How much should we value statistical lives?

June 9 JDN 2458644

The very concept of putting a dollar value on a human life offends most people. I understand why: It suggests that human lives are fungible, and also seems to imply that killing people is just fine as long as it produces sufficient profit.

In next week’s post I’ll try to assuage some of those fears: Saying that a life is worth say $5 million doesn’t actually mean that it’s justifiable to kill someone as long as it pays you $5 million.

But for now let me say that we really have no choice but to do this. There are a huge number of interventions we could make in the world that all have the same basic form: They could save lives, but they cost money. We need to be able to say when we are justified in spending more money to save more lives, and when we are not.

No, it simply won’t do to say that “money is no object”. Because money isn’t just money—money is human happiness. A willingness to spend unlimited amounts to save even a single life, if it could be coherently implemented at all, would result in, if not complete chaos or deadlock, a joyless, empty world where we all live to be 100 by being contained in protective foam and fed by machines. It may be uncomfortable to ask a question like “How many people should we be willing to let die to let ourselves have Disneyland?”; but if that answer were zero, we should not have Disneyland. The same is true for almost everything in our lives: From automobiles to chocolate, almost any product you buy, any service you consume, has resulted in some person’s death at some point.

And there is an even more urgent reason, in fact: There are many things we are currently not doing that could save many lives for very little money. Targeted foreign aid or donations to top charities could save lives for as little as $1000 each. Foreign aid is so cost-effective that even if the only thing foreign aid had ever accomplished was curing smallpox, it would be twice as cost-effective as the UK National Health Service (which is one of the best healthcare systems in the world). Tighter environmental regulations save an additional life for about $200,000 in compliance cost, which is less than we would have spent in health care costs; the Clean Air Act added about $12 trillion to the US economy over the last 30 years.

Reduced military spending could literally pay us money to save people’s lives—based on the cost of the Afghanistan War, we are currently paying as much as $1 million per person to kill people that we really have very little reason to kill.

Most of the lives we could save are statistical lives: We can’t point to a particular individual who will or will not die because of the decision, but we can do the math and say approximately how many people will or will not die. We know that approximately 11,000 people will die each year if we loosen regulations on mercury pollution; we can’t say who they are, but they’re out there. Human beings have a lot of trouble thinking this way; it’s just not how our brains evolved to work. But when we’re talking about policy on a national or global scale, it’s quite simply the only way to do things. Anything else is talking nonsense.

Standard estimates of the value of a statistical life range from about $4 million to $9 million. These estimates are based on how much people are willing to pay for reductions in risk. So for instance if people would pay $100 to reduce their chances of dying by 0.01%, we divide the former by the latter to say that a life is worth about $1 million.

It’s a weird question: You clearly can’t just multiply like that. How much would you be willing to accept for a 100% chance of death? Presumably there isn’t really such an amount, because you would be dead. So your willingness-to-accept is undefined. And there’s no particular reason for it to be linear below that: Since marginal utility of wealth is decreasing, the amount you would demand for a 50% chance of death is a lot more than 50 times as much as what you would demand for a 1% chance of death.
Say for instance that utility of wealth is logarithmic. Say your currently lifetime wealth is $1 million, and your current utility is about 70 QALY. Then if we measure wealth in thousands of dollars, we have W = 1000 and U = 10 ln W.

How much would you be willing to accept for a 1% chance of death? Your utility when dead is presumably zero, so we are asking for an amount m such that 0.99 U(W+m) = U(W). 0.99 (10 ln (W+m)) = 10 ln (W) means (W+m)^0.99 = W, so m = W^(1/0.99) – W. We started with W = 1000, so m = 72. You would be willing to accept $72,000 for a 1% chance of death. So we would estimate the value of a statistical life at $7.2 million.

How much for a 0.0001% chance of death? W^(1/0.999999)-W = 0.0069. So you would demand $6.90 for such a risk, and we’d estimate your value of a statistical life at $6.9 million. Pretty close, though not the same.

But how much would you be willing to accept for a 50% chance of death? W^(1/0.5) – W = 999,000. That is, $999 million. So if we multiplied that out, we’d say that your value of a statistical life has now risen to a staggering (and ridiculous) $2 billion.

Mathematically, the estimates are more consistent if we use small probabilities—but all this assumes that people actually know their own utility of wealth and calculate it correctly, which is a very unreasonable assumption.

The much bigger problem with this method is that human beings are terrible at dealing with small probabilities. When asked how much they’d be willing to pay to reduce their chances of dying by 0.01%, most people probably have absolutely no idea and may literally just say a random number.

We need to rethink our entire approach for judging such numbers. Honestly we shouldn’t be trying to put a dollar value on a human life; we should be asking about the dollar cost of saving a human life. We should be asking what else we could do with that money. Indeed, for the time being, I think the best thing to do is actually to compare lives to lives: How many lives could we save for this amount of money?

Thus, if we’re considering starting a war that will cost $1 trillion, we need to ask ourselves: How many innocent people would die if we don’t do that? How many will die if we do? And what else could we do with a trillion dollars? If the war is against Nazi Germany, okay, sure; we’re talking about killing millions to save tens of millions. But if it’s against ISIS, or Iran, those numbers don’t come out so great.

If we have a choice between two policies, each of which will cost $10 billion, and one of them will save 1,000 lives while the other will save 100,000, the obvious answer is to pick the second one. Yet this is exactly the world we live in, and we’re not doing that. We are throwing money at military spending and tax cuts (things that many not save any lives at all) and denying it from climate change adaptation, foreign aid, and poverty relief.

Instead of asking whether a given intervention is cost-effective based upon some notion of a dollar value of a human life, we should be asking what the current cost of saving a human life is, and we should devote all available resources into whatever means saves the most lives for the least money. Most likely that means some sort of foreign aid, public health intervention, or poverty relief in Third World countries. It clearly does not mean cutting taxes on billionaires or starting another war in the Middle East.

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