Wednesday, July 20, 2011

Kavua Redux: A Pshat from Prof. Aumann

I had the privilege of spending this past Shabbos in New Rochelle, where Prof. Yisrael Aumann was scholar in residence at the Young Israel. Moreover, he, his nephew (and my chevrusa in the Mir back in '84 for Kesuvos), Rabbi Uri Aumann of the extremely important organization Miktze Ha'Aretz (to the benefit of which the Shabbos was dedicated) and his granddaughter were all guests of my father and his wife for Shabbos lunch, which we enjoyed immensely.


In the course of one of Prof. Aumann's presentations, he offered his own explanation of the principle of kol kavu'a k'mechtza al mechtza dami.


The principle of kavua is an old nemesis of ours.


Some other sources that deal with the issue include this post in Avodah:


From: Saul Mashbaum <saul.mashb...@gmail.com>
Date: Fri, 19 Jun 2009 14:14:24 +0300
Subject: 
Re: [Avodah] tannur shel achnai



RMB and RRw discussed probability and the halachot of rov and safeq.
RRW noted that  "And I still don't get the logic for kavua nor have I
heard an explanation that clicks with me so far."

I *highly* recommend "Resolving Uncertainty: A Unified Overview of
Rabbinic Methods", a comprehensive treatment of this subject, by Moshe Koppel,
a talmid chacham and mathematician,  at
http://u.cs.biu.ac.il/~koppel/rov-25.5.pdf.

In this paper, the classic rabbinic concepts of safeq, rubba d'ita
kaman, rubba d'leta kaman and kavua are clearly described in terms of
fundamental probabilty concepts. It is written for the educated
layman, with no complicated formulas or intimidating (to some)
mathematical symbols or notation.

In particular, kavua is discussed in great detail in pages 10-15 of
this 24-page double-spaced paper. Very briefly, the case of kavua is
"indeterminant" (an alternative term considered is "hybrid"), such
that the uncertainty involved canot be resolved by the relative
probablities of the possible outcomes. This is what the term "mechtza
al mechtza" implies.

This paper is IMO a must read for anyone with an interest in this subject.

Saul Mashbaum

A "conventional" pshat in kavua is that of Reb Shimon, found in note 42 here:


The principle of kavua is arguably not based on the laws of probability, but rather serves as a limitation to the principle of rov. See R. Shimon Shkop, Sha'arei ‘Yosher, no. 4, who explains that the principle of kavua is an innovation of the Torah to treat karvua items as part of the larger category to which they belong rather than as individual entities. When an item is considered kavua, the focus is on possibilities, not probabilities. A piece ofmeat from an established location can either be categorized as kosher or non-kosher. When the piece in question is only subject tothese two possibilities rather than the probability that it originated from a non-kosher store, the principle of rov is no longer applicable as the possibilities are equal. If the piece is not subject to kavua, the probability that the meat originated from a kosher store will determine whether the piece is permitted.


Sometimes I think I understand that approach, sometimes not. Depends on atmospheric conditions, I guess... Anyway, another approach is here.


Now, what Prof. Aumann said is that he believes the logic behind kavua is the law of Moral Hazard. You can look up the linked Wikipedia entry. The way Prof. Aumann explained it succinctly is that even if you are perfectly willing to pay double the premiums, an insurer will not issue you a second identical policy on your car. This is because you now have an incentive to disregard your normal parameters of morality and arrange to have your car stolen - after all, you will make a tidy profit on the theft. You might not even make such arrangements - you are, of course, a very moral person - but you may be more negligent about removing your keys from the ignition and locking the door. It might not even be a conscious reaction.


Kol d'parish eliminates any "moral hazard." I was not active in generating the safek, and neither my conscious nor subconscious issues bear on the scenario.


In a case of kavua, however, I was active in creating the safek. I went into the store, I threw the rock, etc. Therefore, my issues bear on the scenario. For example, I might have a subconscious drive to eat treif which impels me to a non-kosher store - of which I myself am not conscious. 


(This bears on the issue that I think I discussed somewhere in the Bigdei Shesh, as to using rov within the kavua - the issue of why every city is not a safek ha'shakul for mikra megillah on Shushan Purim. Lefi Prof. Aumann it would seem pashut that you can use rov within the kavua, v'duk.)


The question I have on this really beautiful approach is:



תלמוד בבלי מסכת זבחים דף עג/ב 
אלא ניכבשינהו דניידי ונימא כל דפריש מרובא פריש

But I think the Tosafos there solve the problem, v'duk.

5 comments:

  1. You mention my discussion with RRW, but not my treatment of qavua. Nothing to do with statistics -- in fact, quite the reverse! I develop R' Akiva Eiger's notion that rov is only an issue in deciding an safeiq in metzi'us, but not in deciding a question of halakhah. So, once the item had a chalos sheim (if I may borrow a Brisker term to non-Brisker usage) if doubt arises in its status, "kimechtza al mechtza dami".

    My addition involves the notion that metzi'us is the world as experienced as opposed to objective reality. Since the experience is one of "I don't know but probably", that's the metzi'us about which we pasqen. We don't have a parallel "as experienced" rationale for din.

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  2. This comment has been removed by the author.

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  3. My approach and Aumann's approach are complementary. My claim is that the kavua/parish distinction is a formal one. If an object is part of a set immediately prior to leidas hasafek (that's the meaning of "kavua"), and the rules of bitul are inapplicable, the object inherits a status of "mixed/indeterminate" from the set (that's the meaning of "mechtza al mechtza" -- it is indeterminate like the mebers of a set of chad be-chad); if the object is not part of the set immediately prior to leidas hasafek (that's the definition of "parish"), it must be assigned a staus relevant to an individual (i.e., "mixed" is not an option), so it is assigned according to the majority of the set from which it came.
    The question is why should the moment *prior* to leidat hasafek be the critical one. Aumann's idea adequately explains that.
    The gemara in Zevachim is not really a problem for that sevara. Clearly, if he took from the set, parish would not apply. (In fact, there is even a gezeirah "shema yikach min hakavua".) "Nichbeshinhu" must be referring to a case where we set them in motion so that (at least) one will then wander off on its own without any possible selection bias on our part. A more serious problem for Aumann is the case in Pesachim where the mouse takes a piece from a set, yet it's called kavua. No possibly-biased person chooses the piece. Aumann would have to say that, since the case must be one in which we witness the event (otherwise leidas hasafek would be after the piece was out of the set), our potential bias consists of somehow not identifying the nature (chametz or matza) of the piece when the mouse takes it.
    Sorry for writing telegraphically.

    Moish

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  4. I just put up a new post with Prof. Aumann's comments on this post:

    http://rygb.blogspot.com/2011/07/kavua-redux-ii-respnse-from-prof-aumann.html

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  5. It seems to me that Reb Shimon's pshat is the same as Moish Koppel's, just in different language. I find that solution quite elegant, and wonder what the nafka mina would be with Prof. Aumann's approach, if any.

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