Saturday, December 27, 2003

Optimal Crime and Punishment

Chris Bertram discusses the extent to which human beings raised under different circumstances can or should be assumed to have the same rational and moral faculties. In the comments box, one commenter argues:
That some people grow up under averse conditions, that incline them to act in violent ways, does not necessarily mean that they should be held less accountable for their actions.

Steven Pinker gave this example, in the Blank Slate. We are all agreed that rape is evil and completely wrong. Say it is proved that 1% of the population is more inclined to rape for genetic reasons. That does not mean that they should not be punished for rape. Instead it means that the punishment for rape for them should be much more severe, in the hope of providing a stronger offsetting force to deter them from raping (this of course ignores a lot of argument about what can deter crime in fact).
I haven’t read the Blank Slate, so I can’t say whether this accurately reflects Pinker’s position. But I can say that the argument is flawed, despite being highly intuitive. To see why, imagine we’re not talking about different classes of potential criminal, but different ways in which to invest your money. If two lines of investment were equally risky, but profits were particularly hard to make in one of them – that is, if the return per dollar invested were low – you would not want to throw more money at that line of investment in order to get a high enough gross return. On the contrary, you’d shift your funds from the lower return investment to the higher return investment. (You might still keep a mix of the two investments because you wished to diversify your portfolio, or because there were diminishing returns in each investment; but the lower return per dollar would bias the mix away from the lower return investment.)

Similarly, you wouldn’t want to throw away crime-enforcement dollars (and resources) on criminals who are resistant to deterrence, when the same dollars could deter a larger number of more responsive criminals. If you want to maximize your net gains from law enforcement, it actually makes sense to spend less on catching and punishing the most resistant, and more on catching and punishing the least resistant, criminals. That’s why, for instance, it makes sense to have lower punishments for children and the mentally insane: they are likely to commit their crimes regardless of our deterrence efforts (unless we spend prohibitively large sums on preemptive efforts), and therefore our efforts are better spent elsewhere.

It’s true, of course, that worse crimes should be punished more harshly, but that’s not the same issue. Bertram’s commenter indicates that we’re talking about different criminals committing pretty much the same crime, rape in her example. If we consider all rapes equally bad, then we should spend our rape-prevention resources on those potential rapists most likely to be deterred. (Even if rapes are not all equally bad, to justify different punishments for different rapists we would have to believe that the least deterrable rapists systematically tend to commit the most heinous rapes.)

If you want an argument for why it makes sense to hold everyone responsible for their actions regardless of their resistance level, here’s one: that we cannot easily distinguish between those people who are more and less deterrable. Children and the mentally insane provide nice categories that we can separate from the general pool, but even these categories do not have well-defined borders. Some legal minors are as rationally capable as adults. Some most-likely-sane criminals attempt to slide through the insanity loophole. Thus, even these seemingly obvious exceptions create some poor incentives for those who shouldn’t, but might, be able to take advantage of them. Other categories, such as poverty, are related to the possession of rational and moral faculties tangentially at best. (The rejoinder that the poor empirically commit more crimes proves nothing, because that is perfectly consistent with rational choice: criminal opportunities are naturally more attractive to people with fewer legal opportunities.) Given the fuzzy boundaries between different classes of criminal, we have little choice but to treat them for the most part as a single class.

1 comment:

David Friedman said...

The actual analysis is more complicated than you suggest. Under some circumstances it is optimal to impose more severe punishments on those harder to deter, under some less. You can find a detailed analysis in my old article "Reflections on Optimal Punishment or Should the Rich Pay Higher Fines?," Research in Law and Economics, (1981), in the more recent "Should the Characteristics of Victims and Criminals Count? Payne v Tennessee and Two Views of Efficient Punishment," Boston College Law Review XXXIV No.4, pp.731-769 (July 1993), webbed at, and in Chapter 15 of my _Law's Order_, webbed at

The simple intuition is that raising expected punishment raises enforcement cost per offense but reduces the number of offenses. It may pay to deal with hard to deter criminals by more severe punishment in order to deter them--think of it as price discrimination--or it may pay to have lower punishment because deterring htem is too costly.

The general rules turns out to be expected punishment equal damage done minus marginal cost of deterrence. Marginal cost of deterrence is positive if the supply of offenses is sufficiently inelastic, negative if sufficiently elastic.

Details of the analysis are left as an exercise for the reader.