The randomness that's fair

Consider the following puzzle. On one hand, pure luck shouldn’t make one person more deserving of punishment than another. To punish on the basis of luck is unfair. On the other hand, we often do exactly this. For example, we judge that a completed murder deserves a harsher punishment than an attempted one, even if the circumstances of the crimes were identical except for a random gust of wind. Likewise, we think a drunk driver who runs over a child deserves a lengthier prison sentence than one who runs over a mailbox, even if the two drivers were equally inebriated when they got behind the wheel.

Many philosophers and psychologists have tried to grapple with this apparent contradiction. Here, I discuss one of my favorite proposals, courtesy of David Lewis.

Leaving punishment to chance

While it’s unfair to leave punishment completely to chance, perhaps it’s okay to leave something to chance. Lewis invites us to consider a type of chance that seems fair: participating in a lottery. While lottery outcomes are randomly determined, their structure is predictable. If you ran the lottery many times over, the average outcome would converge on a single number.¹ Hence, if someone buys a lottery ticket, they know what to ’expect’, in a sense, and they can look up the possible outcomes with their associated probabilities.

If a monetary lottery can be fair, maybe a penal lottery can be, as well. Suppose that our criminal justice system decided to punish crimes by drawing random numbers from a computer-generated statistical distribution, with higher numbers corresponding to harsher punishments (e.g., more years in prison). The system could shape these distributions to scale with the severity of the crime, such that worse crimes have higher expected punishments. Because of the lottery structure, it would be possible for a very bad crime to be weakly punished and vice versa, but a criminal wouldn’t know his exact fate ahead of time. Only the predictable part of the lottery would be known and could function as a deterrent.

In the end, I’ll argue that this is not an ideal system. Yet it has a certain elegance. When a drunk driver decides to get behind the wheel, she subjects the world to a kind of lottery of harm. She could hit a pedestrian, damage property, and so on. This harm is partly random, partly predictable: the more reckless the driver, the greater the expected harm. Why not mirror this lottery with a punishment lottery, in which the expected punishment corresponds to the expected harm?

Better yet, Lewis argues, we don’t need to use a random number generator. Let the outcome itself determine the punishment. If the driver tragically hits a child, she’s punished severely; if she hits no one, she’s punished leniently (or not at all, if her drunkenness is undetected). Punishment will naturally scale with expected harm. Even though the driver can’t predict the exact harm she’ll cause ahead of time, is this any less fair than the decision to buy a lottery ticket?

Defining the odds

Yes, it’s less fair than buying a lottery ticket. To start, there’s a key difference between a standard monetary lottery and the penal one envisioned by Lewis: the former has well-defined odds; the latter does not.

Consider the moment that the drunk driver gets in the car to drive home. How should we define the probabilities of her causing various harms? As Lewis himself notes, this is complex, as probabilities depend on the knowledge that’s assumed. We could take a number of perspectives:

A. From the standpoint of an omniscient Laplace’s demon, the future is predetermined, and chance plays no role at all (excluding quantum effects). The probability that the driver causes a given harm is either 0% or 100%.

B. From the standpoint of the government, with all of its communal resources, much could be pieced together about the weather, traffic patterns, bystanders activity, and so on around the time of the crime. While this information is far more limited than a perfect physical description of the universe, it’s far more constraining than what the criminal knows. Thus, this hypothetical state observer might be able to predict an accident with high confidence.

C. From the standpoint of a ‘reasonable’ person in the position of the would-be criminal, the future should be quite uncertain. This hypothetical actor wouldn’t be able to forecast whether a child is playing on a street she’ll drive by or whether a specific road was just closed. She could only make coarse guesses about various risks.

D. From the standpoint of the actual woman getting into the car, the probabilities could be different still. In her drunken state, she may fail to consider important risks or be overconfident about her driving ability, which could play a key role in her decision to drive drunk.

In a puzzling passage, Lewis argues that we don’t need to settle on any of these descriptions, since we can make all of the above probabilities identical. I must admit that I don’t follow his argument and, hence, may be misrepresenting it.² But to the best I understand it, Lewis thinks that we can liken the actual outcome of the driver’s decision to a hypothetical “reenactment” of the crime. To put a modern spin on things, let’s imagine that this reenactment is created via a probabilistic computer program that simulates real-world events. We input some facts about the circumstances of the crime at the time the driver got in the car and then record the output of the first simulation we run. This simulated outcome determines punishment. According to Lewis, “if the reenactment is perfect, we automatically match the amount of risk in all four senses [described above].”

This is where I get lost. What does it mean for the reenactment to be “perfect”? If it’s too perfect, in the sense that the simulation will always output exactly what actually happened because it has a complete physical description of the universe (as in case A above), there’s no randomness and no lottery. If it’s less perfect, in the sense that it only has access to the information that the court can piece together (case B), the simulations will be stochastic, and the probabilities of simulating various outcomes will depend on assumptions about how the world works, which could be wrong. If the simulation tries to take the perspective of the driver (either an idealized driver, as in case C, or the real driver, as in case D), the program must be structured completely differently, as a model of human psychology in all of its complexity.³ Surely, the probabilities of various simulated outcomes from these models will be quite different than those from the other kinds. Lewis is wrong — we cannot “match the amount of risk” in all of the simulations.

Now recall that Lewis ultimately argues that we don’t need to run the reenactment at all; just use the actual outcome in its place. If the driver kills a child in the “perfect reenactment,” she does the same in the real world, and so on. But, as explained above, only the sci-fi deterministic type of reenactment trivially mirrors the real-world outcome, and this is not a lottery. It’s also not a useful basis for moral judgment, as it doesn’t consider the driver’s actual (or idealized) perspective when she made her decision to get behind the wheel. The driver surely wouldn’t drive drunk if she knew she was going to kill a child!

Presumably, for Lewis’ argument to succeed, we need to be able to simulate a lottery like the one described in bullet C above. What could a “reasonable person” forecast about their risks of harming others while driving in that particular inebriated state with a limited set of information? Are these beliefs calibrated with the true probabilities, as determined by the laws of physics?⁴ This is asking a lot of the proverbial reasonable person. Even just defining the possible outcomes from driving drunk is a tall task. Furthermore, minor details about the driver’s level of impairment could have dramatic implications for her reaction times and ability to avoid tragedy.

Maybe Lewis would argue that the reasonable person’s estimates need not be perfect — they’re close enough to the objective ones to count as a fair lottery. This would have to be verified, though. Do we really want to ground our punishment decisions on such an unstable foundation?

Embracing noise

Even if we grant that a reasonable actor could make fairly accurate estimates of her risks from impaired driving and the like, it’s still not clear that a penal lottery is a fair way to apportion punishment.

Suppose that this driver had barely anything to drink and was well below the legal blood alcohol limit (BAC). She will recognize that there’s still a small probability that her decision to drive in this minor state of fogginess could result in the death of a child or another tragic accident. Because this probability is so small, the expected punishment from the penal lottery will be low. But in the unlucky world in which an accident does occur, the driver would suffer the same punishment as a driver who caused this accident with a much higher level of impairment. Further, she faces a much worse punishment than a much more reckless driver who luckily avoids an accident.

Is this fair? On one hand, we could shrug our shoulders and accept the logic of the penal lottery: although the less impaired driver was less morally blameworthy when she decided to drive, she also faced a lower risk of receiving this severe punishment. So, because the odds of the penal lottery were more favorable for her, it’s fair for her to sometimes receive the same punishment as a more negligent driver or even sometimes receive a harsher punishment than this other driver. On average, moral culpability will be correlated with punishment.

On the other hand, is this the best we can do? If we knew that one driver was clearly more impaired than another at the time of the accident, wouldn’t we want this information to influence punishment? The lottery may be fair in a sense, but it also adds undesirable noise to punishment decisions. Noise is morally problematic, even if it’s unbiased. It feels like an injustice for a driver who barely transgressed to suffer an extreme prison sentence despite other versions of her getting away without punishment. The moral errors don’t cancel out across possible worlds, as each world is experienced only once, by a unique individual. It would be fairer to penalize everyone the same for a given level of recklessness.

Facing up to reality

In short, Lewis’ penal lottery suffers from two major drawbacks. First, in contrast to a casino game with known odds, it’s unclear how to characterize a complex moral decision, such as whether to drive under the influence, as a lottery. Could a “reasonable person” in such a situation assess risks with enough accuracy and precision to define a fair lottery? Second, assuming we could conceptualize these decisions as lotteries, we’d be introducing unnecessary randomness into punishments. Even if this randomness is unsystematic, it still results in some people getting more punishment than they deserve and others less.

At this point, we’ve returned to the puzzle with which we started: why is it sometimes fair to apportion punishment based on factors that are outside of one’s control? While Lewis tried to justify the fairness of this practice through a clever lottery analogy, some people might be inclined to argue that it, in fact, isn’t fair to punish disproportionately. It might feel fair because of irrational quirks of psychology, but on reflection, it makes little sense. Indeed, some researchers have contended that this phenomenon is an example of a more general error known as outcome bias, in which the outcome of a person’s decision unjustifiably shapes judgments about prior mental states.

I share this perspective, to an extent. If a philosophical thought experiment or a study vignette stipulates that two people make a decision to drive drunk under the exact same circumstances and with the exact same level of impairment, there’s no good justification for thinking that the driver who kills a child deserves more punishment than the one who doesn’t. They both subjected the world to an equal amount of risk, and the amount of foreseeable risk should determine punishment.⁵

Here’s where things get messier. When we leave the philosophical world of perfect hypothetical knowledge, we face irreducible uncertainty. We never know the exact circumstances of an accident. Was the driver with a 1.2 BAC who ended up running over a child really no more drunk or reckless than the one with the same BAC who was simply spotted swerving? Could the driver who committed manslaughter have experienced more drowsiness or cognitive impairment when she decided to drive? On the flip side, the swerving driver could have hit someone beforehand, but didn’t. Might she have been less impaired than the average driver with that BAC?

In short, when we’re uncertain about a driver’s true level of impairment, the outcome of her decision furnishes some evidence of her prior state. As Lewis himself notes, this could provide at least some justification for our intuitions to punish differently.

Who’s afraid of a little bias?

This justification for outcome bias might sound weak. A drunk driver who kills a child could end up getting decades more prison time than one who is simply spotted swerving. Chances are, two drivers with identical BACs would not be so different in their level of recklessness to deserve such different fates.

Nevertheless, let me borrow a page from Lewis and offer an explanation for these different punishments without fully endorsing the explanation. This story is grounded in principles from statistics. In short, whenever there’s uncertainty, there are two types of errors to worry about. The first type of error is the one we’ve just discussed — systematic error, also known as bias. Because of our overemphasis on the outcomes of bad decisions, unlucky drivers who cause accidents will, on average, suffer more than they deserve, and lucky drivers who avoid accidents will, on average, suffer less than they deserve.

All else equal, we’d like to minimize bias. But there’s a second type of error to worry about — unsystematic error, also known as noise or variance. Recall that Lewis’ hypothetical penal lottery intentionally added noise to punishment decisions. Although some people may find this unobjectionable, we noted the apparent unfairness in even an unbiased lottery with randomness. From the perspective of any given offender, noise hurts (or fails to hurt) just as much as bias. Hence, our penal system should try to minimize both bias and noise.

Unfortunately, this is a challenging endeavor. Policies that could reduce noise will probably increase bias, and vice versa. Simpler policies will be consistent in their prescriptions (low noise), but lack important nuance about the individual circumstances of a crime (high bias). Complex policies will have the opposite problem.

At one extreme, imagine that the justice system punished solely on the basis of outcomes. A drunk driver who was caught with a high BAC would receive no punishment unless he harmed someone or damaged property. A perfectly sober driver could receive a severe punishment if he killed someone, whether or not he deserved any blame.

Needless to say, this system would be incredibly unjust, even by the lights of ordinary people with “outcome bias.” It is far too simple. Nevertheless, consider one minor advantage of this simplicity: we wouldn’t need onerous trials to piece together the facts (other than the outcome) or juries and judges to make complex judgments based on limited information. Because everyone who caused the same amount of harm would get the same amount of punishment, noise would be held to a minimum.

At the other extreme, the justice system could devote endless resources to reconstructing the precise circumstances of a given driver’s decision to drive. In addition to using BAC (if available), experts could try to make inferences about the driver’s level of alcohol tolerance based on past drinking behavior, body type, genetics, and so on. Witnesses could offer their perspectives in court. Juries could deliberate endlessly about minutia to try to establish the facts as best as they could. And the judge making the sentencing decision could be completely unconstrained by sentencing guidelines. It would be possible for a drunk driver who killed a child to get off with no punishment if it was determined that the death was likely to have occurred even if the driver was driving responsibly, and a driver who caused no harm could receive a severe punishment if it was determined that she posed a massive risk of harm.

Of course, this procedure would cost a lot more money, time, and effort than the pure outcome-based one. But if we imagined that these are negligible sacrifices, would it be the best we could do?

The lesson from statistics is that it might not be. All of the tiny judgments and decisions of experts, jurors, and judges introduce degrees of freedom. Each of these agents — and the measurement devices they rely on — are prone to random errors that compound. In the end, the total amount of error in punishment decisions could exceed even the purely outcome-based policy described above. At the very least, we could reduce error by making the policy simpler, despite introducing bias. One such bias we might introduce is outcome bias. By partly anchoring punishment on the harm that was caused, we reduce noise.

Luck is unavoidable

As I noted earlier, I don’t fully endorse this solution to our original puzzle. If I had to guess, I would bet that ordinary people rely on outcome cues more than they should — perhaps because humans evolved in an environment of limited information — but that it’s also fair for the justice system to incorporate outcomes into its punishment decisions, even when these outcomes might seem to be a matter of luck. When we have more knowledge about the circumstances leading up to a decision, the outcome should matter less.

In the end, while Lewis is correct that there’s nothing intrinsically unfair about punishment depending on factors outside of one’s control, his justification is backwards. We shouldn’t deliberately introduce randomness into our punishment decisions in order to create a lottery; rather, randomness is a necessary feature of our uncertainty about the wickedness of the offense. Whenever somebody chooses to commit a crime, he should recognize that the outcome of his decision could lump him in with a population of offenders who did something much worse, or the opposite. The judges and juries who evaluate the crime will have to do their best with the information that’s most observable, and some of this information will be the result of luck.