On Sun, Jan 25, 2004 at 09:51:47AM -0800, Hal Finney wrote:
> But we can solve this conundrum while retaining symmetry.  Rationality
> should demand allegience to the observed measure.   It is irrational to
> cling to a measure which has been rejected repeatedly by observations.
> If classical definitions of rationality don't have this property, we
> should fix them.  Bob is irrational to hold to M' in a universe whose
> observations reveal M.

There is no need to change measures. When Bob repeatedly observes balls 
falling down, he'll conclude that he happens to be stuck in a low-measure 
universe and will just have to deal with it. The issue is, what does he do 
before making the first observation? At that point he thinks he should bet 
on the ball falling up, and wouldn't be irrational to do so. And Alice 
thinks she should bet on the ball falling down, and wouldn't be irrational 
to do so either.

Maybe a different example will make my point clearer. We could be living
in base reality or a simulation. You can choose a measure in which the
observer-moments like us living in base reality have a greater measure, or
one in which the observer-moments living in simulations have a greater
measure. These two measures have different implications on rational
behavior. The former implies we should plan for the far future, whereas
the latter says we should live for today because the simulation might end
at any moment, and we should try to behave in ways that wouldn't bore the
people who might be running and observing the simulation. (See Robin
Hanson's "How To Live In A Simulation",

Can you offer any arguments that one of these choices is 

> Now, this will demand that in White Rabbit universes, ones where the
> quantum or thermodynamic laws just happen to fail due to bad luck, a
> rational person would have to abandon his (correct!) belief in a lawful
> universe and come to believe (incorrectly!) in miracles.  However this
> is actually a reasonable requirement, since we are stipulating that such
> miracles have been observed.

You can come to believe in miracles without changing measures. You 
just conclude that you're probably in a low-measure universe with 
miracles, instead of an even-lower-measure universe where the White Rabbit 
appeared through pure chance.

The beauty of the universal distributions is that if you adopt one of them
as the measure, you'll never(1) "go crazy" (i.e. start behaving absurdly)
after making any observation, because no matter what you observe, you'll
still prefer the algorithmically simplest explanation for your
observations. But the infinite class of universal distributions leaves you 
plenty of room to choose which universes or observer-moments are most 
important to you.

(1) Well that's not completely true. You would still go crazy
if you observe something that has a logical explanation but not an
algorithmic one, for example if you observe something that can only be
explained by an uncomputable law of physics, which is why I advocate 
adopting more dominant measures based on logic or set theory.

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