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two possibilities rather than the probability that it originated from a non-kosher store, the principle of rov is no longer applicable as the possibilities are equal.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.