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From: Jacques M Mallah <jqm1584.domain.name.hidden>

Date: Fri, 21 May 1999 21:00:43 -0400

On Thu, 20 May 1999 GSLevy.domain.name.hidden wrote:

*> MMM.... there is nothing better than an experiment to resolve the issue one
*

*> way or another.
*

EXCUSE ME?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!

I think I have to refresh your memory a bit. Look at this quote

from a previous post:

You wrote:

*>> Assumption 2)
*

*>> It is common sense that it does not make any sense to switch.
*

*>> Because of the PERFECT SYMMETRY of the situation
*

and I responded:

*> Again, totally obvious and conventional, mentioned in the original
*

*>post that started this.
*

Now you are somehow accusing me of advocating switching! I am

shocked and insulted!

It is totally obvious that with no additional information, there

is no advantage in switching. It is equally obvious that your

"explanation" for that fact, based on a completely mixed up formula for

expectation values, was totally WRONG. I was trying to explain to you why

it was wrong so that you could understand that.

*> Certainly the simple minded expectation value of 0.5(2m + 0.5m) = 1.25m for
*

*> switching does not make any sense. If you believe that it does make sense, I
*

*> think I just have found a way to make a quick buck.
*

Again, that is the correct formula (for a logaritmic initial dist.),

but on average m is either zero or infinity so it's somewhat meaningless.

For decision making, however, it's natural to assume that m came from some

reasonable distribution and then one can show that there's no advantage to

switching, on average.

See http://www.artsci.wustl.edu/~chalmers/chalmers.envelope.html

for David Chalmers' analysis.

From: Gilles HENRI <Gilles.Henri.domain.name.hidden>

Subject: Re: Bayesian boxes and expectation value

*>If you don't know the maximum value M, there is actually no rational for
*

*>switching. The simple minded expectation value 0.5(2m + 0.5m) = 1.25m is
*

*>not totally simple-minded: it evaluates correctly the expectation value of
*

*>the ratio between what you would find in the second box to what you found
*

*>in the first one. It is actually 1.25. However you should not use this
*

*>expectation value to conclude that it is better to take the second box,
*

*>because in the case where the second box contains 2m, it means also that
*

*>the value of m that you found in the first box is lower than the average
*

*>value 0.5*(m+2m) = 1.5m, and the opposite in the second case. The confusion
*

*>arises from the fact that m is not an expectation value of anything, and
*

*>summing 2m and 0.5m does not give an expectation value of what you can win,
*

*>because of course the expectation value of the ratio is not the ratio of
*

*>expectation values.
*

*>That's better seen if you call m0 the (unknown) amount which is really put
*

*>in the first box. Either you open the first box and you find m1=m0. The
*

*>second one contains 2*m1=2*m0. Or you open the second one and you find
*

*>m2=2*m0. The first one ontains 0.5*m2 = m0. The expectation value of the
*

*>content of the first box you opened is <m> = 0.5*(m1+m2) = 0.5*(m0+2*m0)=
*

*>1.5 m0. That of the other box is <m'> = 0.5*(2m1 + 0.5m2)=0.5*(2*m0+m0)=
*

*>1.5 m0, which is the same of course. You see more clearly that the mistake
*

*>comes from the fact that although m denotes always what you found in the
*

*>first box, its expectation value is not the same following which box you
*

*>assumed to have opened. However as I said, if you open systematically the
*

*>second box,and you calculate each time the ratio between box 2 and box 1,
*

*>you will indeed find an average value of 1.25. But it doesn't mean that you
*

*>will gain more than if you kept systematically the first box, because the
*

*>cases where the factor is 2 are just those where the value you found in the
*

*>first box is lower...
*

Yes, that is basically correct.

From: GSLevy.domain.name.hidden

Subject: Re: Bayesian boxes and expectation value

*>Gilles I fully agree with you. Your analysis is great.
*

That's nice. Gilles, I guess you succeeded in convincing him that

his earlier analysis was TOTALLY WRONG. Great.

- - - - - - -

Jacques Mallah (jqm1584.domain.name.hidden)

Graduate Student / Many Worlder / Devil's Advocate

"I know what no one else knows" - 'Runaway Train', Soul Asylum

My URL: http://pages.nyu.edu/~jqm1584/

Received on Fri May 21 1999 - 18:01:44 PDT

Date: Fri, 21 May 1999 21:00:43 -0400

On Thu, 20 May 1999 GSLevy.domain.name.hidden wrote:

EXCUSE ME?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!

I think I have to refresh your memory a bit. Look at this quote

from a previous post:

You wrote:

and I responded:

Now you are somehow accusing me of advocating switching! I am

shocked and insulted!

It is totally obvious that with no additional information, there

is no advantage in switching. It is equally obvious that your

"explanation" for that fact, based on a completely mixed up formula for

expectation values, was totally WRONG. I was trying to explain to you why

it was wrong so that you could understand that.

Again, that is the correct formula (for a logaritmic initial dist.),

but on average m is either zero or infinity so it's somewhat meaningless.

For decision making, however, it's natural to assume that m came from some

reasonable distribution and then one can show that there's no advantage to

switching, on average.

See http://www.artsci.wustl.edu/~chalmers/chalmers.envelope.html

for David Chalmers' analysis.

From: Gilles HENRI <Gilles.Henri.domain.name.hidden>

Subject: Re: Bayesian boxes and expectation value

Yes, that is basically correct.

From: GSLevy.domain.name.hidden

Subject: Re: Bayesian boxes and expectation value

That's nice. Gilles, I guess you succeeded in convincing him that

his earlier analysis was TOTALLY WRONG. Great.

- - - - - - -

Jacques Mallah (jqm1584.domain.name.hidden)

Graduate Student / Many Worlder / Devil's Advocate

"I know what no one else knows" - 'Runaway Train', Soul Asylum

My URL: http://pages.nyu.edu/~jqm1584/

Received on Fri May 21 1999 - 18:01:44 PDT

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