Wednesday, December 24, 2008

Gambling Life for Immortality

Bryan Caplan asks:
Suppose you were offered the following gamble:

1. With probability p, you will live forever at your current age.
2. With probability (1-p), you instantly, painlessly die.

What is your critical value of p? If you combine expected utility theory with the empirical observation that happiness is pretty flat over time, it seems like you should be willing to accept a very tiny p. But I can't easily say that I'd accept a p<1/3.

Caplan seems to be making two false assumptions about individual utility/wellbeing:
(i) Hedonism - all that matters is the felt pleasantness of one's mental states.
(ii) Additivity - the utility of one's life as a whole is simply the sum of the utilities of each moment in the life.

Now, (i) seems clearly false. We care (self-interestedly, even) about things other than subjective happiness. So the mere fact that 'happiness is pretty flat over time' doesn't suffice to show that what we care about is similarly constant in its realization.

More importantly: this sort of case helps to cast doubt on (ii). Rather than evaluating a life indirectly, by summing together one's evaluations of its temporal parts, we may skip to directly evaluating the life as a whole. Such global preferences may take into account the "big picture", including relations between the parts (e.g. we might prefer a life that improves rather than declines with time, even if the net momentary utility is the same), and the overall 'shape' of the life. [See this recent post for more detail.]

But if that is so, then it's no longer so clear that an infinitely long life (of moderate happiness) is thereby infinitely valuable. In fact, it may be only a modest improvement on a life of (say) 80 years -- much less, perhaps, then the gap in value between a life of 80 years and one of just 25 (say). It depends on what you want out of life, and how much of that is achievable between the years of 25-80, as opposed to how much is achievable only with immortality. If most of what I care about falls into the first group, then (unless the odds are very favourable) it would seem downright irrational for me to risk all that for a chance of attaining the lesser goods in the latter group.

An interesting test is to question whether my future self (age 79) would regret this decision. Assuming not -- assuming the decision not to gamble is endorseable from a 'timeless' perspective -- then this would reinforce the claim that it is indeed what is in my best interests. It would really be true, from a self-interested perspective, that the value added by living from 25-80 is greater than the value added by the eternity of 80+. On the other hand, it seems at least possible that my youthful preference is instead a result of temporal bias or discounting (or sheer lack of imagination), of a sort that my future selves would regret. This would clearly undermine my above claims about life utilities. (Though it raises tricky issues about how changing global preferences can be combined into a single 'lifetime utility' -- I'll probably post more on this in future.)

I leave the reader with two questions:

(A) What is your critical value for p? (In particular, is it larger than 'tiny'?)

(B) What do you imagine is the preferred critical value for p from the perspective of your future self? Do you think that, on your deathbed, you would be willing to risk "losing" the last 50 years [supposing that was really possible] for a shot at immortality?


  1. A. My value for p is arbitrarily noninfinitesimally small. Notice, however, that Caplan's scenario may be metaphysically impossible if we understand 'living forever' as 'living an infinite number of years', since it is unclear (to me, at least) whether actual infinities can exist at all.

    B. I'd like to think is the same as my present value.

    Like pretty much everybody else, Caplan feels uneasy about accepting a very low value for p. But this feeling should not be accorded evidential weight, since it trades on intuitions about large numbers, which are generally unreliable. On this, see John Broome's characteristically perceptive remarks.

  2. I don't think "large numbers" play any essential role here. We can consider a more modest gamble: risking instant death for 80 more years of life, or guaranteed 40 years more life. These are numbers we can all grasp perfectly well. And the latter option is (I think) obviously better than a gamble at p = .5, or even moderately favourable odds.

  3. Are you prepared to go all the way? Would you refuse to gamble any arbitrarily small period of time for twice that period at "moderately favourable odds"?

  4. No, I don't think it's a fundamental principle that additional life-time has decreasing marginal utility. As explained in the post, it depends on what one wants out of life and how long is necessary to achieve it. It's entirely possible that on smaller scales the weighting would reverse -- e.g. an extra twenty years might be more than twenty times as valuable to me as an extra one year (if that would enable such important goods as raising a family, etc.), in which case I would take that particular gamble at unfavourable (p<1/20) odds.

    (That's a helpful clarification, actually, since it establishes that it isn't just a matter of time discounting.)

  5. Even if utility decreases with time, there's no reason to think it's a converging series like 1/2 + 1/4 + 1/8...

    If the decrease is more like 1/2 + 1/3 + 1/4... then the sum of future utility is still infinite, despite the decrease.

  6. Just as well I wasn't arguing that "utility decreases with time", then!

  7. An interesting side issue that doesn't seem to have been discussed is that dualism is false. To me, this represents a tradeoff.

    One the one hand, living forever means never suffering the unpleasant side effects of getting old; reductio ad absurdum: instead of dying with probability (1-p), you enter a persistant vegetative state. Same difference.

    On the other hand, some of the hormonally driven changes in my life have been pleasant, or at least I have judged them to be beneficial in retrospect. I have to imagine that in the future, there may be more such changes. An infinitely long life at my current age would rob me of such changes (and hence decrease the potential diversity of my experiences).

  8. The core issue is better illustrated if we tailor the thought experiment to control for such confounding variables. (E.g. assume good health in either case, and in the case of extra longevity suppose your biological "age" is whatever you prefer -- it needn't be constant.) The real issue is whether twice as many good years are thereby twice as good for you.


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