Re: predictions

From: Hal Finney <hal.domain.name.hidden>
Date: Mon, 2 Mar 1998 09:40:25 -0800

What do you think of the idea that the probability of observing heads at
time 1 could be said to be 2/3. The idea is that the later duplication
at time 2 has a retroactive effect, that the subjective probability
that you will see something depends on the whole future history of your
consciousness. Follow your consciousness to the end, and the subjective
probability of an event is the weighted average of the probabilities
observed by all instances of you.

This has the difficulty that it is non-local, that we can't predict
subjective probabilities without complete knowledge. But does it
address the paradoxes? I believe it has the property that subjective
probabilities don't change unless new information is acquired, which
seems axiomatic.

Can we analyze these paradoxes in terms of an axiomatic approach? A
proper theory of subjective probability should have a set of properties.
Then we prove that these properties lead to a contradiction. So we
have to relax one or more of the axioms. Wei departs from the principle
that probability lies in the range [0..1]. Other departures could lead
to different models.

Hal
Received on Mon Mar 02 1998 - 10:00:01 PST