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?