## Thursday, February 22, 2007

### The Utility of Life Extension

What if you could costlessly extend your life by one year? Suppose that the additional year would be a decent one – not a fantastic year, but definitely worth living. By “costlessly,” I mean that you could achieve this life extension with no sacrifice of utility in previous years, so you really would just be tacking one more decent year onto the end of your life. Would you do it? I sure would.

Now, suppose you’ve tacked this additional year onto your life. You now have the option of improving the quality of that added year by slightly reducing the quality of previous years – perhaps by saving more money or improving your nutrition. (This does not violate the costlessness assumption above. You can have the extra year at no sacrifice, but you also have the option of transferring some quality between years.) Moreover, the resulting increase in utility in the last year will outweigh the reduction in utility in the earlier years. Would you do it?

Your answer presumably depends on your rate of time preference. But set that problem aside by assuming no time discounting. (This assumption can be made realistic by assuming the early years that would suffer are still sufficiently far in the future. E.g., you’re 30 now, the sacrifice would occur when you’re 70, and the gain will occur when you’re 90. Given hyperbolic discounting, the rate of time of discounting between sufficiently distant years is essentially zero.) Now, would you do it? I think I would.

But if we repeated the logic above many times – add a year, redistribute utility, add another year, redistribute utility, etc. – we would eventually conclude that it makes sense to have a really really long life with each year just barely worth living. Regular readers know where I’m going here: This is an intrapersonal version of the mere addition paradox that afflicts utilitarianism (of the total, not average, variety) in the interpersonal context; see here, here, and here for prior discussion. (And now I should promise, once again, that Derek Parfit really is at the top of my to-read list.)

I’m not sure how the paradox can be resolved. But I’m wondering if the answer to the intrapersonal problem – if it can be found – might provide the seeds for resolving the interpersonal one. If you really had the option to repeatedly extend your life one year at a time, and then to redistribute quality from earlier to later years in a net-positive way, what would you do? Would you in fact opt for a very long life with years that are just barely worth living? If so, then maybe we should embrace the same conclusion in the social context (perhaps Parfit’s Repugnant Conclusion is not so repugnant). If, on the other hand, you would stop the process somewhere along the way, opting for a shorter number of higher quality years – crucially, with a lower level of total lifetime utility – then maybe your intrapersonal stopping rule could be applied to help strike a bargain between total and average utilitarianism.

At a minimum, I think the intrapersonal analogy helps to explain why average utilitarianism is not appealing: to maximize the average utility of your life, you would have to forgo any year whose utility was below average, no matter how high its utility in absolute terms. If you had a really fantastic life up to the age of 50, and you expected the rest of your life to be pretty good but not fantastic, maximization of average utility would require you to commit suicide!

Ran said...

If you had a really fantastic life up to the age of 50, and you expected the rest of your life to be pretty good but not fantastic, maximization of average utility would require you to commit suicide!

I'm not so sure it makes sense for maximization of average utility to cover the past; it seems like the average-utilitarian's goal should be to maximize his average future utility.

This doesn't lessen your point, though: he would still commit suicide immediately if the derivative of differential utility were negative.

jonathan said...

It's not that different from analyzing whether or not to take distributions from your 401(k), or other pension plan. You can take distributions in earlier years of greater dollar amounts, but it will not last as long, or you can live in relative austerity and make it last until 90.

Glen Whitman said...

Ran -- interesting point, and I've made a new post reacting to it.

Jonathan -- it's similar, but I think it's different in some important ways. Most notably, we're not just talking about redistributing wealth to your later years, we're talking about adding years. So the better analogy is with nutrition, not savings. But even with nutrition, the analogy is not dead on. With nutrition, you're making a simultaneous choice: you can't have the additional years without making the sacrifice now. In my hypothetical, I'm saying you can add years to your life costlessly -- and then you have the option to make those years better by making current sacrifices.

Dr. Leonid Gavrilov, Ph.D. said...

Thank you for your interesting post!
I thought perhaps you may also find this related story interesting to you:
Longevity Science: SENS
http://longevity-science.blogspot.com/2007/01/sens.html