The empirical literature seeking to understand judicial outcomes continues to develop and mature. Judge Posner's book, How Judges Think (2010), places Bayes' Theorem front-and-center. In a qualitative study of judges (N=30), Jack Knight (Duke), Mitu Gulati (Duke), and David Levy (Duke, and a former federal judge) set out to assess what Posner's book assumes. In How Bayesian Are Judges?, the authors conclude: "not at all." The abstract follows.
"Richard Posner famously modeled judges as Bayesians in his book, "How Judges Think?". A key element of being Bayesian is that one constantly updates with new information. This model of the judge who is constantly learning and updating, particularly about local conditions, also is one of the reasons why the factual determinations of trial judges are given deference on appeal. But do judges in fact act like Bayesian updaters? Judicial evaluations of search warrant requests for probable cause provides an ideal setting to examine this question because the judges in this context have access to information on how well they did on their probabilistic calculations (the officers who conduct the search have to file, in every case, a "return" detailing what was found in their search). Based on detailed interviews with thirty judges our answer to the "How Bayesian are Judges?" question is: Not at all. The puzzle we are left with, given that acting in a Bayesian fashion is normal behavior for the rest of us, is why we get these puzzling results for judges in the search warrant context?"