Monday, March 22, 2010

The Value of Your Life

This essay is decidedly less concrete than my usual output. It was sparked by an interesting discussion with some friends including the Big Cajun Man.

We tend to think that our lives have infinite value to us. However, I’m going to argue that your life has a finite value to you and that this value can be quantified is various unsettling ways. I’m not just talking about the value others put on your life, but the value you place on it yourself.

We can see this finite valuation from our choice to engage in risky behaviour such as driving a car. According to this interesting picture, the odds of dying in a motor vehicle accident sometime in your life (presumably at the end) are about 1 in 84. This would be some sort of average US figure, and the real figure for you would depend on where you live, how much you drive, how you drive, etc. The main point is that your figure is some probability larger than zero.

Unless you have an unusual home or hobbies, driving a car is more dangerous than sitting in your home. So, choosing to drive is usually a voluntary choice to trade some increased risk of death for whatever benefit comes from traveling from one place to another in your car.

However, if your life has infinite value, then this increased risk of death has infinite cost. If the benefit from your car trip is finite, then you’ve made a bad choice.

Now I’m not arguing that driving a car or any other risky behaviour is irrational. What I am arguing is that it is inconsistent with a belief that we assign infinite value to our lives. Risky behaviour is sometimes justified if the benefit that it brings is worth more than the lost value due to the increased risk of death. This is true because the value of a life is finite, even to the person in question.

An apparent counter-argument is that it is rational for people to do just about anything to avoid an otherwise certain death. There is no amount of money you could pay someone to get them to stay in a burning building.

However, this doesn’t mean that people value their lives infinitely. What could anyone possibly do with a stack of money in the few minutes before burning up? In this situation, the money has no value. This is equivalent to “I’ll give you nothing if you stay and burn.”

However, things change if there is only a chance of death. Suppose you were offered a million dollars to roll a pair of dice, and you’d get the money if they don’t come up snake-eyes, but you die if they do both come up 1s. I certainly wouldn’t take this deal, and I suspect few people would take it.

What if we made it three dice so that the odds of dying are now 1 in 216? Still no takers? How about 4 dice? As we keep adding dice, the odds of having them all come up 1s will eventually drop below the chances of dying from some other cause while tossing the dice. At some number of dice it would become rational to take the offer, toss the dice, and walk away with the million dollars (assuming that we’re satisfied that the dice are fair and the game isn’t somehow rigged). Your life has a finite value to you, even measured in dollars.

If you live for 30,000 days (about 82 years), the value of your life is the sum total of the value you extract from each of these 30,000 days. If some event manages to steal the value of one of these days from you and the lost day is a typical day for you, then your loss is about one part in 30,000 as bad as if you had died in infancy.

The inescapable conclusion is that we don’t attach infinite value to our own lives.

7 comments:

  1. Then there's the very real possibility that you would sacrifice your life to save your child.

    Running back into a huge house fire, for example. How does that value your life - other than to say your child's is worth more than your own.

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  2. Mark: I suspect that in this situation, the parent imagines an outcome where both parent and child survive. So, this isn't necessarily a sign that the parent values the child's life higher than his or her own. However, it does show that the parent values the child's life at some significant fraction of his or her own.

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  3. Your arguments will certainly evoke some visceral reactions by most, but my statement that I value my life infinitely still stands, whether I drive a car, take a bus, or walk on the street, my life has infinite value (to me).

    As for your statement about cars see http://www.wikihow.com/Avoid-Contributing-to-Traffic-Congestion argument 11, what are the stats of people dieing in bus crashes (or worse if you are on a Greyhound bus!!!).

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  4. Re: child in burning house. My own child is now 25, yet I would still go back into that burning house. While I would hope that we would both survive, the reality is that only my child may survive, or we both may die.

    If only my child survives, it was worth it as I consider my child's continued life to be more valuable than my own. If we both perish, I will at least have been there to comfort my child when it mattered most.

    I disagree that we value our lives finitely. Our lives are not a commodity: one cannot buy a life, or more life. Therefore, to apply such rational arguments to them is like comparing apples and oranges.

    The value of life is in the living, the day-to-day experiences, the relationships we have with people,etc. Such things cannot be quantified, they are intangible.

    Just because there are some extreme instances where we would value something else more than our own single life (usually a greater good of some kind) does not equate to valuing our lives finitely.

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  5. I agree with Michael James. The fact is that we know our lives will eventually end regardless of what we do, so we take little death-defying risks to make it more rewarding.

    By avoiding all risk, we would lead a dull life, and still end up dying. So, we do risky things.

    Of course, we aren't perfect odds makers when it comes to evaluating risk. We may unknowingly engage in behaviour that's riskier than we think. For example, I'm reluctant to go on vacation to Mexico again. I have nothing against Mexico, but I do see that tourists get murdered there occasionally, or drugged, beaten, and robbed (one can limit their risk by avoiding risky behaviour there too, of course).

    I think we would engage in even a smaller amount of risky behaviour if our lives could only be ended in an accident, and were otherwise infinite. I hear that AIDS is more common in some African countries because life expectancy is low anyway. People are more willing to engage in unprotected sex if they don't count on living much longer anyway, say if they expect to die of communicable diseases.

    By the way, I would be tempted by the snake eyes bet. If you framed it in a different way, it might be even more compelling for me. Say you'd been saving diligently for your whole career and a criminal was taking all your money. You have one last chance to stop him, with a 3% chance of him killing you in the process. If you catch him, he will be imprisoned forever, and will no longer pose any risk to you. Do you try to stop him? I think I would.

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  6. I don't know the context of this discussion but isn't it common for people to believe something but act differently. People smoke, drink (and worse, drink and drive), sky dive and indulge in so many other risky activities. That doesn't sound like they put an infinite value on their life.

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  7. This has certainly sparked some interesting discussion. Perhaps I should have explained more directing what I mean by not valuing our lives infinitely. What I mean is that we don't value our entire lives infinitely more than we value a single day of our lives. So, our entire lives have value that is some finite multiple of the value of a single day.

    That said, I understand that many people object to having any type of quantitative discussion of this subject. However, I can infer quantitative information from people's actions, and from everything I observe, my conclusions seem corect.

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