[extropy-chat] Re: monty hall paradox again: reds and green gorfs

[Rafal Smigrodzki]

I meant "1n" zorgs for all the rewards/losses.

And as Eliezer wrote, the assumption of an infinite smooth prior over N is a
bizarre one, a non-prior if there is one, and plays havoc with our intuitive
mathematical reasoning.

Rafal
----- Original Message ----- 
From: "Rafal Smigrodzki" <rafal at smigrodzki.org>
To: "ExI chat list" <extropy-chat at lists.extropy.org>
Sent: Sunday, May 23, 2004 11:59 AM
Subject: Re: [extropy-chat] Re: monty hall paradox again: reds and green
gorfs


>
> ----- Original Message ----- 
> From: "Spike" <spike66 at comcast.net>
> To: "'ExI chat list'" <extropy-chat at lists.extropy.org>
> Sent: Saturday, May 22, 2004 10:48 PM
> Subject: RE: [extropy-chat] Re: monty hall paradox again: reds and green
> gorfs
>
>
> >
> > > Eliezer Yudkowsky
> > >
> > > >  ...The probability that
> > > > the other envelope is larger must go to 1/3, it doesn't
> > > > matter how it gets there."
> > >
> > > Your mathematician friend is flat wrong, and needs to study Bayesian
> > > probability theory. --  Eliezer S. Yudkowsky
> >
> > OK cool, I was hoping someone would say that.  So where
> > is the error?  Are you saying that Bayesian reasoning
> > predicts that there *is* a profit in swapping?  Even
> > if you have no idea how much a zorg is?  How do you
> > set up the Bayesian priors?  How do you set up a
> > sim to prove it?
> >
> ### You have two envelopes, one with n zorgs, the other with 2n zorgs. The
> probability of choosing either one is 1/2.
>
> You want to calculate the reward/loss associated with staying with the
> chosen envelope, vs. swapping after seeing its contents.
>
> The reward for sticking after choosing the 2n zorg envelope is 1 zorgs.
>
> The loss from swapping after choosing the 2n zorg envelope is 1 zorgs.
>
> The loss for sticking with the n envelope is 1 zorgs.
>
> The reward for swapping the n envelope is 1 zorgs.
>
> There are no other courses of action, given the two envelopes. Since you
do
> not know "n" a priori (yes, you do not have a prior, by the definition of
> the problem), you cannot tell whether you have the n or the 2n envelope
even
> after seeing its contents (obvious, right?). This is why the probability
> after opening doesn't "go" anywhere - the contents of the envelope do not
> provide you with any information that could allow you to adjust the
priors,
> or relate the contents to your desires. Since the desires cannot be
> consulted (as in the problem with actual dollar amounts), the emotional
> reward for swapping is exactly the same as the reward for sticking,
always.
>
> I think that a lot of people approach the problem as if there were 3
> envelopes: 1/2n, n and 2n, and opening one of them gave clues to the
> contents of others (which is similar to the three-door opening problem),
> then start calculating erroneous probabilities.
>
> Rafal
>
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