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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

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

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