Does the death penalty save lives? (part 1)

A few days ago, I argued that liberals should support the death penalty because it saves innocent people's lives by deterring murder. But that all hinged on a new crop of empirical studies. That means a lot is riding on the supposedly improved statistical methods. If those methods don't hold up, the argument doesn't hold up. So why should we believe the studies?

First, I think it's worth noting that many death-penalty opponents have no qualms about making the most elementary statistical blunders. They often flatly assert that the death penalty is not a deterrent because the states that have the death penalty have more homicide than non-death-penalty states.

They don't point out that the four-year nationwide abolition of the death penalty in the United States was correlated with skyrocketing homicides (see the second chart in this blog post). Now, that doesn't prove that abolishing the death penalty increased homicides, but by the same token, the higher homicide rate in death-penalty states doesn't prove that the death penalty increases homicides.

So there should be something more than sheer correlation. It looked to me like the new studies went beyond that: the write-up in the New York Times mentioned "multiple regression analysis" by "sophisticated econometricians" and so on.

But John Donohue and Justin Wolfers wrote a law review article that purported to demolish these studies (PDF). (Thanks to LemmusLemmus for bringing this to my attention.)

Unfortunately, I can't understand 90% of it. So I was going to skip that as blog fodder. I prefer to blog about things that I have some comprehension of.

Well, even though I have no idea if Donohue & Wolfers's analyses of "instrumental variables estimates" and "panel data methods" are right or wrong, I was able to grasp a couple of their points. And neither of those points gave me much confidence that they got things right in the parts I don't understand. Here's the first one:

Donohue & Wolfers say it's just not plausible that the death penalty deters crime because it poses such a slight risk that you'd be irrational to be deterred by it.

Similarly, Steven Levitt (of Freakonomics fame) says that "economists who argue that the death penalty works are put in the uncomfortable position of having to argue that criminals are irrationally overreacting when they are deterred by it." The suggestion is that it's implausible to think that "criminals" would be deterred by the death penalty, since the death penalty is so rarely applied that the risk, from the point of view of someone deciding whether to kill, is negligible. (Scare quotes around "criminals" because that's a really poor word choice. We're not talking about some distinct group of marauding ax murderers. We're talking about people who might decide to kill, or might end up being deterred and end up looking like pretty normal citizens, not "criminals.")

Well, wait a minute. Why is it implausible that the death penalty would deter out of proportion with the actual likelihood of being executed? Wouldn't the really implausible thing be to say that people are perfectly rational in how they respond to death-penalty statistics -- and not just perfectly rational, but perfectly well-informed?

A couple examples: Most people overreact to the risk of being killed by a terrorist attack. I myself would be hugely deterred from traveling to Israel, even though I know it's irrational for this to be such a big factor in my decision. I've never been to Israel, but I do see lots of images of gruesome terrorist attacks over there. I'm not calculating the actual likelihood that it would happen to me -- it's much less rational than that. I'm instinctively focusing on the vivid images I've seen, rather than the very high likelihood that I'd have a normal, pleasant vacation. Behavioral economists refer to this as the "availability heuristic" (PDF).

By the way, here's something odd. One person who agrees with me about terrorist attacks is Steven Levitt: "Humans tend to overestimate small probabilities, so the fear generated by an act of terrorism is greatly disproportionate to the actual risk." Well, not only is Levitt the source of the above quote expressing skepticism about deterrence, but he also wrote an article in which he directly argued that the death penalty isn't a deterrent because it's too rarely and slowly applied to affect a rational person (pp. 319-20 in this PDF).

Why would Levitt think the human mind "overestimates small probabilities" when it comes to terrorist attacks, but not executions?

Another example: flying in a plane. I fly a lot, but I'm scared every time I do it because I'm imagining that the plane could go haywire, crash, and kill me. I'm much less likely to think about getting into a car crash, even though I'm statistically more likely to die in a car than on a plane. I'm not looking up statistics or doing calculations -- I'm just thinking of the most vivid scenario that jumps out at me. To drive home how overpowering a deterrent the fear of a plane crash can be: Hillary Clinton's top spokesperson, Howard Wolfson, never flies, which, as the great blogger Josh Marshall points out, is "an astonishing feat given the nature of modern campaigning." (Marshall also talks about his own fear of flying and hints that it might have altered the course of his career.)

I can't believe that those who are weighing whether to commit homicide are dramatically more rational than me (or Wolfson). In fact, they're probably less rational, since murder itself is such an irrational gamble to begin with.

But just because they're irrational in these specific ways doesn't mean they're ignorant of the death penalty's very existence, which seems to be the assumption made by those who say the death penalty can't be a deterrent because it's so rarely applied. If you're in a position where you're considering whether to kill someone, you probably know whether your state has the death penalty. That doesn't mean you sit around perusing the relevant statistics; it could just mean you've seen headlines, or maybe even heard stories about people you know.

I'm largely riffing on Cass Sunstein and Adrian Vermeule's argument about "bounded rationality" (PDF):

[S]uppose that like most people, criminals are boundedly rational, assessing probabilities with the aid of heuristics. If executions are highly salient and cognitively available, some prospective murderers will overestimate their likelihood, and will be deterred as a result. Other prospective murderers will not pay much attention to the fact that execution is unlikely, focusing instead on the badness of the outcome (execution) rather than its low probability. Few murderers are likely to assess the deterrent signal by multiplying the harm of execution against its likelihood. If this is so, then the deterrent signal will be larger than might be suggested by the product of that multiplication.

I always find it surprising that the death penalty is the one punishment about which people say that it's too rarely applied to motivate people to avoid getting it applied to them. It seems to me that it's the one punishment that would vividly stand out in people's minds as something to be avoided, much more so than a relatively abstract distinction like getting 20 years vs. 30 years in prison. Of course, that distinction is anything but abstract for the person who actually has to serve the sentence, but the relevant question is how the prospect of these punishments is likely to affect someone who hasn't gone through them yet. Qualitative differences (death vs. prison) seem a lot more likely to make an impression than quantitative differences (20 years vs. 30).

Ironically, death penalty opponents themselves may be contributing to the deterrent effect by drawing attention to how horrifying the death penalty is, especially if they focus on the vivid details of executions.

One last thing: everything I've said in this post has been assuming that it really would be irrational to be deterred by the death penalty. But that's far from obvious. As Richard Posner put it: "even a 1 percent or one-half of 1 percent probability of death is hardly trivial; most people would pay a substantial amount of money to eliminate such a probability."

I said I have a couple problems with Donohue & Wolfers's attack on the deterrent studies -- that's one of them. The other one is that they ignore the very data that most clearly show deterrence, which seems to throw off their whole metastudy. I'll explain why soon.

UPDATE: Uh, wow. See the comments for an enormous amount of material criticizing the Donohue & Wolfers article. Thank you, Dudley Sharp.