[Avodah] Kavua and Monty Hall

[Micha Berger]

On Thu, May 27, 2010 at 09:35:10AM -0400, Yosef Gavriel Bechhofer wrote:
: In a totally different note, it struck me yesterday that perhaps kol
: kavua k'mechtza al mechtza dami has something to do with the "Monty
: Hall Problem"
: <http://en.wikipedia.org/wiki/Monty_Hall_problem>
: <http://www.marilynvossavant.com/articles/gameshow_print.html?t=64>
: - but I can't articulate it. Can you help me out by either explaining
: why I'm right or why I'm wrong?

In the Monty Hall Problem, someone picks one out of three doors at the
game show To Make A Deal. The host of TMAD was Monty Hall. After you
make your choice, Monty would show you that behind one of the other
doors, that you did not choose, there was a donkey -- a losing choice.
He offers you a chance to stick to the door you have, or switch to the
remaining closed doors.

YOu might think that since there are two doors left, a winner and a
loser, and everything started out equal, they should remaing equal --
50:50.

Counterintuitively, your odds of winning if you stay with the current
door is 1/3, and your odds of winning if you switch is 2/3.

The description I find most useful to understand this lopsided result
is that it is caused by an assymetry in Monty Hall's choices. If you
picked a winning door, he could open either of the other two. But if
you picked a losing door, he could only pick the other losing door.
So while everything really did start out being equal, the setup didn't
stay that way.


As for RYGB's question:

The appearance that probability doesn't matter -- kemechtza al mechta
dami -- seems to be entirely in the number of doors. If you started out
with 4 doors, then sticking to your choice gives you a 1/4 chance of
winning, but switching to one of the two remaining doors increases it
to 3/8. (The remaining 3/4 split two ways.) The MHP has no connection
with ignoring odds.

Just as qavu'ah having no connection with someone who knows the emes
making different decisions based on that emes.


HOWEVER:

As you might recall, I built a whole philosophy about qavu'ah based on R'
Aqiva Eiger. It includes eidus, terei kemei'ah (also ignoring majority)
and migo as tolados of the same av, as well as chazaqa demei'ikara as
a first cousin. (Whereas rov and chazaqa disvara belong to a different
family of birur.) Literally a philosophy, as I use RAE's chaqira to
argue for the correctness of hashkafos that see mitzvos in terms of
cognitive changes -- whether as deveiqus or a definition of sheleimus.

Leshitas RAE, qavua isn't statistical because it's resolving a safeiq
in din. The metzi'us was once known -- that's why it's called qavu'ah
-- and at that time it had a definite din. The din exists, but we are
mesupaq as to what it is. Rov only works when pasqening where the safeiq
is in the metzi'us; the din is established about an unknown reality. A
different kind of birur.

Thus my connecting qavu'ah to eidus, which is also about the metzi'us once
being known. In a case of terei uterei, or terei kemei'ah, the question
is who correctly reports that metzi'us. And chazaqah demei'iqarah also
works off an established reality -- albeit a historical one.

The ideas were hammered out on mail-jewish and here, and since became
the following blog entries:
http://www.aishdas.org/asp/2009/03/halakhah-phenomenology-1.shtml
    Birkhas haChamah and microscopic bugs -- the gap between the
    experience and reality

http://http//www.aishdas.org/asp/2009/04/halakhah-phenomenology-2.shtml
    Birur of din (qavu'ah, eidus, etc..)

http://www.aishdas.org/asp/2009/04/halakhah-and-phenomenology-3.shtml
    Birur of metzi'us (rov, etc...)

http://www.aishdas.org/asp/2009/04/halakhah-and-phenomenology-4.shtml
    How the above rules play out in some otherwise-hard-to-explain
    cases.

So the mehalakh you're proposing isn't likely to appeal to me -- it
contradicts my "baby". I lack objectivity, having my own pet theory.

Tir'u baTov!
-Micha

-- 
Micha Berger             A pious Jew is not one who worries about his fellow
micha at aishdas.org        man's soul and his own stomach; a pious Jew worries
http://www.aishdas.org   about his own soul and his fellow man's stomach.
Fax: (270) 514-1507                       - Rav Yisrael Salanter