Question If someone died at age 95, we wouldn't think him unfortunate--it isn't a bad thing, for him, not to have lived much longer. However, if someone died at age 15, we would thing him unfortunate. Why? I suspect that our intuition here has to do with the fact that 95 is well above the average life expectancy for humans, while 15 is well below average. But why should that matter here?

Accepted:
October 4, 2010

Comments

I suspect that your suspicion is partially correct: there is the intuition that someone who is doing worse than average and worse than most is unfortunate. But two other factors come in as well.

There is the fact that only a very small percentage of those who reach age 15 fail to reach 16 -- whereas a rather substantial percentage of those who reach age 95 fail to reach age 96. And people perceive it as more unfortunate to be among a very small fraction who suffer harm than to be one in a larger fraction. (If you're among 20 people worldwide to catch some infectious disease, you'll feel very unfortunate, much more so than if you got a cold along with 3 billion other people.)

And there is the further fact that life beyond the 95th birthday tends not to be all that good -- the person who dies at 15 is losing many probably very good years of life whereas the person who dies at 95 is losing just a few bad ones. (If you lose $5000 you'll probably feel a lot more unfortunate than if you lose just $1.)

Now you ask whether the first factor should matter. To test this, let's recreate the world so that the other two factors are absent. So imagine the world modified as follows. Once human beings reach adulthood, they do not age and remain in full possession of their faculties. However, people do die, as they do now, from various diseases and accidents. Let's say that persons have a 1.5% chance of dying each year. In this case life expectancy would be 67 years, just about what it is now. The big difference would be that people's life expectancy would be entirely independent of their age: even those who have already lived 100 years, or 1000 years, still have a life expectancy of 67. (About one third of all people would live to 100, and about 4 in a million would live to 1000 - just in case you're curious.)

Now in this imaginary world the other two factors do not come into play. The person dying at 15 and also the person dying at 95, they both had the same 98.5% chance of reaching their next birthday. And both had, just before their death, a life expectancy of 67 good years ahead of them.

In this imaginary world, then, the only difference is that one ended up with more of a good thing (95 good years of life) than most while the other ended up with much less (15 years of good life). And I don't see a good reason to deny that this matters. Suppose Bill Gates decided to give his money away, running a lottery over US citizens with a similar distribution of dollars as the distribution of life years in my imaginary world. So US citizens are receiving $67 on average, and most are receiving over $45. Would you not feel unfortunate if the lottery assigned you only $15 (and fortunate, maybe, if it assigned you $95) under these circumstances? Most would.

BTW, Bill Gates actually has enough money to fund this give-away, twice over.