Chapter 7: Coin Flips and Car Crashes: Ex Post vs Ex AntePost versus Ex Ante


Someone offers you a bet on the flip of a coin: Heads he pays you two dollars, tails you pay him one. You agree. He flips the coin. It comes up tails, and you pay him a dollar.

Whether you should have made the bet depends on whether you judge it ex ante or ex post.ante or ex post. Ex ante, judged by the information available to you at the time, it was a good bet, since on average you could expect to come out fifty cents ahead. Ex post, judged by the information available to you after the coin was flipped and you had lost, it was a bad bet, since it cost you a dollar.

When dealing with decisions under uncertainty, it is important to distinguish between these two ways of evaluating them. Ex ante, almost all gambles in Las Vegas are losing ones; the casino, like an insurance company, sets its rates so that the money that comes in when it wins covers not only the money it pays out when it loses but also its operating expenses. Nonetheless, some gamblers win their bets ex post.

The same distinction is useful in analyzing how the legal system can be used to prevent undesirable outcomes such as automobile accidents. One approach punishes people for doing things that increase the probability of accidents ex ante: speeding, drunk driving, failing to get their brakes inspected. The other punishes the undesirable outcome observed ex post, via tort liability for the damage done to the car you collide with or criminal penalties for drunk drivers who run over people.


Why Punish Attempts?


For a less obvious example of the ex post/ex ante distinction, consider the puzzle of why we punish attempted murder. I shoot at you, and the bullet goes into a tree instead. Judged ex post, based on the damage done, there should be no punishment: Both you and the tree are fine.

The explanation is that punishment for attempted murder is, like a speeding ticket, an ex ante punishment, a way of preventing undesirable outcomes by punishing behavior that increases their probability. Driving fast makes it more likely that you will run into someone. Shooting at people makes it more likely that you will hit them. The odd thing about punishment for attempted murder is that the ex ante behavior is discovered only after we know that it did not actually produce the undesirable outcome—this time. A different way of putting it is that our legal system imposes an ex ante punishment for trying to kill people plus an additional ex post punishment for succeeding.


Choosing the Right Rule(s)


These examples of ex post and ex ante punishments suggest an interesting question for the economic analysis of law: Why does the legal system sometimes uses one approach, sometimes the other, and sometimes both? What are the advantages and disadvantages of each?

The ex post approach has one important advantage over the ex ante: By making it in the driver's interest to avoid accidents, it exploits his private knowledge of how to do so. Consider, for a simple real-world example, my own behavior. The most dangerous thing I do when driving is not speeding, nor driving drunk, nor driving an unsafe car. The most dangerous thing I do is to pay attention to my conversations with other people, real conversations with real people sitting next to me or arguments inside my head with radio talk show hosts or imaginary opponents, when I ought to be paying attention to my driving.

That is the most dangerous thing I do as a driver, but I have never gotten a ticket for it. Ex ante punishments can be imposed only on behavior that a traffic cop can observe; so far, at least, that does not include what is going on inside my head. Ex post punishments can be imposed for outcomes that can be observed due to behavior that cannot—when what is going on inside my head results in my running a red light and colliding with another automobile. Ex ante punishment makes it in my interest to take those precautions that the legal system, here represented by the legislature and the traffic cop, knows I should take and can tell if I am taking. Ex post punishment makes it in my interest to take any precautions that I know I should take and can tell if I am taking.


Ex post punishment takes account of two sorts of private information that ex ante ignores: information about what I am doing (paying attention to my thoughts instead of the road) that cannot be observed by others, and information about what I should be doing. The speed limit is the same for everyone, from the race car driver to the teenager with a brand-new license, because the traffic cop has no easy way of distinguishing competent drivers from incompetent ones. I, on the other hand, know when I am sleepy and inattentive, or upset, or distracted, and thus a worse driver than usual; ex post punishments make it in my interest to drive slower at those times than at others. And I can (and do) exploit my knowledge of my own inattentiveness by letting my wife drive when we are both in the car.

We have seen this argument before in a different context. The advantage of ex post over ex ante punishment is very much like the advantage of an effluent fee over direct regulation. Direct regulation controls inputs to pollution—scrubbers, coal quality, smokestack height—just as speed limits control one input to having accidents. Effluent fees punish the unwanted output, pollution, and leave it to the polluter to decide how best to reduce it, just as liability for accidents punishes the output, accidents, and leaves it to the driver to decide how best to avoid them. Both effluent fees and ex post punishment thus reduce the amount of information the legal system requires to do its job. But both still require some information. The EPA must estimate the damage done by additional pollution in order to set the fee, and someone must estimate the damage done by an accident in order to decide just how high the ex post punishment should be.

Seen from a somewhat different perspective, however, the speeding ticket looks more like an effluent fee. Drivers who believe that getting somewhere fast is very important are free to speed and pay for it, at least as long as they are not caught too often. Thus even ex ante punishment takes advantage of some private information, not about what the driver is doing or how it affects the chance of an accident but about how costly it is to him to take precautions that the law wants him to take, such as driving slowly.

The example of using private information to decide how fast I should drive suggests a possible disadvantage, as well as a possible advantage, of ex post punishment. Ex ante punishment provides incentives based on the beliefs of the people making the laws; ex post provides incentives based on the beliefs of the people the law applies to. If I believe that I can drive just fine after a shot of whiskey and two beers, the knowledge that if I have an accident terrible things will happen to me provides no special reason to avoid driving when drunk. The knowledge that if I am stopped and fail the Breathalyzer exam I will go to jail does.

It is said that if you poll people on their driving ability, you discover that the vast majority are above average drivers. The teenager with a brand-new license may not actually be a race car driver, but that does not keep him from believing that he could win the Indianapolis 500 if he only had a chance to enter it. If people consistently misestimate their abilities, and if the legislators setting ex ante rules are better informed, then the ex ante rules have the advantage of substituting the legislators' opinion of what behavior lead to accidents for the drivers' opinion.

This argument depends on more than mere ignorance. If the legislators know facts about driving—that roads are especially slippery when it has just started to rain, for example—that drivers do not know, the legislators can (and do) pass that information on to the drivers in safety ads or in the booklet that everyone reads before taking his driver's test. That does not work perfectly, since the driver may not see the ad or pay attention to the booklet. But the same problem of getting information to the drivers exists if the legislators try to use ex ante punishment to make the drivers embody the legislators' expertise in their driving decisions. A law requiring all drivers to slow down when it has just started raining works only if the driver knows the law exists. It is only when drivers not only don't know things but think they do, and are therefore unwilling to believe what the legislators tell them, that ex ante punishment has an advantage—assuming, of course, that the drivers are wrong and the legislators are right.

So the advantage of ex post punishment is that it utilizes the driver's information about what he is doing, which is almost always better than the legal system's information about what he is doing, and the driver's information about what he ought to be doing to avoid accidents, which is often but not always better than the legal system's information. What are the advantages of ex ante punishment?

The obvious answer is that the ex ante approach prevents accidents before they happen, while ex post only punishes afterwards. Like many obvious answers, it is wrong.

Being found liable for an accident does not prevent that accident—but then, getting a speeding ticket does not prevent that act of speeding. The point of giving speeding tickets is that the knowledge that you might get one gives you an incentive not to drive fast. The point of punishing people for being in accidents is that the knowledge that if you are in accident you will get punished gives you an incentive not to have accidents. Both speeding tickets and tort liability are approaches to preventing accidents before they happen.

To see the real advantage of ex ante punishments, consider two alternative patterns of punishment, each of which collects the same number of dollars. Under the pure ex ante rule you end up paying $200 in speeding tickets every year, and, if you injure someone else's person or property in an accident, there is no penalty. Under the pure ex post rule there are no speed limits, and each year, you have one chance in a thousand of being in an accident and having to pay a two hundred thousand dollar fine. Unfortunately, you don't have two hundred thousand dollars in your bank account. So the result of an accident is that you forfeit everything you own, including your house, and must spend the next five years working sixty hours a week to pay back the rest of the fine.

Most of us would prefer the former pattern of punishment because most of us are risk averse. All else being equal, we prefer a high probability of a low cost to a low probability of a high cost. Ex post punishment is imposed only when an accident occurs, which is rarely, so in order to provide a significant incentive to avoid accidents ex post punishments must be large. If we are risk averse, ex ante punishment can provide the same incentive at a lower cost.

So far I have assumed that you can and must pay the ex post fine, even though doing so may be very difficult. But suppose the ex post fine necessary to give you an adequate incentive to avoid accidents is ten million dollars, and there is no way you can expect ever to pay that much. How can we give you an incentive equivalent to the ten million dollar fine you cannot pay?

The obvious answer is to switch from fines to other sorts of punishments, such as execution or imprisonment; even if you don't have the money to pay a fine, you can still pay with your life or liberty. But while such punishments may provide adequate deterrence, they do so at a high cost. If you pay a fine, whether for speeding or being in an accident, someone collects it; your loss is someone else's gain. If the fine is a speeding ticket, the money goes to the state; if it is a liability payment, it goes to the victim. But if your punishment is execution, you lose a life and nobody gains one. If your punishment is imprisonment, you lose your liberty, and the rest of us have to pay for the jail. Hence both execution and imprisonment are costly punishment compared to fines. Here the relevant cost is not simply cost to the person being punished—imposing a cost on him is the point of the punishment, after all—but net cost on everyone affected, including the person punished, the people who collect fines, and the taxpayers who pay for prisons. It is net cost to everyone that is relevant to economic efficiency.

It follows that while the advantage of ex post punishment is that it takes advantage of the private information of the people whose behavior it is intended to control, the advantage of ex ante punishment is that it can be done efficiently, using relatively small fines imposed with relatively high probability. Doing so avoids both the cost of risk aversion from very high fines imposed with low probability and the high net cost of such inefficient punishments as execution and imprisonment.


Does the Law Get It Right?


We now have some idea of the advantages, from the standpoint of economic efficiency, of each approach. By combining that with Posner's conjecture that the common law tends to be economically efficient, we should be able to predict and explain when ex post punishment will be used, when ex ante, and when both.

Risk aversion is important for large losses but not for small ones, since the value to you of a dollar does not change much when your income changes by only a few dollars. That is one of the reasons you buy insurance against your house burning down but not against spilling ink on your best pair of pants. The difficulty of collecting fines, and thus the need to substitute less efficient punishments, arises only when the fines are large relative to the offender's assets. It follows that where the damage done by accidents is small enough so that the appropriate ex post fine is one that everyone can easily pay, there is no reason to use ex ante punishments.

This seems to fit what we actually observe. Traffic accidents do lots of damage, and the legal system attempts to prevent them by both ex ante and ex post punishments. Many other activities that do small amounts of damage, a broken window due to overly enthusiastic baseball playing in a neighbor's yard, for example, are controlled by a pure ex post approach via tort law.

Criminal law typically relies on costly punishments, at least in part because convicted criminals cannot pay adequate fines. Tort law typically relies on damage payments. I argued earlier that punishment of attempts was a form of ex ante punishment. If so, the argument I have just offered implies that attempted crimes should be punished and attempted torts should not. That corresponds reasonably well to actual law. If I try to photocopy your copyrighted book but carelessly put the pages into the copier upside down, I owe you no damages for the resulting blank copy. If I set off to trespass on your property but lose my way and end up somewhere else, you have no tort claim against me.

A second prediction is that we should never observe systems of pure ex ante punishment, such as a legal system that punishes speeding but fully insures drivers against all costs of accidents. Low levels of ex post punishment, such as a fine equal to a month's salary, are almost always superior to ex ante punishment, since they can be paid in money, impose little cost through risk aversion, and provide an incentive for actors to use their private information to avoid accidents. So an efficient system that uses ex ante punishments will supplement them with at least some level of ex post punishment. I cannot think of a real-world counterexample to this prediction; perhaps you can.

For a hypothetical exception, consider pollution regulation, not in the real world but in books such as this one. Polluters are required to obey a variety of regulations specifying the precautions they must take to keep down their pollution. Having met those regulations they then pay no cost for whatever pollution occurs.

If this pattern existed in the real world, it would be inefficient—although, since pollution regulations are set by legislators and regulators, not by courts, it would not contradict Posner's conjecture that common (i.e. judge-made) law is efficient. But it does not. Even if a polluter obeys the regulations, he is still at risk of being sued by the downwind victims. Obedience to the regulations provides him a defense, but not an absolute defense.


A Market for Legal Rules


So far I have been discussing legal rules made by legislators and judges. One problem with all such systems is that even if we know what rule is efficient, it is not obvious that it is in the interest of legislators or (pace Posner) judges to set efficient rules. That observation suggests that it might be worth looking for other ways of generating efficient legal rules—in particular, an efficient mix of ex ante and ex post.

One such mechanism was described in the previous chapter: insurance. The inefficiency of ex post rules comes in part from risk aversion. The inefficiency of ex ante rules comes from the fact that unobservable decisions by me, such as how much attention to pay to my driving, impose costs on others, costs I ignore when making such decisions. The last time we encountered that problem we called it moral hazard.

Insurance provides a market mechanism for trading off costs of risk aversion against costs of moral hazard in order to find the least costly combination; could that mechanism be applied here? Imagine that the optimal pure ex post system imposes a fine of two hundred thousand dollars for an accident and that that is a fine that drivers can (barely) pay, making the problem one of risk aversion rather than the need to shift to less efficient punishments. We abolish all speed limits and similar regulations, set a two hundred thousand dollar fine and permit drivers to insure against having to pay it.

The more insurance I have, the lower my incentive to avoid accidents, just as, in the previous chapter, the more insurance I had on my factory the lower my incentive to avoid fires. Insurance companies will take account of that in setting rates. They will also consider ways of reducing the risk. One obvious approach to reducing the risk of fire is requiring sprinklers. One obvious approach to reducing the risk of accidents is requiring speed limits.

There are practical problems in the second case, since while insurance companies sometimes employ fire inspectors they do not normally have their own traffic cops. We could solve that problem by making the traffic cops subcontractors to insurance companies. Instead of enforcing laws, they enforce contracts. A customer who has agreed not to drive over sixty miles an hour as a condition of his insurance has a giant bar code on his bumper announcing the fact. Traffic cops are provided, along with their radars, with equipment for automatically reading bumper bar codes. When they spot a car driving faster than it should, on goes the siren and flashing lights.

Under such a system the insurance company has an incentive to calculate the optimal tradeoff between ex post and ex ante, the optimal amount of the former, and the optimal pattern of the latter. The higher the fraction of the loss it insures, the lower the costs due to risk aversion but the greater the costs due to moral hazard. It can control those costs via ex ante punishments, contractually set. The degree to which that is worth doing depends on how well or badly ex ante punishments work relative to ex post, given the advantage of using the latter to exploit the driver's private information. The full analysis of such a system would carry us well beyond the limits of this book, but the general logic should be clear.

In some contexts, such as buildings burning down, private insurance is routinely used to trade off costs of risk aversion against costs of moral hazard. In the context of traffic regulation, of course, it is a fantasy, at least at present—as fantastic as the idea of auctioning off parts of the electromagnetic spectrum was when Ronald Coase first suggested it in 1959.


The Rational Voodoo Killer: Should We Punish Impossible Attempts?


In explaining why we punish attempted murder, I argued that it was a form of ex ante punishment. Shooting at people sometimes kills them, so we punish you for it even if you happen to miss. But what if I am attempting murder by a method that never works, such as sticking pins in a voodoo doll? Should that be criminal? Should we punish impossible attempts?

The argument against is obvious: Sticking pins in voodoo dolls does no harm, so why punish it? Why pay the cost of catching people and locking them up in order to deter behavior that we have no reason to deter?

To see what is wrong with this argument, imagine that I am considering committing a murder in one of two ways—poison or voodoo. The poison I am considering is invariably lethal, whereas sticking pins in a voodoo doll will have no effect at all on the prospective victim's life expectancy. If I were aware of these facts, I would either choose poison or not attempt the murder at all. The problem arises because I am not aware of them. I know that one of the methods works and one does not but not which is which. The legal rule we are considering is Attempts by impossible means are not punishable. Since I do not know which method is impossible (if I did, I would not bother using it), this does not translate, for me, into attempts by voodoo are not punishable.

Since I am unsure which method works I must allow in my calculations for the possibility that I will choose the wrong one. If impossible attempts are not punished, then the wrong choice means that I will not succeed in my crime but will also not be punished, even if caught. If impossible attempts are punished, I risk using an impossible method and being punished for doing so. That risk is one of the costs to take into account in deciding whether or not to try to kill someone.

So a policy of punishing impossible attempts tends to deter real murders, murders with poison, by people who do not know whether what they think is poison will actually work. The cost of that deterrence is that some people caught making attempts that actually are impossible must be punished for doing so.

Even if punishing impossible attempts provides some deterrence, would it not make more sense to get that deterrence by punishing possible attempts (and successful murders) instead, thus concentrating our efforts on those most likely to do damage? The answer is that it would if we could costlessly impose adequate punishments. We are back again to the ex post/ex antepost/ex ante argument.

Punishing the outcome does a better job of putting the punishment where it does the most good—some attempted voodoo killers, after all, may be people who know perfectly well that voodoo does not work and are merely posturing for less well-informed friends. But punishing attempts, even impossible ones, lets us increase the probability of the punishment and thus achieve the same deterrence with less costly punishments.

A different way of making the same argument is to assume that there is some maximum punishment we are willing to impose—life imprisonment but not execution, or execution but not by torture. Supplementing that maximum punishment for murder with a lesser punishment for unsuccessful attempts allows us to increase the ex ante cost of the attempt to the aspiring murderer. We can increase it still more by including punishment for impossible attempts.

One thing you may find a little bizarre about this discussion is the assumption that the behavior of voodoo killers will be affected by the incentives provided by legal rules. How likely is it that anyone sufficiently irrational to believe in voodoo will be well enough informed about the law to know whether or not impossible attempts are punished, or sufficiently prudent to care?

One reply is that while rationality may not always be an accurate way of predicting behavior, it is the best tool we have—and ignorance in one part of life does not guarantee ignorance or irrationality in others. All of us, after all, get quite a lot of our beliefs about what does or does not work from the people around us, and a rational person may accept irrational beliefs if everyone he knows accepts them.

Another reply is to point out that impossible attempts are not limited to voodoo. Voodoo is unlikely to kill anyone, but so is shooting a tree. Trying to pick an empty pocket is perfectly rational behavior but unlikely to succeed. There is a sense in which all failed attempts are impossible, judged by what we know after they fail.

Seen from this perspective, the question of whether to punish impossible attempts is simply the question of whether to punish attempts. In either form, the essential argument is the same: Since someone does not know whether his attempt is impossible before he makes it, the knowledge that it will still be punished even if it turns out to be impossible, whether in the obvious sense of voodoo or the subtler sense of picking an empty pocket, is an incentive not to make the attempt.

Readers interested in a more extensive analysis of these issues will find it in:

Friedman, D. "Impossibility, Subjective Probability, and Punishment for Attempts," Journal of Legal Studies XX, (January 1991).

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