# Re: self-sampling assumption is incorrect

From: Wei Dai <weidai.domain.name.hidden>
Date: Sat, 15 Jun 2002 02:04:01 -0700

After writing the following response, I realized that my argument against
the self sampling assumption doesn't really depend on E1 and E2 being
experiences. They can be any kind of events. Suppose they're prizes that
the copies can win for the original. E1 is a TV and E2 is a stereo. You'd
prefer a TV over a stereo but would rather have one TV and one stereo
instead of two TVs. Then my argument still works.

The issue of whether substitution effects can apply to experiences of
copies is of independent interest, so my original response still has a
point.

On Fri, Jun 14, 2002 at 07:42:27PM -0700, Hal Finney wrote:
> Instead of B1 and B2 both getting E1, let B1 get E1 and B2 get E1'.
> E1' is another experience than E1 that is just about as good.
> U(E1) > U(E2) and U(E1') > U(E2). The idea is that this eliminates
> possible issues regarding whether two people (B1 & B2) who get exactly
> the same experience should count twice.

I think in that case it's still possible for U({E1,E1'}) < U({E1,E2}), if
for example E1 and E1' are very similar.

> It does seem that the SSA pretty much implies that if U(E1') > U(E2) then
> U({E1,E1'}) > U({E1,E2}). Is it really rational for this to be otherwise?

Yes, I believe it can be. If you believe otherwise you have to convince me
why it's impossible to value diversity of experience in your copies, or
why having that value would lead to absurd consequences.

We all know the law of diminishing marginal utility, which says that the
marginal utility of a good decreases as more of that good is consumed, and
the existence of substitution effects, where the marginal utility of one
good decreases when another similar good is consumed. I suggest there is
no reason to assume that the value of experiences of one's copies cannot
exhibit similar cross-dependencies. Actually I think the reason that
we have diminishing marginal utility and substitution effects, namely that
they provide an evolutionary advantage, also applies to the value of
experiences of copies.

> We know that rationality puts some constraints on the utility function.
> We can't have cyclicity in the utility preference graph, for example.

Our normative theories of rationality (i.e. decision theories) do put
constraints on preferences, but the history of decision theory has been
one of recognizing and removing unnecessary constraints, so that it can be
used by wider classes of people. The earliest decision theories for
example where stated in terms of maximizing expected money payoffs rather
than expected utility, which implicitly assumes that utility is a linear
function of money. Today, of course we recognize that utility can be any
function of money, even a decreasing one. Another example is the move from
objective probabilities to subjective probabilities.

> But in the case above, where U({X,Y}) means the utility of having two
> different independent experiences X and Y, maybe it does follow that
> U({X,Y}) and U({X,Z}) must compare the same as U(Y) and U(Z). You don't
> have any choice but to accept the equivalence. As Lewis Carroll wrote,
> "Then Logic would take you by the throat, and FORCE you to do it!"