[extropy-chat] monty hall paradox again

[Brett Paatsch]

Spike wrote:

> Between David's idea and Eliezer's I think I see where my
> sim might have lead me to the wrong answer, but I still
> do not see how you would know to stick or swap in the
> 10 zorg example.  #1  The reason I think I was getting so
> tripped up is that when you write a sim, you *must*
> give the sim some range over which to generate the
> random number, and this violates the premise of the
> puzzle.  #2

#1 I see your original hypothetical restated thus:

> 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 [explaining that the currency inside is not dollars
> but zorgs that can be redeemed for dollars at your local
> Foreign exchange dealer.]  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 [zorgs].  Now the messenger offers to trade
>  your ten [zorgs] for the contents of  the other envelope.
>  Would you trade?  Why?

Therefore.

Depending a bit on my mood on the day and the demeanour
of the messenger and the cost of time (negligable), I'd play.

Heck to get my attention the messenger has already interrupted
me. (I can be a bit grumpy about that sometimes alas). 

So I'd figure why not play its some money and an experience
for very little time? 

I'd chose an envelope and find I now had 10 zorgs. 

The messenger then offers to trade my 10 zorgs for the
other envelope which contains either 5 or 20 zorgs. He only
has one other envelope and I've already seen what was in
the first one. 

12.5 zorgs has got to be better than 10 zorgs (you said they
came from a benefactor - a zorg isn't a debt) so I'd switch
thereby risking 5 zorgs for the chance to get 20 zorgs. 

Total cost of time for the two separate transactions to me
is very little. Total gain for transaction 1 = 10 zorgs. 

For transaction 2 either a loss of five zorgs or a gain of 
10 more zorgs.  Was I acting rationally to risk five to make
ten?  I reckon so.  Am I absolutely certain? No. But I am
certain I was not acting irrationally. Perhaps a-rationally,
thats ok. I'd be ashamed (just a bit) to discover I'd acted
irrationally (if it was pointed out that I had) but just a little
bit, say enough maybe to make me want to not be irrational 
next time. 

Its probably a-rational to participate in this thread at the
cost of time (no zorgs :-). Irrational?  Nah.  Its optional. 
Just like chosing to take the first envelope is optional. And
just like switch or stick on the second transaction was 
optional. 

#2 Sims that use random numbers seem to be tricky in
themselves. I liked Hal's post in this thread. And Eliezer's
response to Hal was interesting too. 

[Hal wrote]
> > The problem is that the paradox as stated is simply logically
> > impossible. It contains a contradiction.  And once you start
> > with a contradiction, it should be no surprise that you can
> > derive one.

[Eliezer]
> I can take money from my wallet, put one-third into one envelope,
> and two-thirds into the other envelope, and flip a coin - a 
> quantum coin, if  need be - to decide which envelope to give you.
> It is definitely physically possible.

Eliezer has a quantum coin !!!  Quite a collectable in itself 
I'd imagine.  Too rare a collectable for Eliezer to offer to Hal to
toss or examine perhaps  :-)

Brett Paatsch