The Bayesian approach to litigation
In contrast to previous approaches to legal studies, our approach is Bayesian or probabilistic, since our model of the litigation game is derived from Bayes’ theorem or Bayes’ rule of conditional probability. In summary,Bayes’ theorem can be expressed in algebraic terms as follows:
Pr(A|B) = ([Pr(B|A)] × [Pr(A)]) ÷ Pr(B)
Explained in words, Bayes’s formidable-looking formula may be broken down into the following five parts:
(i) The term on the left-hand side of the equation, Pr(A|B), refers to the conditional probability (or posterior probability) of event A, given the occurrence of event B.
(ii) The right-hand side of the equation is a fraction: the numerator contains two parts, Pr(B|A) × Pr(A), while the denominator consists of one term, Pr(B).
(iii) The first term in the numerator, Pr(B|A), refers to the conditional probability of event B, given the occurrence of event A.
(iv) The second term in numerator, Pr(A), refers to the prior probability (or unconditional probability) of event A, that is, the probability of A in the absence of any information about event B.
(v) Lastly, the denominator, Pr(B), is the prior probability (or unconditional probability) of event B in the absence of any information about event A.
In the remainder of this paper, we will equate the term ‘guilty’ (or the letter ‘A’) with the event that the defendant in a particular litigation game has committed a wrongful or unlawful act, that is, an act for which he should be civilly or criminally liable. In addition, we will equate the term the symbol + (or the letter ‘B’) with the event that the defendant is actually found liable at trial for the commission of a civil or criminal wrongful act. In other words, B or + is the probability of a positive litigation outcome from the perspective of the moving party in the litigation game, the plaintiff (in a civil trial) or the prosecutor (in a criminal trial). In other words, the main idea here is that the moving party—the plaintiff or prosecutor, as the case may be—obtains a favorable or positive outcome, which is denoted by the symbol +, when the defendant is found civilly or criminally liable at trial. Our Bayesian model of the litigation game thus poses the following fundamental question: what is the posterior probability that a defendant in a civil or criminal trial will be found liable, given that the defendant has not, in fact, committed any wrongful act?
At this point, we must introduce and formally define the technical concepts of ‘sensitivity’ and ‘specificity’. In the context of our Bayesian model of the litigation game, these concepts refer to the underlying reliability of a civil or criminal trial to distinguish between guilty and innocent defendants. Since civil or criminal liability should be imposed only on guilty defendants, i.e., defendants who have in fact committed an unlawful wrongful act, sensitivity and specificity are thus important values. Specifically, the ‘sensitivity’ of the litigation game—written as Pr(B|A) or, in our model, Pr(+|guilty)—indicates how well a civil or criminal trial is able to correctly impose liability on guilty defendants. In summary, this measure is defined formally as the probability of a positive litigation outcome (i.e., liability imposed on the defendant, which represents a ‘positive’ outcome from the plaintiff’s or prosecutor’s perspective), given that the defendant being tried has actually committed an unlawful wrongful act.
By contrast, the ‘specificity’ of the litigation game, which may be written as Pr(–|innocent), reflects how well a civil or criminal trial is able to correctly screen out innocent defendants. This measure is defined formally as the probability of a negative litigation outcome (i.e., no liability imposed on the defendant, which represents a ‘negative’ outcome from the perspective of the moving party, plaintiff or prosecutor), given that the defendant has not committed a wrongful act.
Before presenting our Bayesian model in section 4 below, we wish to make three general points about Bayesian reasoning in general. First, the basic idea behind Bayes’s theorem is the idea that the conditional probability of event A, such as a defendant being found liable, 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, notice that 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). For example, the probability that a defendant will be found civilly or criminally liable, given that the defendant has committed some wrongful act (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. We will explore this idea further in section 4 below, when we present our Bayesian model of the litigation game.
Lastly, it is also worth noting that our Bayesian model of the litigation game does not rely on any unrealistic assumptions about human rationality, nor does it 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 hunches, verbal arguments, and the inevitable ‘thrust and parry’ of competing interpretations of indeterminate rules and doctrines, our Bayesian approach to the litigation game attempts to understand the legal process from a probabilistic perspective.
