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Stuff [Aug. 5th, 2009|01:50 am]
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This probably should have been posted to Less Wrong, but I feel like it would have been preaching to the choir there, and I was annoyed enough that I had to post it somewhere.

Recently on both sides of the health care debate I have been hearing people make a very dangerous error. They point to a situation in which someone was denied coverage for a certain treatment because it was expensive and unproven, and say: "This is an outrage! We can't let 'death panels' say some lives aren't worth saving! How can people say money is more important than a human life? We have a moral duty to pay for any treatment, no matter how expensive, no matter how hopeless the case, if there is even the tiniest chance that it help this poor person."

All of these are simple errors. Contrary to popular belief, you can put a dollar value on human life. That dollar value is $5.8 million. Denying this leads to terrible consequences. Let me explain.

Consider the following question:

A man has a machine with a button on it. If you press the button, there is a one in five million chance that you will die immediately; otherwise, nothing happens. He offers you some money to press the button once. What do you do? Do you refuse to press it for any amount? If not, how much money would convince you to press the button?

When you have an answer, and only when you have an answer, check underneath the cut.



If you answered something like "Never for any amount of money," or "Only for a million dollars", you're not thinking clearly.

One in five million is pretty much your chance of dying from a car accident every five minutes that you're driving. Choosing to drive for five minutes is exactly equivalent to choosing to press the man's button. If you said you wouldn't press the button for fifty thousand dollars, then in theory if someone living five minutes away offers to give you fifty thousand dollars no strings attached, you should refuse the offer because you're too afraid to drive to zir house.

Likewise, if you drive five minutes to a store to buy a product, instead of ordering the same product on the Internet for the same price plus $5 shipping and handling, then you should be willing to press the man's button for $5.

When I asked this question to several friends, about two-thirds of them said they'd never press the button. This tells me people are fundamentally confused when they consider the value of life. When asked directly how much value they place on life, they always say it's infinite. But people's actions show that in reality they place a very limited value on their life; enough that they're willing to accept a small but real chance of death to save five bucks. And this is a very, very good thing. A person who literally placed infinite value on their own life would be eternally miserable.

People make decisions through a complex method, but it approximates simple weighing of benefits and costs. If a certain action has benefits worth 5 Arbitrary Units and costs worth 3 Arbitrary Units, then the total gain is 5 - 3 = 2 AUs, and it's a good decision. If the action has benefits worth 5 Arbitrary Units, and a 1 in 10 chance of losing 10 Arbitrary Units, then the total gain is 5 - (1/10)(10) = 5 - 1 = 4 AUs, and it's still a good decision. If the action has benefits worth 5 Arbitrary Units and a 1 in 10 chance of losing 100 Arbitrary Units, the total gain is 5-(1/10)(100) = 5 - 10 = -5 AUs. That is, on average, you lose five Arbitrary Units by taking the action, its costs are greater than its benefits, and you should decide against it.

Now, imagine the poor guy who has literally assigned infinity value to his life. Anything times infinity is infinity, so even the slightest risk of losing his life trumps any possible benefits. Drive to work in the morning? There's a tiny chance he might get in a car crash, so no. Have another cookie? There's a small chance he might choke on it; that's out too. Go to the ball game? There's a small chance he might get hit on the head with a fly ball and killed instantly; no way. The person would be limited to staying in a locked room, getting out only to pick up food delivered by grocery van to his front step, purchased with the disability benefits he would no doubt get after the world deemed him insane.

In reality, we don't do that. We value our lives highly, but we also value other things like having fun, and making money. We value our lives only a finite amount more than we value these other things. The same is true of other people's lives. Although we value other people's lives highly, since we're willing to get in a car when we know we might accidentally run one of them over, we can't value them infinitely highly.

Let's return to the topic of health care. A poor woman, let's call her Blanche, has cancer. Her doctors have said her case is hopeless and she has only a few months to live. However, a renegade doctor claims to know of an experimental treatment that could help her. It hasn't been proven to work, but there's a tiny chance that it might. The treatment costs ten million dollars. You are the insurance company worker assigned to Blanche's case. How do you decide whether or not to give her the treatment?

One idea is to treat her on the principle that everyone should get every possible treatment. Would this cause any problems?

Insurance companies have a finite amount of money; they can only spend money they have. In one insurance company, customers might pay hundred million dollars in fees each year, so the total amount of money the insurance company can spend on all its customers that year is a hundred million dollars. In reality, since it is a business, it wants to make a profit. Let's say it wants a profit of ten percent. That means the total amount of money it has to spend is ninety million dollars.

As a simplified example, let's imagine an insurance company with one hundred customers, each of whom pays $1. This insurance company wants 10% profit, so it has $90 to spend (instead of our real company's $90 million). Seven people on the company's plan are sick, with seven different diseases, each of which is fatal. Each disease has a cure. The cures cost, in order, $90, $50, $40, $20, $15, $10, and $5.

We have decided to give everyone every possible treatment. So when the first person, the one with the $90 disease, comes to us, we gladly spend $90 on their treatment; it would be inhuman to just turn them away. Now we have no money left for anyone else. Six out of seven people die.

The fault here isn't with the insurance company wanting to make a profit. Even if the insurance company gave up its ten percent profit, it would only have $10 more; enough to save the person with the $10 disease, but five out of seven would still die.

A better tactic would be to turn down the person with the $90 disease. Instead, treat the people with $5, $10, $15, $20, and $40 diseases. You still use only $90, but only two out of seven die. By refusing treatment to the $90 case, you save four lives. This solution can be described as more cost-effective; by spending the same amount of money, you save more people. Even though "cost-effectiveness" is derided in the media as being opposed to the goal of saving lives, it's actually all about saving lives.

If you don't know how many people will get sick next year with what diseases, but you assume it will be pretty close to the amount of people who get sick this year, you might make a rule for next year: Treat everyone with diseases that cost $40 or less, but refuse treatment to anyone with diseases that cost $50 or more.

This rule remains true in the case of the $90 million insurance company. In their case, no one patient can use up all the money, but they still run the risk of spending money in a way that is not cost-effective, causing many people to die. Like the small insurance company, they can increase cost-effectiveness by creating a rule that they won't treat people with diseases that cost more than a certain amount.

There is a similar argument for not spending money on a treatment that's unlikely to work. Once again you have $90. There are four patients with four different fatal diseases, A, B, C, and D. Each costs thirty dollars to cure. In this case, your only option is to cure A, B, and C and tell D that unfortunately there's not enough left over for him.

But what if the cure for A only had a 10% chance of working? In this case, you cure A, B, and C and have, on average, 2.1 people left alive. Or you could tell A that you can't approve the treatment because it's not proven to work. Now you use your $90 to treat B, C, and D instead, and you have on average 3 people left alive. By denying someone an unproven treatment, you've saved .9 lives. An insurance a hundred times bigger than this one has saved ninety lives by denying unproven treatments, and so on.

It would certainly be nice if the insurance companies had more than $90 to spend on health. But there are only a few ways to do that. One is to charge more for insurance. This is what's been happening the past several years. Unfortunately, insurance now costs more than many people can pay, so the insurance companies can't keep raising prices forever.

Another way is to ban the insurance companies from making a profit. This has two downsides. One, it doesn't free up all that much more money, as we saw in the example where the insurance company had $100 instead of $90 to spend on health. Two, it's just plain mean to the insurance companies. We don't force people in grocery stores to work without pay because we think it's important that the poor get food, so why should we force people in insurance companies to work without pay because we think it's important that the poor get health care?

A final way is to give control of insurance to the government. This will help a little. For one thing, the government doesn't want to make a profit, so if it collects the same $100 in taxes that the insurance company did in fees, it can spend the full $100 on health. For another, the government can raise taxes if it wants more money to spend. This seems slightly better than the insurance companies charging more, because the government practices progressive taxation and so a bit more of the burden would fall on the rich, who can afford it. But this only goes so far. You can only tax the rich just so much before it's mean to the rich, and in any case you can't tax them more than 100%.

The point is that in any case, you will only have a finite amount of money to spend on health care. You can either give it to everyone on a first-come first-served basis, in which case lots of people will die unnecessarily, or you can ration it out by denying treatment to some people, in which case many more people will live.

When people say "I heard about poor Blanche with cancer on the news, and the greedy insurance companies denied her treatment. I think they should treat her regardless of how much it costs them!", what they are really saying is "I think the insurance companies should devote proportionally more money to treating cases of sympathetic-sounding people who make it onto the news, and proportionally less money to everyone else."

So, in the real world, how should we decide how much money is a good amount to spend on someone?

I mentioned before that people don't act as if the lives of themselves or others are infinitely valuable. They act as if they have a well-defined price tag. Well, some enterprising economists have figured out exactly what that price tag is. They made their calculations by examining, for example, how much extra you have to pay someone to take a dangerous job, or how much people who are spending their own money are willing to spend on unproven hopeless treatments. They determined that most people act as if their lives were worth, on average, 5.8 million dollars.

Most health care, government or private, uses a similar calculation. One common practice is to value an extra year of healthy life at $50,000. So if a treatment costs $60,000 and will only let you live another year, they'll reject it. If a treatment costs $600,000 and will let you live 20 more years, then since 600000/20 = 30000 which < 50000, they'll approve it. If a treatment costs $100,000 and has only a one in ten chance of letting you live another two years, then since [(100000)/(1/10)]/2 = 500000 which is > 50000, they'll reject it.

I'm not claiming I have any of the answers to this health care thing. I'm not claiming that $50,000 is or isn't a good number to value a year of life at. I'm not saying that government health care couldn't become much more efficient and save lots of money, or that private health care couldn't come up with a better incentive system that makes denying treatments less common and less traumatizing. I'm not saying that insurance companies don't make huge and stupid mistakes when performing this type of analysis, or even that they aren't the slime of the earth. I'm not saying the insurance system is currently fair to the poor, whatever that means. I'm not saying that there aren't many many variables not considered in this simplistic analysis, or anything of that sort.

I'm just saying that if you demand that you "not be treated as a number" or that your insurance "never deny anyone treatment as long as there's some chance it could help", or that health care be "taken out of the hands of bureaucrats and economists", then you will reap what you have sown: worse care and a greater chance of dying of disease, plus the certainty that you have inflicted the same on many others.

I'm also saying that this is a good example of why poorly informed people who immediately get indignant at anything packaged by the media as being "outrageous", even when their "hearts are in the right places", end up poisoning a complicated issue and making it harder for responsible people to make any progress.

Inspired by a comment thread on Reddit
linkReply

Comments:
[User Picture]From: minion_for_hire
2009-08-05 10:30 am (UTC)

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Your point is well made, but I'm still not pressing the button... Similar psychology applies to the Trolley problem. http://en.wikipedia.org/wiki/Trolley_problem The logic might be perfect, but I'm not going to push the fat man onto the tracks.
[User Picture]From: squid314
2009-08-06 06:12 am (UTC)

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I don't care if you press the button or not; your loss. But on the trolley problem and the health insurance problem, I care.

A wise man once said that the importance of logic appears only when you have something that is more important to you than feeling good.

If your goal is to feel good, you can have whatever health care system and whatever solution to the trolley problem you want. I mean, knowing that I didn't let that poor old cancer patient die would make me feel really warm and fuzzy inside too. And I'd also feel really awful about pushing a fat man onto the tracks.

But if your goal is to save lives, you lose the right to do whatever you want, and you'd better start doing what's logical. The logical solution to the two problems does, of course, save more lives than the warm fuzzy alternative.

So the question is: which is more important? Feeling good, or saving lives? I quote Eliezer Yudkowsky:

You know what? This isn't about your feelings. A human life, with all its joys and all its pains, adding up over the course of decades, is worth far more than your brain's feelings of comfort or discomfort with a plan. Does computing the expected utility feel too cold-blooded for your taste? Well, that feeling isn't even a feather in the scales, when a life is at stake. Just shut up and multiply.
[User Picture]From: titaniumdragon
2013-07-14 04:45 am (UTC)

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The trolley problem actually illustrates one of the major flaws with utilitarian philosophy (actually, a number of them, but one in particular), and that is that a lack of consistency in and of itself is a problem.

There is a fundamental difference between throwing the fat man on the overpass in front of the trolley and diverting the trolley onto a separate set of tracks that kills the same guy, because in one case, the person had put himself in danger (on the tracks), while in the other he did not. Thus there is a fundamental moral difference between the two because their behavior differed.

As there are general societal rules against throwing people in front of trains, and also rules about putting yourself in danger, there's a large moral difference between the two.
From: (Anonymous)
2009-08-05 06:16 pm (UTC)

Choice and Preference

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It is important to recognise that there are different conceptions of value and that choices don't necessarily reveal preferences

http://plato.stanford.edu/entries/preferences/

It might be that in expanding the question to one of balancing risk in all settings you are missing out on explaining people's gut reaction to risk and fairness in a medical setting. Although revealed preference might have a lot to say about the monetary value people put on lives, their stated reasons for questioning these numbers in a desperate medical situation might not capture every thought or calculation about costs, justice and equality going through their heads.

That said, I'm pretty much on board with this post and utilitarian theories of value, it just seems like a straw man.

-John

-John
[User Picture]From: gryphonavocatio
2009-08-05 07:52 pm (UTC)

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I wonder if there's something wrong with me when I thought...oh, $5 or $6...
From: (Anonymous)
2011-12-27 01:50 am (UTC)

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Fun fact: I would push it for 10 cents, repeatedly, if the pushing weren't itself tedious work. I'd take a 1 in 500 death chance each month to get $1000 without employment. But it would depend on the dying process, if it is especially agonizing, I might not push the button, at least not for little money.
[User Picture]From: yahalomay
2009-08-06 03:22 am (UTC)

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I read this and was very interested in it. Thank you for taking the time to post it.
[User Picture]From: pentacruz
2009-08-07 01:58 am (UTC)

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i'd press that button for a thousand dollars and i'd do it like two thousand times.
[User Picture]From: pentacruz
2009-08-07 01:59 am (UTC)

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also, i laughed when i read ¨For one thing, the government doesn't want to make a profit¨