

Do Democrats hate women?

Dr. Jason Kissner is associate professor of criminology at California State University, Fresno.  You can reach him at crimprof2010@hotmail.com.