From: Benja Fallenstein (benja.fallenstein@gmail.com)
Date: Wed May 20 2009 - 11:52:26 MDT
On Wed, May 20, 2009 at 7:00 PM, Matt Mahoney <matmahoney@yahoo.com> wrote:
> Do there exist two computable real functions A(t) and B(t) defined over t in R+ such that
>
> integral_0^infinity A(t) dt > integral_0^infinity B(t) dt
>
> and
>
> integral_0^infinity A(t)P(t) dt < integral_0^infinity B(t)P(t) dt
>
> for all P != I?
No. If P(t) is constant, then integral_0^infinity cF(t) = c
integral_0^infinity F(t) (or am I missing something?). Thus, if the
second inequality holds for all P != I, it must also hold for P = I.
> In other words, are there A and B such that a rational agent that is certain of its immortality would always choose A, and a rational agent that is uncertain would always choose B?
>
> If not, then I claim that rational certainty of immortality is impossible.
As I hinted at in my other mail, I think that the right way to extend
decision theory to a potentially immortal agent is to compare the
expected utilities of all possible strategies over the whole lifetime
of the agent. What you are doing is that you are trying to compute
expected utilities for the actions taken on day one (= prefixes of
whole-lifetime strategies), and you define the expected utility of an
action to be the supremum of the expected utilities of all lifetime
strategies that start with that action, even if the supremum is not a
maximum (ie, when the set of strategies starting with that action does
not have a maximum). This doesn't seem like a good definition of
"rational decision" to me; if by picking A the agent can get a higher
payoff than with any strategy that starts with picking B, then IMO the
agent should pick A, and the fact that the "expected utilities" of A
and B are equal just means that the proper definition of the expected
utility of an action is the maximum, not the supremum of the EUs of
the strategies starting with this action (so B does not *have* an EU).
However, while I don't think your mathematical argument stands in the
way of it, I don't see how we could ever be rationally *completely*
sure of anything, so I don't expect to have your (1) and (3). However,
if we could get evidence that makes it exponentially probable that
we're immortal, that seems just fine to me at least on the face of it.
All the best,
- Benja
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