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

[Spike]

> Harvey Newstrom wrote:
> > Spike writes:
> >
> >> ...most people say red and green gorfs are equal but a
> >> small and perhaps not very credible minority insist
> >> reds are better, while no one is actually claiming the
> >> greens are better, then I would choose a red gorf,
> >> assuming the same price.
> > 
> > Spike, this would lead you to superstition...

OK I get ya, but Im glad you introduced superstition:
this 2 envelope problem is driving me crazy(er).  Recall
you are given a choice of two identical envelopes with 
unspecified amounts of money.  All you know is one envelope 
contains twice as much as the other.  You choose one, open
it to find 10 zorgs, a zorg being some unknown unit of
money that can be anything between pocket change and
a gatesian pile.  The other envelope contains either 5 zorgs
or 20 and you may swap if you wish, in a one-time irreversible
swap, your ten for the 5 or 20.  My mathematical mind assures
me that the mathematical expectation of the value of 
the other envelope *must* somehow come out to exactly 10 zorgs.
But almost superstitiously, I would be sorely tempted
to swap, just in case my logic is flawed.

Sorta like the gorf problem where most people think 
reds and greens are equally good but a few say reds
are better, compelling you to choose red, the 10 zorgs
problem would compel me to choose swap over stick.
Reasoning: the logic for stick says that sticking is
*exactly* as good as swapping, but another line of
suspected erroneous logic says that swapping gains you 
a virtual 25% zorg profit.  You can imagine no logic that 
says sticking is actually *better* than swapping, only 
that sticking is exactly as good as swapping.

With that choice, either swapping is equal or swapping
is better, then I would swap *even if I knew I was
being superstitious*!  Can you imagine?  Me?  Superstitious?

A possibly irrelevant factor: a certain jupiter brain
who shall remain nameless (but whose initials are 
Eliezer Yudkowsky) sat in my living room Monday and 
expounded an argument for sticking which I think may 
have been erroneous.  If the Bayesian Master could 
miss it, then I could waaaaay miss it, in which case 
the simple intuitive swap really might be the right way 
to maximize your zorgs.  If you didn't swap and later
discovered the error in your reasoning, you would
forever curse your own Vulcan brain for not swapping!
Your human brain was telling you: "Spike!  Swap, fer
cryin out loud!  You are betting 5 against 10 in an
even-chances bet!  Whats wrong with you?"  etc. 
Of course I might be just waxing superstitious.

Nowthen, do let me tie all this together.

I have asked a number of people what they would do
with the 10 zorg problem.  The people being asked
are technically trained, all.  They turned out to
be about 80% swappers, 20% stickers.  I asked for
their reasoning, and most of the swappers trotted out
the mathematical expectation calculation without the
slightest hesitation, .5*5 + .5*20 = 12.5 > 10, swap,
no brainer.  When I then pointed out the paradox of
non-convergence (the expectation argument still works
if you dont look in the envelope, and so it would
*still* be beneficial to swap *after* you have swapped)
there was much bafflement going around.  Arguments
ensued, productivity was lost.

Of the stickers, only one person derived an equation
that suggested that the probability of the other envelope
containing the twenty zorgs somehow reverted to 1/3,
and the probability of the fiver reverted to 2/3.  I
agreed that this must somehow be true, however (this
is a good one) this conclusion *also leads to a 
paradox*!  If true, one must conclude that until
one opens one of the envelopes, the mathematical
expectation of the two envelopes is identical, 50-50.
After opening one, the probability collapses to 
1/3-2/3, and this works *even if one knows not
how much a zorg is*!  {Insert Twilight Zone music here}

So that is how I got back to this red-green gorf
problem.  If one line of reasoning says red and
green are the same, another says red is better,
then green cannot be better, only equal, then 
superstition be damned, pass the salt and I
choose red.

If one line of reasoning says sticking and
swapping are equal, and another line of reasoning
(even if highly suspicious) says swapping is better,
then sticking cannot actually be advantageous, so
pass the salt, I choose swap.  I will take my
zorgs and endure the ridicule.

Another insight: of those who chose stick, the
reasoning they gave for sticking was (with only
one exception) illogical, self contradictory, 
flippant, clearly erroneous, intuitive or just plain
irrelevant.  Examples of sticker reasoning: 

1.  I dislike gambling.

2.  I don't want to take advantage of the kindness
of the gift giver.

3.  How do I know these are not counterfeit zorgs?

4.  My first guess is usually the best.

5.  I couldn't risk losing half my zorgs, even for an
even shot at twice as many.

6.  I might be able to retire, if zorgs are big enough...

etc.  These people are all registered voters.

There was no real insight on the part of the stickers,
and the insights of the swappers apparently leads to a
wild paradox.  One bachelor offered the survivor solution: 
propose marriage to the messenger, then you get both
envelopes.  An old married man pointed out that on the
contrary, you would get neither: your new bride would 
get both.  {8^D

I pointed out that one might already be married, or
perhaps one might look like, well... one of us extropians,
in which case the messenger would politely refuse
your proposal.  {8^D  <--- (see that?  Eyes of different
sizes, no pupils, pointy nose, mouth shaped like the 
letter D, oy vey!  Lets face it guys, we are not exactly
the most handsome bunch you ever saw.)

I came up with a neat solution however.  If looking in 
one envelope somehow collapses the probability wave
distribution (insert zen quantum mechanics here)
then simply have the messenger open her envelope
first, which then would cause your envelope to mysteriously
become worth 1.25 times whatever amount she saw there.  
Then you stick and take your envelope to the bank.  You 
get to be a scientific and logical sticker, yet still 
follow your superstitious gut feel, all at the same time.

spike