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Thursday, May 14, 2020

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.

Posted by Adam Kolber on May 14, 2020 at 08:00 AM in Symposium: Legal Discontinuities | Permalink


Yes Omer, although, not in too many extreme cases, highly scrutinized or reported in media, when the public opinion, is agitated by horrors, demanding justice on every cost, almost lynch. Then, such relative attitude,can become very nasty.


Posted by: El roam | May 15, 2020 11:05:51 AM

Many thanks, Al.
I recognize the problem you're referring to, mainly that by awarding remedies based on the average of all possible factual states instead of picking one most likely state might seem counterintuitive or at odds with public sentiment.
I would argue, however, that the current state is not better. The public sees through the Charade. Everyone knows that the factfinder is uncertain about the facts. A decision that acknowledges this unavoidable state of uncertainty may seem more just than the alternative.

Posted by: Omer Pelled | May 15, 2020 10:32:15 AM

Correct Omer, there are many reasons for it. But the main one, is that it does run against basic principles of how to treat innocence or guilt. At the outset, each party, claims typically, that he is totally just and innocent and victimized in fact ( whether civil dispute, or criminal, or even administrative). The court must prevail. Must satisfy fundamental principals of justice, seeking truth, and publicly so.

So, instead of sending message of, wrong from right, in the plain meaning of it, such relative notion, may hurt the sense or public sentiments. May be perceived as wrong education. Bad service to justice.

Justice, should be served, not only in substance terms, but, should be also demonstrated publicly.Should be seen as such.

I am not sure, that you would comply with such reasoning, yet, that is the perception of the system not once.


Posted by: El roam | May 14, 2020 11:06:54 AM

Distribution according to guilt assumes full information - the court knows how each party behaved, and how said behavior contributed to the accident, and awards damages to reflect their relative fault.
this is similar but different from awarding partial compensation to accommodate factual uncertainty.

Posted by: Omer Pelled | May 14, 2020 10:43:40 AM

Correct Adam, but it does exist anyway. In many judiciaries, there is distribution of guilt by the way. Means:

Once, all factual and legal issues has been established, the judge, may grant compensation to the damaged person, but, deduct, his guilt ( if there is) in accordance. So, if the person damaged, bears some guilt ( suppose he had taken risk, undue one, and bears guilt due to it) the judge may decide:

That 20 percent, on him. The rest on the wrongdoer. So, I think such notion, fits your perception about continuity/ discontinuity, or beyond threshold attitude.

Posted by: El roam | May 14, 2020 9:40:52 AM

El, Thank you for your comment!
you are right that in many tort cases the main factual dispute is over factual causation. nevertheless, the argument stands - think about your micro-trauma example - after going over all the evidence, the trier of facts faces two possible states - either the cumulative effect of the micro-trauma caused the harm or it did not. Furthermore, the factfinder can state her beliefs regarding the probability of each state, given the evidence.
You can think of it as a binary random variable with a Bernoulli distribution, which takes the value 1 (full recovery) if causation exists with probability P or the value 0 (no recovery) if it does not, with probability (1-P).
The median of the random variable is either 1 or 0, according to the more probable outcome. that is - the factfinder would decide that either the micro-trauma caused the injury, or that it did not, and award accordingly.
The weighted mean of the random variable is -P. By awarding damages according to the mean, the court would award partial compensation according to the probability that causation exists.

Posted by: Omer Pelled | May 14, 2020 9:32:37 AM

Interesting. Just to draw your attention, that typically, we know who was the wrongdoer ( in tort claims).Whether he was negligent, also not always a real issue. This is because, it is typically based on well recognized standards ( of precaution). What constitutes more frequently, the legal problem, is the nexus, or causation ( between the wrongdoing and the damage ). Just as illustration:

Micro-trauma for example:

A person, is slightly damaged, but many times, or, spread all over years ( sitting or standing too much, or slight strikes at the back , while driving) So, finally, one micro one, couldn't constitute damage per se, but, over the years, with hundreds or thousands, could indeed. Then causation is more problematic for proving it. Or:

Radiation Simply. It takes time. It is invisible. So, we don't know for example, whether exposure over years, has created one tumor, or for other reasons, hard to prove.


Posted by: El roam | May 14, 2020 8:56:49 AM

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