Should Trial Outcome Be Based on the Median or the Mean? (by Omer Pelled)

Posted on behalf of Omer Pelled as part of the Legal Discontinuities Online Symposium:

Factual uncertainty is a frequent problem in legal disputes. Whenever the parties disagree on the facts, the trier of facts, be it a jury or judge, must examine evidence and infer the facts. Commonly, the evidence provides limited information, making it impossible to determine the relevant facts with certainty. Thus, based on the evidence, the factfinder might consider several alternative factual states, each of which can be associated with a different likelihood.

In civil disputes we usually think that factfinders are required to adopt the most likely factual state, and ignore the rest, under the preponderance of the evidence rule. In statistics, this rule is equivalent to choosing the median value to describe the center of a distribution. Interestingly, when confronted with actual statistical data, for example when examining the lost income of an injured child, courts adopt another central value – the weighted mean. These two options – the median and the mean – can be implemented to any factual dispute. For example, in a tort case if the jury decided that the probability that the defendant was negligent is 40%, awarding zero damages is equivalent of choosing the median, and awarding damages equal to 40% of the harm is equivalent to awarding the weighted mean. 

The choice between the median or mean is not limited to civil disputes. In criminal law, for example, when the punishment is determined by a three-judge panel, the law states that the punishment is determined by the median judge. E.g., is two judges supported a punishment of one year imprisonment, and the third thinks that the defendant should be imprisoned for four years, the punishment would be one year imprisonment (the median) and not two years (the weighted mean).

Each measure of central location – the mean or the median – has some appealing attributes. The median minimizes errors (in absolute values), making factual decisions most accurate. Furthermore, the median is much less sensitive to outliers, disincentivizing the parties from making wild factual claims. The weighted mean however, in many cases, creates better incentives regarding primary behavior.

Notice that the choice between median or mean has an important implication regarding the continuity or discontinuity of legal outcomes - When courts adopt the median, legal outcomes become less sensitive to changes in the probabilities, leading to the “all-or-nothing” feature usually associated with the legal process, especially when the court considers only two possible factual states. The value of the weighted mean, however, changes with every variation of the distribution, making the legal outcome continuous over the changes in probability.  

In a forthcoming article in Theoretical Inquiries in Law, dedicated to discontinuity in the law, I argue that the choice between these two possibilities in civil disputes should depend on the normative goal of private law. If the law is designed to promote corrective justice, courts should always adopt the median outcome. If, however, the goal of private law is to create optimal incentives, it should sometimes adopt the weighted mean. In the article I show under what conditions the mean creates better incentives than the median.

This post is adapted from a draft paper to be published in a forthcoming symposium issue in Theoretical Inquiries in Law. The papers were part of the Legal Discontinuities conference held at Tel Aviv University Law School’s Cegla Center in December 2019.