If Prison Were a Disease, How Bad Would It Be?

by sarahconstantin1 min read7th Dec 201620 comments


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Cross-posting a comment from Sarah's blog:

Comparing life expectancies of people who have and have not gone to prison, as if “prison” were a disability, they compute that white males lose 19,665 person-years of life to prison per 100,000, black males lose 139,507 person-years, and Hispanic males lose 45,766 person-years. For comparison purposes, here is a table of person-years of life lost to the most common diseases in the US. Cancer, the top killer, only appears to cost 2882 person-years of life per 100,000. All causes together only cost 38,211 person-years of life per 100,000.

The prison YLL estimates were pretty hard to interpret, but I think the reason the numbers are so big is because it’s in different units than the NIH disease mortality numbers. From the paper you linked:

To provide context, rates of imprisonment and person-years of life lost to imprisonment were first calculated. Rates were calculated for each year, 2000 through 2004, for the age group 18 to 44 years. Rates of imprisonment in this age group were the average of the number of persons in prison per 100,000 population. Person-years of life lost to imprisonment were calculated by multiplying the number of persons imprisoned in a specific age group by years left to 45 years. Person years were then totaled for each gender and racial group and expressed as person years lost per 100,000 population.

As far as I can tell, here’s what they did. They assumed that everyone in prison is released at the age of 45. (This seems like a weird assumption but maybe it gives you numbers close to the true ones?) To repeat, since this was apparently unclear: Their calculation is assuming nobody incarcerated in a given year gets out before the age of 45, at which point they’re released with certainty.

So they limited their analysis to people age 18-44. For each calendar year reported, they counted the total number of people in prison in each group, and divided this by 100,000, to get the “Rate of imprisonment.” Then, to calculate “Person-years of life lost to Prison”, they multiplied this by the difference between the average inmate’s age and 45. Another way of putting this is that they summed the difference between each inmate’s age and 45, and divided by 100,000. (I backed out the multipliers and they’re all in the range 10-15, implying average ages in the range 30-35, about what you’d expect.)

This means that there’s substantial carry-over from year to year. For instance, the paper reports 141,108 “Person-years of life lost to Prison” per 100,000 African American men in 2000, out of 9,885 incarcerated per 100,000. The way they calculated it, if no one were imprisoned after 2000, the number reported in 2001 would be 141,108 – 9,885 = 131,223. In 2002 it would be 121,338, and so on.

By contrast, the NIH table is counting years of life lost due to disease-related deaths each year:

Person-Years of Life Lost is measured as the difference between the actual age stemming from the disease/cause and the expected age of death due to a particular disease or cause. Specifically, this measure is estimated by linking life table data to each death of a person of a given age and sex. The life table permits a determination of the number of additional years an average person of that age, race, and sex would have been expected to live.

These don’t carry over. Each year, a certain number of people die from a disease. For each person who dies, the NIH calculates the difference between the person’s age, and the life expectancy at birth of someone with their demographic characteristics. This is their estimate of that person’s years of life lost due to their cause of death. They then sum these estimates, and divide by 100,000. So, if I have terminal cancer this year, and die next year, this year I have 0 years of life lost, but next year my cancer is responsible for lost decades. This is an imperfect measure but at least measures a rate of some kind.

Comparing these two rates is comparing a stock and a flow. To get the “flow” numbers for years lost to prison, you would want to count total expected years incarcerated for people newly imprisoned each year. You can do this by taking “Person-years of life lost to Prison” in one year, and subtracting the number you’d expect if there were no new incarcerations (i.e. the reported “Person-years of life lost to Prison” for the previous year, less the reported “Rate of imprisonment” to account for each existing prisoner being a year closer to getting out.) For example, in 2001, the reported “Person-years of life lost to Prison” for African American men is 141,602. As calculated above, the expected number with no new incarcerations is 131,223. Therefore, new incarcerations between the 2000 and 2001 reporting dates account for 10,379 “Person-years of life lost to Prison” per 100,000 African American men. This is only half an order of magnitude more than cancer – by this estimate the average African American man spends 3x as many years in prison, as the average American’s lifespan is shortened by cancer. A bit of an odd comparison, but at least we’re not mixing stocks and flows.

Note that this backing-out method doesn’t give very accurate estimates. Some year the number is negative, presumably because the rule “prisoners are released at age 45” isn’t a perfect fit for the data, and some years many more people were released than that model expected, driving down the estimate of # of years left.

I put together a spreadsheet to illustrate the above calculations.

I feel like the appropriate comparison here isn't between prison and disease, but between prison and alcoholism or obesity. Like, prison isn't just some scourge that manifests wherever the wrong microorganisms gather. It is a consequence of certain behavior. It falls upon those who sin. It is punishment, and not tragedy.

If you let the bad guys take themselves hostage you have already lost. You can never rescue someone from themselves. When the sufferer and the sinner are one and the same you must close up your ears to the sufferer's wails, or you will soon find yourself wailing.

I feel like the appropriate comparison here isn't between prison and disease, but between prison and alcoholism or obesity

In that case it may be worth reviewing this post. (I'm sorry to say that the diagram seems to have disappeared.)

This wasn't intentionally misleading -- I deliberately just wanted to look at costs and not benefits, and it didn't occur to me that people would interpret that as a claim that prisons only had costs and no benefits. In retrospect, I've noticed that some people are reading this as a way stronger claim of the terribleness of prisons than I meant it (including quoting the numbers that I myself don't believe because the study is super dodgy.)

How did the cited studies try to argue causality?

In other words, it is expected that certain behaviour (drug use, "criminal lifestyle") both causes time spent in prison and lowered life expectancy. Just correlating time spent in prison and life expectancy does not cut the cake.

You would need some kind of randomized control group. For example: Suppose the judges responsible for granting parole were assigned on a last-name basis. Different judges have different statistics on granting parole. Then you compare life-expectancy vs last name of delinquents.

I like the article but agree with this. I also agree with a comment I saw on facebook that "victimless" crime would be a much better metric than "nonviolent" crime.

If you restrict attention to cases in which the criminal/accused definitely did nothing to harm others, all criminal justice issues would involve far fewer people, and I'm not sure if they'd even show up on the EA-scale radar in magnitude. Most people in prison probably did commit a non-victimless crime, many (?) shot by police were violent towards police, certainly most people executed are guilty of serious crime, probably a lot of people who plea bargain are guilty, etc. If you actually didn't care about harms to the guilty, your perspective would be VERY different.

certainly most people executed are guilty of serious crime, probably a lot of people who plea bargain are guilty

There are also people too poor to afford a good lawyer (or too stupid to realize they need one), so the question is how large fraction of those who were executed or accepted a plea bargain they make.

The whole system of a plea bargain is essentially a lottery -- imagine a situation where (a) you didn't commit a crime, but (b) you are quite aware that from outside you seem quite suspicious. For example, you accidentally walked near the crime area, but for completely unrelated and difficult-to-explain reasons. Or you actually had a conflict with the given person yesterday, then you went home, but you don't have any alibi for the night because you live alone and you didn't expect you would need one, and the next day the person is found murdered. So, you can either play the lottery, insist that you are innocent, without having any good proof, and with some indirect evidence pointing against you... and depending on how the jury and judge will feel at the moment, you might walk home, or spend 10 years behind the bars. Do you feel lucky? Or you may accept the plea bargain, where you are promised an order of magnitude less serious punishment (and later it may turn out they actually lied about some details, but you didn't know that at the moment).

In the past some people were executed, and when later the DNA evidence was examined it turned out it was actually someone else. Oops, shit happens.

To be clear, I think plea bargains are bad for exactly that reason.

The list of controls in the "prison reduces lifespan" study seems a little on the short side--race, age, gender, education, and the crime. It's fine if that's all that was available, but if you had some other data as well, I would expect to see the life span reduction reduced as well. Particularly if the major causes of death are homicide and drug overdose right after getting, a strong linear relationship between time spent in prison and life expectancy seems weird. I'm not sure how that would work, causally.

But mostly I agree with chron--you can't just completely ignore the possibility that the existence of prisons reduces crime.

I saw an article last month about prisoners being released, and having AIDS, HepC, and other transmissible disease treatment cut. They showed that the re-infection rates from just these released, and untreated inmates was infecting more folks than any other reservoir. Another community cost that is rarely mentioned

I didn't get that impression. Sarah wasn't stating: Here is a cost vs. benefit of Prisons. She was instead writing about how we could measure the costs of prison. If she doesn't write at all about benefits, there is no reason to infer that she is deliberately leaving them out to be misleading. Actually, I think this sort of inference towards what she is actually trying to say based on what you think she left out is misleading.

Gwern doesn't say anything interesting. He points out that you do, in fact, need to measure benefit for cost vs. benefit. I guess that would be an interesting point if there was any reason to suspect Sarah wasn't aware of this idea. Also, as far as what 'surprises' him as being a metric for reasonableness is useless. It's no secret to anyone who reads about this stuff that the incarceration system in the US has a rich history of being incredibly disturbing.

Evidently Gwern thinks that so long as it registers as 'bad', that's okay, because hey, bad is a deterrent! Whereas Sarah is taking the more methodical approach of actually measuring how bad it might be.

I don't think someone writing about only costs, or only benefits, is necessarily bad. I never go the impression the article was advocating for widespread release and abolition of the prison system. It was instead quantifying the measured cost. You can stop there, that's all the article intended to do.

I guess that would be an interesting point if there was any reason to suspect Sarah wasn't aware of this idea....Whereas Sarah is taking the more methodical approach of actually measuring how bad it might be. I don't think someone writing about only costs, or only benefits, is necessarily bad. I never go the impression the article was advocating for widespread release and abolition of the prison system.

The same person you're saying is being modest and merely examining one part of the problem is the one who dismisses out of hand any talk of deterrence as being (I quote) "cartoon supervillain" thinking.

If she really wanted to approach this sensibly, she would've started with it being an explicit cost-benefit approach and compared a widely-agreed-upon inefficiency in the prison system - for example, if she had started with a discussion of the net QALY loss due to incarceration for marijuana-related crimes (which I believe now a majority or near-majority of the USA, and supermajority of LWers and her readers believe should be decriminalized and/or legalized as having minimal social & health costs) and compared that to existing disease death tolls. That would be an interesting, valid, and intellectually relevant comparison.

To talk about the system as a whole and dismiss out of hand any discussion of the (huge, enormous, by many orders of magnitude, because it makes it possible for there to be a USA at all with anything approaching its current population size compared to a hunter-gatherer tribal equilibrium) benefits of a working legal system is just plain bizarre.

She's not even correct when she tries to excuse her dismissal by saying

like, how much could improving criminal justice buy, if it were done optimally?

The current cost of prison in lives is nothing remotely like the marginal profit from shifting to an optimal system, and amusingly, this fallacy is directly addressed by a recent submission: "Costs are not Benefits".

Costs are costs - that is all.

Saying that you can estimate how much the benefit from optimal criminal justice from how much it currently costs is like saying, 'this random house costs $500k, so the profit from finding the best real estate investment must also be somewhere around $500k!' No, the profit from the optimal decision could be anywhere from -$500k (the Detroit market is in a bubble and you don't want to buy anything because it will soon be worthless after property taxes) to $0 (efficient market, no expected profit or loss) to hundreds of millions (huge mine soon discovered under the land). 'This surgery costs $1000, the benefit from an optimal decision to do it or not do must be around $1000!' No, it could be anywhere from +$10m (cures a horrible disease which is tantamount to being dead, giving you a normal life with full statistical value of life) to -$10m (kills you as a child, costing you everything).

I think you're being disingenuous and taking semantic laziness on Sarah's part as a fundamental flaw in the reasoning itself. I think it's fair to say she wasn't trying to dismiss any talk of deterrence as being cartoon villainy (I didn't see a super prefix there? But maybe it was an edit. Doesn't really matter). But was responding to your specific, separate from the argument of her post, comment noting that she wasn't willing to consider the benefits of, in the example you gave, deterrence based rape. Which is different from her considering deterrence in the original post, and saying it's only worth considering for 'cartoon supervillians.' Whether deterrence based implied prison rape is a benefit is a totally different beast.

I mean, the analogy might not be great. And the post might not seem useful to you (or others) if it's strictly studying costs. But I think the argument "This wasn't a useful post because it excluded benefits, which is something I think is integral to this study. It also wasn't useful because it used a lazy analogy that seems to misrepresent the reality, even if that wasn't your intention." Is different than what you're saying. I think you'll agree with me on that, no?

I think you're being disingenuous and taking semantic laziness on Sarah's part as a fundamental flaw in the reasoning itself.

It is a fundamental flaw. A cost is not a benefit, nor is it a profit. This is a hard and fast point, similar to: p-values are not posterior probabilities; probabilities are not utilities; correlations are not causations; maps are not territories; and so on.

When Sarah asks

like, how much could improving criminal justice buy, if it were done optimally?

This is a great and valid question! I have many strong opinions on the topic, such as the high human cost of the War on Drugs and whether the prison rape epidemic is a good idea. However, it has next to nothing to do with the raw total of how many people are in prison. Because the deterrence tremendously affects everyone else and costs are not benefits.

With something like cancer, it is totally reasonable to ask how many people have cancer to estimate an upper bound on the value of researching cancer. If 1m people have skin cancer, this is a good starting point for upper bounding the value of skin cancer research - maybe skin cancer research is totally intractable and it's worth $0, but you can be sure the value is <1m people. And if $1b gets spent on treating skin cancer every year, it's reasonable to suggest that the value must be at least $1b. This is because cancer is a very nicely behaved problem and we do not live in a world where if you cut skin cancer treatment budgets by 50%, the skin cancers might start exploding and infecting everyone in a chain reaction of ever growing Akira-sized cancer blobs causing the collapse of skyscrapers and the end of Western civilization and life as we know it and everyone agrees as they roam the wastelands looking for gasoline that this is very unfortunate and we probably should've not cut the skin cancer budget.

Alright, I think if you and I sat down and talked about the cost vs. benefit of incarceration and the war on drugs, we would be in almost complete agreement. The costs are in equilibrium with benefits, so it's sort of like trying to see where you can save the most utility a year by looking at your financial records: Sure, the more expensive items are more likely to have a high magnitude of savings, but they also could generate more utility. You haven't ever read anything I've written, but I've read your site, so you'll have to take my word on that :)

That means our disagreement here has more to do with our almost-legal interpretation of the article, which is sort of a boring thing to disagree on honestly. I'm willing to give her reading a more charitable interpretation, I am probably filling in the gaps in her article with my own reasoning, which perhaps is too charitable or incorrect. I still think you are not being charitable enough, but again, that's a boring thing to disagree on. So let's call it good.

"Prisons are supposed to be terrible" just sounds like a cartoon villain statement when you think about the actual ways in which prisons are terrible, though, tbh. I'm inclined to trust my instinct to just go NOPE YOUR OPINION IS NOT MY PROBLEM when I see someone who responds that way.