Crime and Punishment

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When most people think about economics, they think about markets and prices. However, there is nothing that requires that the tools of economics be limited to markets. Non-market activity involves the same sort of decision-making as market activity. If an action is costly, one can assume that the reason someone took that costly action was that the benefit exceeded the cost. This should be true for someone who is buying an apple and someone who is stealing an apple. Both actions are costly ways of acquiring an apple.

The cost of buying an apple is that a person has to give up the ability to purchase something else. Buying one apple might mean giving up two bananas. Stealing an apple, on the other hand, does not require giving up any bananas. However, theft can be costly to both the thief and the victim. The seller of apples not only loses the ability to sell the apple, but the very prospect of theft will cause potential victims to incur costs to prevent theft. For the thief, their actions will certainly violate norms and, in modern society, the law. However, the thief only suffers some of the costs if he or she is caught in the theft.

Some costs of the theft (to the thief) are certain. If one puts effort into planning and carrying out the theft or circumventing existing anti-theft measures, the time spent in these activities is time that cannot be spent in another way. Other costs associated with theft are in terms of expected costs. That is, the thief faces an additional expected cost that is the probability that the thief is caught (and prosecuted) multiplied by the punishment for theft. The more costly that theft becomes, the less likely people are to commit theft. Given that the cost associated with theft is the expected cost of punishment, there are two ways in which society can increase the costs to thieves. The first is to increase the likelihood of detection and prosecution. The second is to increase the severity of the punishment.

If theft is punishable by law, then a natural question arises about how to design the optimal punishment through the legal system. One can think about this in terms of the costs and the benefits. The law (and enforcement thereof) should be designed such that the marginal benefit in terms of deterrence is equal to the marginal cost of deterrence. There are a lot of moving parts there. Increasing the probability of detection and prosecution potentially means hiring more police or investigators and better prosecutors. That is costly. If the method of punishment is imprisonment, then increasing the punishment might mean something like longer prison sentences. For a given amount of crime, longer prison sentences mean more prisoners at a given period of time and potentially costs associated with over-crowding or the construction of more prisons. Of course, longer prison sentences will deter some amount of crime, but this also depends on the probability of detection and prosecution. If longer sentences are coupled with a reduction in policy presence or lower salaries for prosecutors, the effect on deterrence might be ambiguous.

Police, prosecutors, and prisons are all costly. Enforcement of the law therefore requires choosing the how to allocate that spending to deter theft. This is made more complicated by the fact that in the real world, theft isn’t the only possible crime and you are going to use the same legal system for those other crimes.

One way to think about optimal punishment might be to try to get the most possible deterrence at the lowest possible cost. If that is your objective, something that might seem like an optimal strategy could be something like having the same very severe punishment for every crime. More specifically, when someone is accused committing a crime, they could be given the option to admit guilt and pay a fine, the magnitude of which depends on the severity of the crime. If the person is unwilling or unable to admit guilt and pay the fine, their prosecution is determined by a dice roll with the number of sides on the die inversely related to the severity of the crime. Some die might have six sides. Other die might have thousands of sides. (You don’t actually need to use dice. Just a random draw.) If the prosecutor rolls a 1, the perpetrator is sentenced to death. Otherwise, the perpetrator is set free.

This seems like things that were observed in ancient legal systems. For example, Drew Fudenberg and David Levine have studied the interaction between superstition and the law. They note the second law of Hammurabi’s Code read:

If any one bring an accusation against a man, and the accused go to the river and leap into the river, if he sink in the river his accuser shall take possession of his house. But if the river prove that the accused is not guilty, and he escape unhurt, then he who had brought the accusation shall be put to death, while he who leaped into the river shall take possession of the house that had belonged to his accuser.

The implication here is that the punishment for the accused is the death penalty. What makes this example unique is that it relies on a form of superstition. There is some divine intervention that determines whether the person thrown into the river lives or drowns. The success of this strategy depends on the degree to which people believe in such divine intervention. The example that I gave above just replaces divine intervention with a random number generator.

All of this sounds a little crazy (we’ll get to that), so why would anyone argue that this seems like the optimal strategy for a legal system?

Well, it appears to be a cost-minimizing strategy. This sort of legal system does not require the best prosecutors nor does it require that society build and maintain any prisons nor hire any prison guards. Courtroom trials disappear. All you need are fair dice — and probably some with a ridiculous number of sides for petty crimes. And yet, if you choose the probabilities just right, you should be able to deter as much crime as you would under any other system. In fact, you could design the expected cost to equal the social cost of the crime. In that case, the expected cost functions like a sort of Pigouvian tax on criminal behavior. This system seems like it could be designed to create the socially optimal level of crime deterrence at the lowest cost.

Of course, when we look around at various modern legal systems, none of them look even remotely like the hypothetical system. What gives? Are modern legal systems just really bad at minimizing costs? Does the system just seem crazy because it is so different than our own? Or is this discussion missing something?

One is immediately tempted to look for non-economic arguments. Maybe people are made uneasy by the uniform penalty of death. Perhaps people simply don’t like the thought of someone suffering the death penalty for a petty crime — even if it occurs only very, very rarely.

I don’t want to be dismissive of these types of arguments. There might be truth to them. However, this is a newsletter about economics. Thus, one might wonder what economics has to say about all of this. And, as David Friedman has pointed out, there are economic arguments that can explain why this sort of legal system isn’t as cost-minimizing or efficient as it might sound.

To set the stage, let’s consider a particular example of a harm and how it was punished in the past. In California, when cattle would trample crops in a field, social norms required the rancher apologize to the farmer. If the problem reoccurred, the rancher would be required to assist with repairs and cleanup. Still further infringement by the cattle might be met with the farmer loading up the cattle and driving them some distance away from the rancher’s land. One thing that was not an acceptable norm was for the farmer to turn one of the cattle into steak.

To some extent, these norms seem odd. The rancher’s cattle harmed the farmer’s crops. The farmer is allowed to punish the rancher by making the rancher help with repairs or driving the cattle some distance away, but not by confiscating one of the cattle and turning it into dinner? Why are only certain types of punishment acceptable?

The simple answer is that the repairs and retrieval of the cattle are costly to the rancher, but do not allow the farmer to extract some benefit from the rancher. Since turning cattle into steak provides a benefit to the farmer, the farmer might have an incentive to punish the rancher even when it wasn’t warranted (e.g., the rancher would be punished the first time a cow trampled the crops rather than after multiple infractions). The farmer might even be willing to entice the cattle onto his land if the value of the steak was greater than the trampled crops. In other words, if the farmer can benefit from punishment to the rancher, then the farmer will have an incentive to inflict punishment. In this case, over-enforcement can occur.

Now, let’s carry this over to the hypothetical cost-minimizing legal system that I presented above. The way that I presented the problem with the design of the legal system put the entire focus on deterring potential criminals from committing crimes. What I failed to consider is the behavior of law enforcement in that system. But consider the incentives that people in law enforcement face in that system. Law enforcement might use the supposedly cost-minimizing system to threaten non-criminals with false accusations in an attempt to obtain money or information from these innocent parties. Faced with the threat of a significant fine and a positive (though possibly low) probability of being put to death, many are likely to comply — and, in fact, might give useless or false information to avoid the threat of punishment.

Given the incentives for over-enforcement or extortion, it would seem to make sense to vary the penalties for different crimes. As long as crime comes with a punishment, the incentive for extortion can persist. However, by reducing the severity of punishment for less severe crimes, this increases the cost of extortion (reduces its effectiveness without altering penalties for extortion itself). Therefore we should get less of it.

It is important to realize that the lesson here goes far beyond this little thought experiment about an optimal legal system. Too often when people are studying policy or the design of particular institutions, they treat the behavior of a particular set of real-world decision-makers as given. Law enforcement officers, regulators, and politicians are just a few examples of decision-makers that are treated this way. These decision-makers are treated as though they simply follow “the rules of the game” (despite the fact that the exercise is often about how to design the rules!). But all decision-makers face tradeoffs. One should never assume that certain decision-makers are immune to incentives. Everyone weighs costs and benefits.