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

[Alan Eliasen]

Spike wrote:

> You wish to buy a gorf but you are unsure of
> what kind to buy.  You ask a number of people and find
> that opinion is divided.  Most say the red gorfs
> and green gorfs are indistinguishable, that they
> taste exactly the same.  A small but vocal minority
> says that red gorfs are better than green gorfs,
> and will even pay much more for them in times of
> red gorf scarcity.  No one is actually arguing
> that the green gorfs are superior, only that they
> are *equal* to the reds in every way.
> 
> Which do you buy?  If their prices are equal would
> you bet that the minority *might* be right?  Or that
> there is a small chance they are right?  If even a
> small chance exists, you would choose the red gorf, right?
> Does this constitute a logical fallacy?
> 
> I see a compelling reason to not trade envelopes
> in the previous 2 envelope MH paradox, since the mathematical
> expectation is equal, but a small vocal minority insists 
> it is good to switch envelopes.  Should that effect my 
> decision to trade or stick?  Since it costs me no more
> to get a red gorf, would I not choose a red?  And since
> it costs me nothing to trade envelopes, would I not
> assign a small probability that my reasoning is
> wrong and trade?  Is there a name for this logical
> fallacy?

   I'd call it something like the "flat earth" fallacy.  Just because millions
of people once believed the earth was flat didn't make it so.  Maybe even the
majority thought it was flat.

   I guess that this creates three questions for the players:

   1. How confident are you in your math skills?

   2. Is usable information somehow being leaked?  (e.g. is the amount of
money in one envelope not divisible by 2, or have you played this game before
and know the usual amounts?)  These options, however, were intended to be
eliminated by the original problem statement, so I'll disregard them.  To
avoid the "discreteness" problem, it should probably be posited that the
amounts are real numbers, with no minimum.

   3. How *much* more will you pay for the red gorfs, which is equivalent to
asking "how much will you pay to switch envelopes?"

   Actually, questions 1 and 3 are the same thing.  To see who's better at
math, you can play the game against the other person.

   Your original formulation said that you'd expect to gain 1.25 times the
value in the envelope just by switching.  Well, then, let your math-challenged
opponent pick the first envelope, then generously offer to let him trade it in
and buy the other envelope for a reduced cost... say 1.20 times the cost of
the first envelope.  (So, he gives back the original envelope plus 20% out of
his pocket.) In his mind, that's still an expected profit.  He should be glad
to pay it.

   If you find a sucker that will play the game on these terms, please mark
his back with chalk and send him my way.  ;)

-- 
  Alan Eliasen                 | "You cannot reason a person out of a
  eliasen at mindspring.com       |  position he did not reason himself
  http://futureboy.homeip.net/ |  into in the first place."
                               |     --Jonathan Swift