Re: another paradox and a solution

From: Wei Dai <weidai.domain.name.hidden>
Date: Mon, 23 Feb 1998 14:07:05 -0800

On Mon, Feb 23, 1998 at 09:07:09AM -0800, Hal Finney wrote:
> I have trouble with probabilities adding to be greater than 1, and in
> particular with individual probabilities being greater than 1.
>
> I have an intuitive sense of what it means for a probability to be
> in the range [0..1]. What does it mean for an event to happen with
> probability 2? Is it more likely than one with probability 1?

I certainly agree that it is not intuitive. One thing to keep in mind is
that we're not talking about the probability of events. Under the AUH
(all-universes hypothesis) it no longer makes sense to talk about the
probability of events, since all events happen in some universe or
another. Rather we're talking about the probability of perceiving
something at a certain subjective time into the future. Even so I agree
that it's not clear what probability 2 means intuitively. However since
this seems to be the only way to "fix" probability, maybe we can use it in
a shutup-and-calculate mode for a while and see if it makes intuitive
sense later.

> Would you say, that if you are going to be duplicated tonight, that the
> probability that the sun will rise tomorrow is 2?

Yes.

> How about your paradox? Won't it still be the case that both parties
> are happy to make the bet? If so, then you have redefined probability
> to mathematically eliminate some inconsistencies but it no longer serves
> as a guide to decisions, which was its original point.

No, because the experimenter would believe she will hear a click with
probability 0.5, so the bet would be an expected loss for her. One of the
reasons to redefine probability as I suggest is to make it more compatible
with decision theory, in addition to eliminating inconsistencies.
Received on Mon Feb 23 1998 - 14:07:46 PST