Re: another paradox and a solution

From: Hal Finney <hal.domain.name.hidden>
Date: Mon, 23 Feb 1998 19:37:28 -0800

I think we discussed this somewhat on extropians, but I don't remember
the resolution.

Given the scenario:
> Ok, here's another probability paradox. Suppose in the quantum suicide
> experiment the assistant offers the experimenter a bet. The experimenter
> gives the assistant $2 before he pulls the gun, and in return the
> assistant will give $3 to the experimenter after pulling the gun, if the
> result is a click instead of a bang. The assistant clearly has a positive
> expected return from this bet. But if the experimenter believes she will
> hear a click with 100% certainty, she also has a positive expected return.

I wrote:

> > 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.

Wei replied:

> 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.

It seems to me that the experimenter is rational to make the bet, because
her expected return, given that she is alive afterwards, is positive.
And she presumably doesn't care, if she is dead. She can reason this
way regardless of whether other universes exist.

This would not necessarily be true in all cases, for example if the
experimenter had an estate and heirs whose welfare was important to
her, she might not take the attitude that nothing matters if she is dead
(likewise if she believes in an afterlife).

But if she only care about her own life, then wouldn't it be rational to
only consider outcomes where she is alive?

Hal
Received on Mon Feb 23 1998 - 19:56:06 PST