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Monday, January 30, 2006
math + legal doctrine = ?
Last week, BusinessWeek had an interesting cover story on how "math geeks are calling the shots in business." The influence of math in business seems pretty natural to me (e.g, analyzing data and numbers, figuring out purchasing patterns, etc.). But I wondered about the question BusinessWeek's cover asked: Is your industy next to see the power of math?
The skeptic in me says probably not. First, lawyers are not trained in math in law school and usually are not noted for their math abilities. Of course, some lawyers are quite gifted at math, but I'd gather that the majority of lawyers are not (speaking at least from my own experience). Larry Tribe is one of those exceptional lawyers who majored in math and excelled at it in college (see here). By contrast, business students do get a fair dose of stastistics and accounting in B-school. Second, legal doctrine and legal rules may be difficult to conceptualize in terms of numbers and math, since the law often lacks the kind of precision found in math.
This is not to say that the law is devoid of math, or that courts and legislatures shouldn't consider maybe making more use of it. Maybe math can help us formulate or apply legal rules and doctrine more consistently and effectively. Here are a few quick examples of how math figures into legal doctrine already, apart from the most basic inclusion of math in calculating damages -- if you have any more examples, please write in:
1. Torts: comparative negligence (50% fault or 49% fault) asks juries to apportion fault by assigning percentages.
2. Equal protection: quotas are prohibited, but race can be a + factor; "critical mass" implies some number of people.
3. Fair use: 4 statutory factors require some crude weighting; factor 3 asks how much of the copyrighted was taken; and factor 4 asks what effect the use will have on the market for the copyrighted work. It's quite possible that we could make fair use less vacuous by delineating some guidelines about number of copies made and amount taken, such as in the Guidelines for Classroom copying (see here).
4. Punitive damages: Under one of the BMW factors for reviewing the constitutionality of punitive damages, the Court has looked to the ratio between punitives to compensatory damages, indicating in State Farm (here) that going beyond 4:1 ratio might be pressing the outer limits.
Posted by Elee on January 30, 2006 at 12:47 AM in Legal Theory | Permalink
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Comments
Logic is a segment of mathematics. That's what I studied. And logical reasoning is the basis of almost any legal argument.
Posted by: Mel Gibson | Jan 31, 2006 1:19:53 PM
Ed: all areas of law that I mentioned rely on math (and its progeny -- statistics, finance, and accounting) in very explicit way. E.g., you need math to demonstrate antitrust violations; to show mistreatment of minority investors in corporate cases; to put together a merger agreement; to set up (and litigate) a profit distribution arrangement in a private equity fund; to establish causation in securities class actions and mass torts; to figure out fancy tax-efficient structure; to argue damages in just about any business case... The sentencing guidelines’ "math" is baby talk in comparison.
Posted by: Kate Litvak | Jan 30, 2006 7:10:10 PM
Thanks for all these wonderful comments. I'm sure that math is important to a lot business related areas of law. Thanks for the suggestions.
I'm most interested with those legal doctrines and legal rules that actually rely upon math in some more or less explicit way. In other words, I'm curious when courts actually rely upon math in deciding legal issues. The Federal Sentencing Guidelines are a great example (yes, from my friend the sentencing maven).
Posted by: edlee | Jan 30, 2006 5:26:09 PM
In many of the practice areas mentioned by Kate Litvak, game theory comes into play as well -- once again requiring a mathematical background. Furthermore game theory is useful in any government investigation, where who the defendant is may shift based on where the investigation is heading. Math background not required, but very very useful.
Posted by: MathGeek | Jan 30, 2006 4:23:39 PM
Bayesian probability is usually present in criminal trials. You need it to figure out how all the little pieces of evidence should be combined together to determine the overall likelihood of guilt. Unfortunately, juries don't, and probably can't, use math to do this. The correct answer is can easily be different from the 'common sense' answer, e.g. the Monty Hall problem.
And of course, math is more about logic than numbers, and logic is very important in the law.
Posted by: Nigel Kearney | Jan 30, 2006 4:00:43 PM
Add the following popular practice areas: corporate, securities, commercial, bankruptcy, tax, antitrust, mergers and acquisitions, banking, insurance, complex mass torts (substantially beyond “jury awards 50%”), project finance, structured finance, derivative instruments… should I continue? Both transactional and litigation attorneys in these fields need math. And good attorneys also need a decent knowledge of finance, accounting, and the ability to understand statistical analysis.
Posted by: Kate Litvak | Jan 30, 2006 1:18:43 PM
It's probably true that arithmetic and calculation have little application in law, but math is much more than that. I think basic set theory can be useful in law. When I'm dealing with an issue with exceptions and exceptions to exceptions and so on, I like to think of the problem in terms of set notation.
Posted by: FXKLM | Jan 30, 2006 12:56:56 PM
If you will allow some shameless self-promotion, I have written about the uses (and abuses) of mathematics in
The Law and Large Numbers, 19 Const. Comm. 459 (2002)
For some non-trivial uses of mathematics in election law see:
Making Votes Count in Local Elections: A Mathematical Appraisal of At-Large Representation, 4 Elec. L. J. 258 (2005)
and
Getting the Math Right: Why California Has Too Many Seats in the House of Representatives" (August 2005). Vanderbilt Public Law Research Paper No. 05-25 http://ssrn.com/abstract=783949
The fact is that within a certain limited domain (but an interesting domain, I think) mathematics can shed a light that other methods can not.
Posted by: Paul H. Edelman | Jan 30, 2006 10:51:56 AM
As my students and many federal practitioners know, the federal sentencing guidelines, because they unwisely seek "the kind of precision found in math," have made remembering algebra more important to those working in the federal criminal justice system.
Not only do the federal guidelines require sometimes complicated calculations of offense levels and criminal history points, but they always test one's ability to divide by 12: the guideline ranges are stated in months and it is not always easy to convert a range of 151-188 months into an exact term of years.
Posted by: Doug B. | Jan 30, 2006 10:36:39 AM
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