relevance of the real measure

From: Wei Dai <weidai.domain.name.hidden>
Date: Thu, 20 Dec 2001 01:19:18 -0800

Suppose there are only two logically possible deterministic universes A
and B, and you know that A has measure 0.9, and B has measure 0.1. Suppose
that until time T the history of these two universes are identical. At
time T an experiment will be done in both universes. In universe A the
outcome of the experiment will be "a", and in universe B the outcome will
be "b". If before time T you were given an opportunity to bet $10 that the
outcome is "a" at 1:1 odds, so that in universe A you would gain $10, and
in universe B you would lose $10, Would you take the bet?

The standard answer is yes, you should take it because A has greater
measure. But that assumes you care more about universes that have greater
measure than universes that have less measure. But you could say that you
don't care about what happens in universe A, only about what happens in
universe B, in which case you wouldn't take the bet. So it seems that the
measure only affects your decisions if it enters into your utility
function somehow, and it's not clear that it must.

Even if you knew that only universe A is real, that is, A has measure 1,
and B has measure 0, you could still rationally not take the bet. After
all, even if universe B doesn't have "real" existence, whatever that
means, it still has some sort of platonic existence, and you can still
care more about what happens in universe B than what happens in universe
A.

If people's utilities functions could ignore the "real" measure, then what
relevance does it have? Why are we arguing about whether the real measure
is the Speed Prior or a more dominant prior?

You might argue that most people aproximately behave as if they use the
real measure. But by using the word "most" you're already presuming that
the real measure is relevant. In the above example (where universe B has
measure 0), universe B might be filled with people who ignore the real
measure and only care about universe B, and if you yourself only cared
about universe B, then you'd act as if you expected most people to ignore
the real measure.
Received on Thu Dec 20 2001 - 01:21:42 PST