However wrong it may be to maintain the death penalty at all, it is surely wrong to execute members of our society based on a jury’s conclusion that they are factually guilty “beyond a reasonable doubt.” As I put it a few years ago on Twitter on the evening of the execution of Troy Davis:

If you wouldn't bet your own life that Troy Davis is guilty based on this evidence, you shouldn't be willing to bet his. Simple as that.

Is that the right standard? I think in death penalty cases that it is. A risk of erroneous conviction will exist in any justice system, and, as a consequence, any society must sometimes punish the innocent (and, necessarily as further consequence of that, fail to punish the guilty) if it punishes at all. If imprisonment is one such punishment, there will always be among us the wrongfully imprisoned. One source of error, but not the only one, is inherent in the standard we ask juries to apply to determine guilt: “beyond a reasonable doubt.”

Confidence

I have asked students from time to time what they think “beyond a reasonable doubt” means or should mean in terms of probabilities. They have ranged from about 60% confidence in guilt (a number I found absolutely shocking) to about 98%, with most students seemingly inclined toward 95%. I wonder, though, what this even means. One way to understand this apparently probabilistic description would be to say that the 95% threshold reflects the required level of confidence in one’s judgment such that if presented with a large enough random sample of judgments to make, a wrong judgment of guilt would be reached 5% of the time. So if we tried massive numbers of randomly selected people for crimes, 5% of the small number of people found guilty would in fact not be guilty. (Note that the higher this threshold, the greater the number of factually guilty who are found not guilty.)

There is a problem, though, with ignoring the role played by police and prosecutors, who do not conduct themselves by charging everyone with a crime and letting juries sort things out. They only charge if they believe it will lead to a plea bargain or, at worst, a guilty verdict at trial. And so our sample of suspects appearing in front of juries is not random. You might still try to argue that the erroneous conviction rate would be about 5%, because the prosecutor and police would, more or less, charge all defendants who are likely to be found guilty. So all potential defendants who they estimate are, say, 92% likely or more to have committed the crime will be charged. If any defendant whom a jury would find 95% likely to have committed a crime would be estimated 92% likely to have committed a crime by the prosecutor (and if there is no bias toward guilt among detected suspects), then all identified suspects who would be found guilty by a jury using a 95% threshold would be charged. And therefore all potential erroneous convictions among identified suspects will in fact occur. (Very limited research tells me that conviction rates at trial hover between 75% and 90% in the United States. This number reflects, though in ways too complicated for me to analyze in the few hours I have to give to this post this morning, prosecutorial success in predicting what juries will do.)

This, though, is far too simple and not only because likelihood estimates by prosecutors are not so precise. The wrongful punishment rate depends on the standard of proof that is required, yes, but also on the rate and distribution of systematic deception practiced by police and prosecutors on the one hand and defendants and their attorneys on the other, the degree of post-conviction effort put into factual review, and, obviously, much more.

Moreover, the distribution of guilt likelihoods among defendants is not uniform across all possible crimes. For some crimes, it might be nearly certain whether an individual is guilty or innocent. This depends on the definition of the crime and social facts about how it is committed and detected. Among potential sources of error: wrong identity, wrong inferences about mental state, wrong guesses about what actually occurred? For example, if it is a crime to think negatively about the king, there are some rather evident proof problems, and the way we infer a person’s thoughts will affect our stated level of certainty regarding guilt. We should expect a lot of borderline cases of this crime and thus perhaps a significant probability juries will have to wrestle with cases in and around the 95% level. If, in contrast, it is a crime to sing the national anthem of another country at a sporting event attended by more than 10,000 people and if (1) it is clearly defined statutorily and culturally what a sporting event is and (2) always clear, owing perhaps to technology and culturally embedded meticulousness, whether attendance is at least 10,000, then the rate of erroneous charging would surely be very, very low. These examples of absurd crimes are only meant to illustrate that erroneous conviction and punishment rates depend on the rate at which plausibly guilty but innocent defendants are put in front of juries and the distribution of uncertainty among the plausibly guilty.

The inequality of “reasonable doubt”

Getting the right estimate of wrongful punishment matters. It is impossible to answer whether the forced sacrifice we require of imprisoned innocents is worth the benefits of punishing the guilty without knowing how many innocents we are sacrificing and how severe their burdens are.

I strongly suspect that the level of confidence we vaguely require for conviction is far too low. Further, I think it is in practice too low because the risk of erroneous conviction is not distributed equally among us. Put differently, I hypothesize that a politically influential person’s preference for the confidence level to use in criminal trials is, generally, much lower than the strength of their preference to avoid their own (or a family member’s) wrongful conviction would imply. And further, this owes to the fact that those in a position to affect the operation of the law are far less likely to be put in jeopardy of wrongful conviction than those who lack such power. (Yes, this is Rawlsian: if people believed they were as likely to be wrongfully convicted as anyone else, they would probably prefer a higher conviction threshold than if they believed the probability of wrongful conviction fell disproportionately on others.)

A recent paper by Gross, O’Brien, and Kennedy attempts to use the unusual level of post-conviction scrutiny of death sentences to estimate, conservatively, the wrongful conviction rate:

There is no systematic method to determine the accuracy of a criminal conviction; if there were, these errors would not occur in the first place. As a result, very few false convictions are ever discovered, and those that are discovered are not representative of the group as a whole. In the United States, however, a high proportion of false convictions that do come to light and produce exonerations are concentrated among the tiny minority of cases in which defendants are sentenced to death. This makes it possible to use data on death row exonerations to estimate the overall rate of false conviction among death sentences. . . . . We . . . estimate that if all death-sentenced defendants remained under sentence of death indefinitely, at least 4.1% would be exonerated. We conclude that this is a conservative estimate of the proportion of false conviction among death sentences in the United States.

And that’s conservative. In 2012 there were about 600,000 people newly imprisoned in state and federal facilities. It is likely that at least 24,000 people should not have been. (Interestingly, that is in the same neighborhood as other social risks we seem willing to take: Car and gun deaths both hover around 30,000 people a year.) All told, though, there were about seven million people in the U.S. in prison, on probation, or on parole. Among them, very likely, were at least 280,000 innocent people. 280,000.

Achieving justice in risk bearing

Part of the solution to the problem of imprisoning the innocent surely lies in more elaborate review, reducing inflated prison sentences (thus reducing the cost of uncorrected wrongful convictions), severely cutting back on reliance on eyewitness testimony, and implementing trial and police procedures that minimize racial and other biases. This is ground that has been exceedinly well covered by Brandon Garrett in, among other works, Convicting the Innocent.

Even if it is impractical to encourage a hypothetical internalization of risk of error in every jury trial, I believe it is both possible and incumbent upon us to do so in death penalty cases (which, to be up front about it, I think there should be zero of). This follows from the simple fact that the required level of confidence in guilt or innocence should not rationally be the same number in all cases.

In tort law, it has long been recognized that the level of care we expect from people in society should be based on both the probability and gravity of harm a behavior generates on the one hand and the “burden” of altering the behavior to avert the harm on the other. So whether I should install a handrail on steps should depend on whether the cost of the rail is exceeded by the risk-adjusted cost of injuries that would occur in the rail’s absence. This formulation has rather obvious problems, and a marginal analysis of the multitude of substitute behaviors would alleviate some of them. But the basic idea that more care should be taken when a greater risk of harm looms is sound.

Our criminal law does not work that way. (The standard of proof in tort law is similarly insensitive to potential damages.) We often do not even allow jurors to know the range of penalties that might result from their finding guilt. And we certainly do not instruct them to achieve a greater confidence in guilt before rendering that verdict in cases in which punishment is more severe than in cases in which it is less severe. One surely should ask whether this is sensible. But I’ll leave the general question to others for now.

Instead, let us focus on death penalty cases, in which no post-punishment error correction is possible and no compensation for wrongful punishment could possibly be adequate. Here, it would be useful to disentangle the jury’s decision whether the defendant should be punished at all, perhaps with life in prison, from whether the defendant should be put to death. Indeed, the law does this by requiring one decision as to guilt, reached (at least as a matter of the law on the books) according to “reasonable doubt,” and a second decision concerning whether the death penalty is deserved, the defendant’s guilt being assumed fully decided.

But I would propose that after the so-called “guilt phase” of a capital case, the question of guilt or innocence should return. Having decided that the defendant is guilty beyond a reasonable doubt and that at least imprisonment is justified (because the tragic but omnipresent risk of erroneous imprisonment is deemed acceptable on account of “what else can we do?”), the jury should then ask, “Are we prepared to order the defendant killed?” And this question should not assume guilt but must be sensitive to the risk of error.

Here we should ask whether it makes sense to risk another’s person’s life. To be quite honest, I think the answer to this question in this context is always no. But assuming it is ever sensible to risk the life of another when confinement is an option, it should only be on grounds that it would be fair to risk anyone’s life in case of error. That is, if the slain defendant turns out to be innocent, we would have killed an innocent person in order to achieve a broader social purpose of deterrence, incapacitation, retribution, or whatever. And whatever that purpose is, we will have determined that, despite the risk the defendant may be innocent, the execution should occur in order to further it. If that is so, then we have deemed the purpose important enough that we are willing to place upon the defendant’s very existence whatever the risk of error is to pursue it. But an innocent defendant is no more blameworthy than anyone else and has no special burden to carry such risks for us. And so we should only pursue the death penalty in a case if we would be willing to kill a randomly selected person if we turn out to be wrong about the verdict.

The price of the death penalty is that, at a rate commensurate with the aggregate confidence levels in our verdicts, we will kill innocent people who have no more cause to be killed than anyone else. That confidence level, then, simply must be calibrated so that it calls for no more risk than we would ask anyone in society to bear to achieve the death penalty’s purposes.

At the guilt phase the jury should be instructed:

You have determined that the defendant is guilty of the crimes charged beyond any reasonable doubt. This, of course, did not require you to determine to a certainty that the defendant is guilty. At this stage, I instruct you to reject the death penalty in this case, and impose life in prison without parole, unless you are so certain of the defendant’s guilt that you would offer to take his or her place and be executed should his or her innocence later be established. Of course, this would not literally be required of you. But you must not decide to impose the death penalty unless you would honestly be willing to bet your own life on the defendant’s guilt.

Could it seriously be objected that by so personalizing the decision to impose the death penalty, the jury will be unduly dissuaded from doing so? If a juror is unwilling to take this bet, what does it say about the propriety of imposing that bet on another? While, tragically, we impose that risk on the imprisoned, that is because there is no other way and because there is at least the possibility of correction and compensation.

It is, indeed, part of the price of civilization that we must all live under the threat of erroneous imprisonment. We must, though, recognize that this risk of error is not equally shared and that in death cases it represents the ultimate consequence. If we cannot share it equally, we should at the very, very least be asked to imagine that we do.