[extropy-chat] monty hall paradox again

[Brett Paatsch]

Coming late to this thread, partly to see what all the fuss is about,
I see that. 

Spike initially wrote:

> Suppose an unknown but whimsical benefactor has chosen 
> to give you a monetary gift.  A messenger is sent with 
> two identical envelopes and offers to give you one of
> them.  The messenger knows not the amounts of money
> in either envelope, but tells you that one of the
> envelopes contains twice as much as the other.  You
> are to choose an envelope.  You choose, and inside you
> find ten dollars.  Now the messenger offers to
> trade your ten dollars for the contents of
> the other envelope.  Would you trade?  Why?

Yes I'd trade. 
 
> I reason that there is a 50% chance the other envelope
> contains 5 dollars and 50% chance it contains twenty,
> so mathematical expectation value of the other envelope
> is .50*5 + .50*20 = 12.50 so I would trade.

12.5 > 10.  And time spent trading is negligable, so I'd trade.

>  Same reasoning
> applies if the first envelope contained 500 or 5000
> dollars or a billion, all under the assumption that seems
> so natural to me, that money is good, so more is
> better and too damn much is just right.  You trade
> 5 dollars for a 50% shot at 20.  Such a deal!

Maybe not. Some pertinent counterpoint on scaling of
exchangable currency already outlined by Rafal and
Eliezer.  But in any case it doesn't matter Spike as you 
had specified as the creator of the hypothetical that 10 dollars
not 500 or 5000 dollars was found to be in the first envelope.  

> Nowthen, since we have concluded that for each dollar
> in the envelope you choose, the other envelope contains
> an expected buck twenty five, you would *always* trade,
> regardless.   

Nowthen, Spike, you have confounded your own hypothetical.
i.e. You've changed it without acknowledging that you have
changed it. 

Could it really be that you don't realise?  Could it be that you
do realise and some others don't and that you enjoy that? 

> For that reason, there really is no reason  to bother opening 
> and looking in the envelope you chose first.  

Re-read what you wrote when you first outlined the hypothetical
at the top.  It is only AFTER an envelope is chosen and opened
revealing that it contains 10 dollars that the messenger offers a 
second trade. The messenger did not say from the outset that
whatever the first envelope contained the contents could be
exchanged after being determining for the contents of the other
envelope prior to their being determined. If that whats you
wanted the messenger to say thats a different hypothetical. 

How long has this list been discussing a twisted hypothetical?

> Regardless of the amount therein, you will immediately trade 
> it away for the other one since you expect it to contain more.

This is not the original hypothetical you outlined. You have 
changed the hypothetical in the very same post as you raised it.

> So why not skip the step of choosing the first envelope
> and subsequently trading it (opened or unopened) for the second?

Because that wasn't an option available at any time in the scenario
as you outlined it.  

> Why not just decide which one you would choose, then take 
> the other one instead?  Or if you choose one, then trade
> it, you might go thru the same line of reasoning that
> you did before and conclude that regardless of the amount
> in the envelope you now hold, the other one contains 25%
> more, and since you still haven't opened either envelope,
> you can still trade back.  Then of course the same line
> of reasoning *still* applies, so you trade again.  And
> again.  And so on to infinity and beyond.

This is changing the scenario from the original. One can't
apply probability theory sensibly to a non sensible problem. Or 
to an internally inconsistent hypothetical scenario. 
 
> So, is this not a strange situation?  Ideally of course
> you could smite the messenger and run off with both
> envelopes.  Or you could keep trading unopened envelopes
> until you lose track of which one you chose first.  Or
> you could trade envelopes until the messenger perishes
> of age-related infirmities, then run off with both.  But
> you notice that the messenger is both stronger and younger
> than yourself, and so would be unlikely to precede you
> in death, and if you were to smite her she would likely
> knock you silly and take both envelopes herself.  So a
> choice must be made.

Ideally? When in trouble, when in doubt don't just run in
circles scream and shout. Really smite that messenger - knock
him out? 

[snipped stuff ]

Do you still really have a question or see a quandry if you ever
really did?  

Or could it be that you are posting just for the sheer fun of it.
'Spiking' the metaphorical drink like an extropy-list socialising 
Bacchus? 

If so, cheers

Brett Paatsch