Content Summary: 1400 words, 7 min read.
Original Author: Scott Alexander
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.
On The Risks of Dying
Consider the following:
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?
What do you think?
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 their 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 limited value on their life; enough that they’re willing to accept a small but real chance of death to save five bucks. And as we will see, that is a very, very good thing.
Insurance Example: Fixed Costs
Consider the following:
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. 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.
Insurance Example: Probabilistic Costs
There is a similar argument applies to medical decisions that involve risk. Consider:
You have $900. There are four different fatal diseases: A, B, C, and D. There are 40 patients, ten with each disease. with four different fatal diseases. Each disease costs $300 to cure.
In this case, your only option is to cure A, B, and C… and tell patients with D that unfortunately there’s not enough left over for them.
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, 21 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 30 people left alive. By denying someone an unproven treatment, you’ve saved 9 lives.
Computing the Value of a Life
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 = 30,000 which is < 50,000, they’ll approve it.
- If a treatment costs $15,000 and has only a one in ten chance of letting you live another two years, then since [(15000)/(1/10)]/2 = 75,000 which is > 50,000, 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 am 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.