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Probability And The Death Penalty

I don't mean to harp on this at a time when everyone's attention is rightly focused either on college football or Iowa, but in response to my post below on the death penalty, commenter jm_rice writes:

As it is, no one can name a case, where someone who was executed in America was later exonerated.  Even if theoretically possible, it is still less likely than walking out the door and being struck by lightning.

And commenter psantillana responds:

And do you believe the rewards of killing the convicted murderer - versus life imprisonment - are so great that they justify killing innocent people? If so, what would be the largest acceptable ratio of innocent to guilty executed?

These are absolutely the right questions to ask death penalty supporters, and if they want to be taken seriously they need a better response than jm_rice's (sorry, jm_rice). I personally believe the answer to psantillana's first question is "yes." The question of what ratio is acceptable is more difficult, and necessarily hinges on subjective moral intuition. Since the death penalty was reinstated in 1976, 1,099 people have been put to death in America. My instinct is to say that if two or three of them were innocent, that would probably be an acceptable (though still, obviously, tragic) price to pay.

The problem is that it's all but impossible that the actual figure is that low. Anyone with a modicum of quantitative sense ought to recognize the absurdity in jm_rice's comment (again, sorry--just using you as an example!). Your chances of getting struck by lightning in a given year are one in 700,000; assuming you walk out your door a thousand times in a year, that makes the odds one in 700 million. I doubt the odds of executing an innocent person are as low as one in 70. At the time Illinois suspended its death penalty in 2000, it had exonerated 13 people from death row and put to death 12. Given that astonishing rate of error in initial convictions and sentencing, it defies credulity to suggest that the overburdened appeals system could catch all the trial courts' mistakes. (And it's curious that those who seem so sure that government can be so precise and effective in this one instance are usually the same people who deride its capacity for doing almost anything else competently.) It is true that there hasn't been a definitively proven case of wrongful execution (though there are some where it seems highly probable), but there are good reasons for this: comparatively few people spend their time investigating crimes that led to past executions, and absent an unlikely confession from someone else, proving innocence is exceptionally difficult. Moreover, "innocence" and "guilt" are not binary here; because the death penalty tends to be imposed in cases where aggravating circumstances are present, a prisoner can be wrongly executed, even if he or she was involved in the crime, if a jury errs in its finding about the applicability of the death penalty.

It would be nice to have a criminal-justice system in which we could be certain enough about the guilt of condemned prisoners to put them to death, but such a system, if even possible in the first place, would likely be prohibitively expensive.

--Josh Patashnik