In criminal justice, mathematical models are put forth to "prove" various propositions relevant to important questions of policy.  Does a particular rehabilitation program "work," such that people who go through the program have a lower recidivism rate than the same people would have had if the program were not offered?  Are death sentences handed out in a way that depends directly on the race of the defendant or the victim, or are the reported "disparities" merely the result of the correlation of race with legitimate factors?  Does the death penalty deter some murders?  If so, how much of this effect is the simple existence of the penalty and how much is due to actual executions?

Derman's main point, applied to these questions, would be that you can't really prove any of these propositions with mathematical models, not like you can in physics.  That is assuredly correct.

Catchy and clever as the book title is, though, it is not the models that are behaving badly.  The subtitle is more accurate, though not as pithy: "Why confusing illusion with reality can lead to disaster, on Wall Street and in life."  It is the people claiming more for models than they actually show who are behaving badly.  That is at the root of the controversy in North Carolina over the so-called Racial Justice Act, repeal of which was unwisely vetoed by the Governor today.  The death penalty opponents claim their mathematical models show discrimination, but it is highly debatable whether they show anything at all.

[Derman] sums up his key points about how to keep models from going bad by quoting excerpts from his "Financial Modeler's Manifesto" (written with Paul Wilmott), a paper he published a couple of years ago. Among its admonitions: "I will always look over my shoulder and never forget that the model is not the world"; "I will not be overly impressed with mathematics"; "I will never sacrifice reality for elegance"; "I will not give the people who use my models false comfort about their accuracy"; "I understand that my work may have enormous effects on society and the economy, many beyond my apprehension."

Those are good points for criminal justice policy makers to keep in mind as well.  Models can tell us some things that are useful if we keep their limitations in mind.  For convicted felons who will be released at some point in the not-too-distant future, should we offer rehabilitation Program A, Program B, or none at all?  Given that we have to choose, a well-designed study with accompanying mathematical model can help us make a choice that is better than throwing darts. 

On the other hand, should we overturn a just sentence for a horrible crime because a mathematical model purports to show that other people who have committed similar crimes have gotten off with less?  Before we do that, we should require compelling proof, which may be beyond the capacity of the model to provide.