Bayes 8: three additional features of Bayesian reasoning

Note: This is my eighth blog post in a month-long series on the basics of Bayesian probability theory

Thus far, by way of background, I have explained how Bayesian methods help us “test” the accuracy of our judgements, I have explained the logic of Bayes’ theorem (the equation in my “Bayes 6” blog post), and I have defined the technical concepts of sensitivity and specificity (Bayes 7). Here, before presenting my Bayesian model of litigation, I wish to make three more points about Bayesian reasoning:

First, the basic idea behind Bayes’s theorem is the idea that the conditional probability of event A, such as a defendant being found guilty, given the occurrence of another event B, the defendant’s commission of a wrongful act, not only depends on the strength of the relationship between A and B; it also depends on the prior probability of each event. Thus, according to Bayes’s theorem, the probability that a defendant in a civil action will be found liable (for tort, breach of contract, etc.), given that a plaintiff has brought an action against the defendant, will generally depend on two sets of probabilities: (i) the likelihood of the defendant being found liable given the strength of plaintiff’s claim, and (ii) the prior probabilities or success rates of plaintiffs and defendants generally.

Secondly, the probability of some event A conditional on some other event B is not the same as the conditional probability of event B given event A, or stated formally: Pr(A|B) is not equal to Pr(B|A). (See image below.) For example, the probability that a defendant will be found civilly or criminally liable, given that the defendant has committed some wrongful act–such as the commission of a tort, a breach of contract, a crime, etc.–, is not the same as the probability that the defendant’s wrongful conduct will result in liability, given that the plaintiff brings an a civil or criminal action against the defendant.

Lastly, it is also worth noting that Bayesian methods do not rely on any unrealistic assumptions about human rationality (unlike the standard assumptions of game theory or economics), nor does my Bayesian model of litigation require any detailed information about any particular rules of procedure or about substantive legal doctrine. Since such procedural rules and legal doctrines are often unclear, contested, and subject to manipulation, one can begin to appreciate the advantage of the Bayesian approach to civil and criminal litigation. In place of judicial hunches, indeterminate verbal arguments, or the inevitable ‘thrust and parry’ of competing interpretations of imperfect rules and doctrines (Karl Llewellyn, The Common Law Tradition (Little Brown 1960), pp. 522-529), my Bayesian approach to the litigation game attempts to understand the legal process from a probabilistic perspective.

About F. E. Guerra-Pujol

When I’m not blogging, I am a business law professor at the University of Central Florida.
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