Science and numbers go hand-in-hand. As the foundation of science is the use of empirical research in a search for knowledge, to interpret and apply science, one requires at least a basic understanding of mathematics and its close cousin statistics. And because the use of numbers has been shown to be as equally persuasive in both science and propaganda, one needs to learn to evaluate the use of numbers with a critical eye—especially when using numbers to decide a legal issue. Early in my academic career, a statistics professor told me to never forget that statistics never lie but that only liars use statistics. Of course that was hyperbole, but the admonition has served me well through the years.
A couple of mathematically astute legal commentators have lamented the deficiency in mathematics in the legal profession:
“The fact that many judges suffer from an estrangement from, resistance to, and incapacity in mathematics should not be surprising. This condition, after all, afflicts most lawyers, as it does most Americans. One need not conduct a study to know that law students are typically smart people who do not like math. Law professors are of little help to their students, because legal academics tend not to have a background in, or use statistical analysis, or are unfamiliar with empirical data collection. Indeed, it is clear that there is a prevalent (and disgraceful) math-block that afflicts the legal profession.”[i]
There are a couple of good books I can recommend related to the use of mathematics in the law. The first is Calculated Risks-How to Know When Numbers Deceive You, by Gerd Gigerenzer. This is an excellent book with many examples related to the law. The other one is Proofiness – The Dark Arts of Mathematical Deception by Charles Seife. Seife covers the use of math in science, elections, and propaganda.
There is one illustration of the use of statistics that both books discuss which is called either the prosecutor’s or defense attorney’s fallacy—depending on which side is using it. The example that is referenced in both books comes from the OJ Simpson trial where a defense attorney attempted to preclude any evidence of former domestic violence on the grounds that it was irrelevant.
The argument went something like this. A past domestic violence perpetrator is on trial for now killing his victim. Statistics show that there is only a 1 in 5,000 chance that a defendant with a history of domestic violence with a victim will kill his victim. Therefore, the defense attorney argues, there is only a 1 in 5,000 chance that his or her client has killed his victim, making any evidence of domestic violence irrelevant.
The error in this example comes in confusing the odds that a defendant with a domestic violence history with his victim will murder his victim with the odds that given that his victim is murdered, that a defendant with a domestic violence history with the victim was the murderer. A murdered domestic-violence victim is relatively rare, but once a domestic violence victim has been murdered, the odds are much higher that the former domestic violence perpetrator was the murderer.
The way to look at this is that a 1 in 5,000 chance that a defendant with a history of domestic violence with his victim will kill his victim means that for every 100,000 victims of domestic violence, 20 will be murdered by individuals who had previously perpetrated a domestic violence incident on the victim. If we also know that an additional 5 women per 100,000 will be murdered by someone other than someone who had previously perpetrated a domestic violence incident on the victim, then we know 25 women per 100,000 (20 plus 5) will be murdered. Of the 25 women who are murdered, 20 will have been killed by a former domestic violence perpetrator, or 20 out of 25 women who are murdered (80%) are murdered by a former domestic violence perpetrator —a chance far higher than the 1 in 5,000 chance argued by the defense attorney.
Meyerson et al (2010) (which I also recommend), as well as the authors of the two books referenced above, argue that people, including judges, are quite easily swayed by mathematical arguments. Oliver Wendell Holmes Jr. once wrote that numbers “flatter that longing for certainty and for repose which is in every human mind. But certainty generally is illusion, and repose is not the destiny of man.”[ii]
Meyerson et al (2010) argue that judges’ misunderstanding of mathematics and statistics sometimes result in decisions that unwittingly favor one side of a dispute over another. [iii] These authors conclude:
“It is not necessary for judges to become ‘amateur mathematicians’ in order to reclaim their rightful role. However, they must be aware that the apparent objectivity of mathematics often masks subjective judgments, and not be fooled when ‘hard’ numbers are really based on little more than intuition and guesswork. Numbers can communicate important information. Judges just need to make sure that they are able to comprehend what those numbers are trying to say.”[iv]
[i] Meyerson, Michael I and William Meyerson, 2010, “Significant Statistics: The Unwitting Policy Making of Mathematically Ignorant Judges.” 37 Pepp. L. Rev. 771.
[ii] Ibid, p. 10., quoting Holmes’s The Path of the Law.
[iii] Ibid. p. 14. The article also discusses the problems of a court adopting science’s risk of error, which leads to tipping of the equities in favor of one party or the other..
[iv] Ibid. p. 33.
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