Kavu'a and Parush
Yeshivat Har Etzion would like to take this opportunity to congratulate Prof. Aumann on his receiving the Nobel Prize for Economics.
The Gemara in Ketubot 15a states:
[If there were] nine shops, all of them selling meat of a ritually slaughtered animal, and one selling meat of a nevela [= which had not undergone ritual slaughter], and someone bought from one of them but does not know from which of them he bought, [the meat] is forbidden on account of the doubt. But regarding [meat that] was found, go after the majority.
This is the classic example of the principle "Any doubt concerning something or someone while it is fixed in its place [kavu'a] is considered an evenly balanced doubt. And anything or anyone that has separated from the group in which it or he is normally found [parush] is assumed to have separated from those who form the majority of that group." This rule appears seventeen times in the Talmud in a variety of contexts. When a forbidden article is fixed in its place – that is, there certainly exists a shop that sells non-kosher meat, but it is not known whether or not a particular piece of meat was purchased in that shop – then the doubt is considered as evenly balanced, and one must be stringent. When, however, the forbidden article has separated – that is, when its status is altogether unknown – we follow the majority, and there is room for leniency.
At first glance, this rule is astonishing: What is the difference between the two cases? In both instances there are ten stores, only one of which sells non-kosher meat. What difference does it make where the meat was found?
Much ink has been spilled with regard to this issue, and I must admit that I have not seen everything that has been written on the topic. But this may work to my advantage: I come to suggest an understanding rooted in the realm of economic theory, an understanding that is quite modern and may shed light on this issue. For this reason, I prefer not to relate to the various commentators (with the exception of Rashi and Tosafot, as local commentators who explain the plain sense of the Gemara). In a certain sense, therefore, we shall try to ignore all that has been said on the topic by the various rishonim and acharonim.
The Principle of Moral Hazard
As stated above, I wish to borrow an insight rooted in economic theory in order to explain the Gemara. An idea exists in economic theory called "the principle of moral hazard." The most striking example of moral hazard is found in the insurance industry. A cardinal principle in the insurance world is that an article is never insured for more than its value. At first glance, there doesn't seem to be any justification for this practice. It goes without saying that an insurance company wishes to make a profit on every deal (otherwise it would go out of business), and the larger the account, the larger the profits. This is no different than a greengrocer who prefers selling two kilograms of potatoes to selling only one kilogram. Why then should an insurance company refuse to insure my car for twice its value? Surely the risk is the same if I insure the car for twenty thousand dollars or fifty thousand dollars!
The answer is simple: The size of the policy affects the behavior of the policyholder. Thus, the probability of an accident or theft depends upon the size of the policy. First of all, if the car is insured for more than its value, there are people who will see to it that it is stolen or involved in an intentional accident. At the very least, they will be inclined to act in a negligent manner, failing to lock the doors, even if only unintentionally. This is an example of "the principle of moral hazard": a moral hazard exists when the action of an interested party is likely to effect the result or the likelihood of obtaining a certain result.
Another example of moral hazard involves a person at a shooting range, where a question arises regarding the probability of his hitting the target. This is a pure and classic case of moral hazard, for it is the person's action that determines whether he will hit or miss. At any given time, he may have an interest in missing; or else he may be nervous, and therefore fail to hit his mark in his usual manner.
In such cases, when the probability of obtaining a particular result depends upon the actions of interested parties, the ordinary rules of probability do not apply, and generally speaking, one is unable to predict the outcome. Another example of this principle is the stock market: A person who buys stocks assumes a certain risk; he may enjoy a profit or suffer a loss (as opposed to money deposited in a savings account or in bonds that yield a fixed income). A person does not know how much money he will gain or lose, and so the purchase of stocks involves a state of uncertainty, which people are willing to enter because of the possibility of making a large profit.
Now, the owners of a certain company (as well as the workers) can buy and sell shares in their own company. This raises not only moral problems, but also technical problems: The way a company is managed affects the value of its shares, and company managers have prior knowledge about what is happening in their company. Let us assume, for example, that the value of the company's stock is high, but a quarterly report is about to be published indicating significant losses. If the company's manager knows that the company suffered losses in the previous quarter, he is likely to sell his shares prior to publication of the report, and thus avoid his own personal financial losses. This phenomenon is called "insider trade" and is severely limited by the rules of the stock exchange.
I wish to argue that this principle of moral hazard underlies the distinction between kavu'a and parush. In the second case, a person finds a piece of meat that had been lost. He does not know where the meat came from, but it left the store at a time when nobody could control or had an interest in having an effect on the place the meat came from. In such a case, we follow the majority, and the probability that the meat is from one of the stores that sell ritually slaughtered meat is ninety per cent. In the case of kavu'a, the person who bought the meat does not know in which store he bought it. Why does he not know? Did he forget? Perhaps, there is a reason that he forgot, for, indeed, the meat looks tempting. We are dealing, of course, with an observant Jew, but nevertheless the meat beckons him. His forgetting where he had purchased the meat may indeed be sincere, but nevertheless you must decide whether or not you know, and it was you who bought the meat in the first place, and it was you who chose the meat. Thus, we are dealing here with the factor of moral hazard. I don't mean to say that this meat is not kosher, God forbid, but the ordinary rules of probability, of nine versus one, no longer apply. We are dealing here with the effect of an interested party, who is at one and the same time the one who wishes to eat the meat and also the one who must establish its halakhic status. Thus, we cannot invoke the ordinary rules of probability, and so there exists a case of uncertainty. An uncertainty that cannot be resolved is regarded as evenly balanced, and thus one must be stringent.
This idea must, of course, stand the test of the various talmudic passages dealing with kavu'a and parush, and there are many of them. We shall not go into all of them, but we shall try to analyze some of them to see whether the principle that I have suggested works in their regard.
A Girl that was Raped
The Mishna in Ketubot 14b states:
Rabbi Yose said: There was a case involving a little girl who went down to fill [a jug with] water from the spring and she was raped. Rabbi Yochanan ben Nuri said: If the majority of men of the town marry [their daughters] into the priesthood, this [girl] may marry into the priesthood.
Rashi explains: "If the majority of [the men of] the town are fit to marry their daughters and their widows into the priesthood – i.e., where the majority of the men of the town do not disqualify a woman for the priesthood by way of their intercourse – she too may marry into the priesthood." The Mishna is followed by a complicated discussion. We shall not study all of it, only the last line of the Gemara which states as follows (15a):
If [one of] them went to her, let us say, "Anyone who separates, separates from the majority"! – No. It is necessary where she went to [one of] them, so that he was fixed. And R. Zera said: All that is fixed is considered as an evenly balanced doubt.
The young girl was certainly raped, and the question arises whether or not she is now disqualified for the priesthood. The Gemara determines that a distinction must be made between two cases: If the rapist came to the girl and raped her – then she is not disqualified for the priesthood, because the majority of the men of the town do not disqualify for the priesthood, and he "separated" himself from the town and went to rape the girl. In such a case, she did not come to him, but rather he came to her, and the initiative was not in any sense hers. On the other hand, if the girl went to him – and it makes no difference why she did so – she then had a part in what happened, and the issue of moral hazard applies. The moment that she approached him and asked him the time, she affected the results. From that moment, the ordinary rules of probability no longer apply, and the matter remains as an uncertainty. It seems to me that in this case, it is very clear that the Gemara's distinction between kavu'a and parush is whether the girl served as an object or as a subject in the case at hand.
The Principle of Clear Halakha
In addition to the principle mentioned above, there is another principle that may help us understand the various passages. This principle we shall call "the principle of clear halakha." The principle of moral hazard is scientific, whereas this second principle is halakhic. According to this principle, we aspire to clear and unequivocal halakhic rules that do not require interpretation. Amorphous considerations like public interest, communal benefit, and the like do not fit this principle, for they are not clear cut and unequivocal, and the uncertainty that they cause generates economic uncertainty and the natural human tendency to distance oneself from risks. When a person does not know whether the bank will or will not confirm a contract, he will refrain from entering into that contract despite the fact that it is for the public benefit and good for both parties. We should aspire to clear laws, and thus, at times, we must be decisive. In the case of the raped girl, Chazal may have decided the law according to the rules of kavu'a and parush: Even though the case is borderline – for the girl certainly did not approach the man in order to be raped – Chazal decided to stick to the guiding principle, namely, whether or not the decision was made by an interested party.
2. Sheratzim [Creeping Animals] and a Frog
In the continuation of the passage, the Gemara returns once again to the law of kavu'a and wishes to bring support for it from the case of nine sheratzim and a frog:
Rabbi Zera said: All that is fixed is considered an evenly balanced doubt, both for leniency and for stringency… from [the Baraita which states: If there were] nine sheratzim and one frog among them, and he touched one of them but does not know which of them he touched, if in the private domain, he is ritually impure on account of the doubt, [and if] in the public domain, he is ritually pure because of the doubt.
This is another case of kavu'a: There are nine dead sheratzim that render a person touching them ritually impure and one dead frog that does not render a person touching it ritually impure, and the person who touched one of them is an interested party, because he wishes to know what law applies to him. Since the action that led to the uncertainty was performed by the same person who wishes to know the law – there exists the factor of moral hazard, and so the uncertainty remains in place and we do not decide it according to the rules of probability. When the uncertainty involves ritual impurity, there is another way to resolve it – by way of the rule that "a doubtful case of ritual impurity arising in the public domain is decided leniently," and the rule that "a doubtful case of ritual impurity arising in the private domain is decided stringently."
3. Throwing a Stone into a Group of People
Later in the passage, the Gemara attempts to find a biblical source for the law of kavu'a:
And how do we know this from the Torah? The verse says: "And he lies in wait for him, and rises up against him" (Devarim 19:11)… - to exclude someone who throws a stone into a group [of people]… How do we visualize such a case? If we say [that] there are nine non-Jews and one Jew [and for the killing of a non-Jew one is not liable for stoning], then let him derive it from [the fact that] the majority are non-Jews. Or also, [even if they are considered] half and half, [where there is] a doubt concerning capital cases, [we rule] leniently. - No. It is necessary where there are nine Jews and one non-Jew among them, so that the non-Jew is fixed [in his place], and all that is fixed is considered an evenly balanced doubt.
In a case where there is a group of ten people standing together, nine Jews and one non-Jew, and someone throws a stone into the group and kills one of the Jews – he is exempt from stoning, because of the law "to exclude one who throws a stone." What we said earlier applies in this case as well. Even though there is a clear majority of Jews and the killer did in fact kill – since the person standing trial is the person who threw the stone, the principle of moral hazard applies. Thus, the uncertainty remains in place ("all that is fixed is an evenly balanced doubt"), and we do not decide according to the ordinary rules of probability.
In this article we have tried to explain the rationale underlying the rule that "all that is fixed is considered an evenly balanced doubt," which states that in a case of "kavu'a," despite the fact that the ordinary rules of probability indicate that we should follow the majority, we do not act accordingly. We have suggested that this rule is based on the principle of moral hazard. That is to say, a person who is the subject of a halakhic discussion is an interested party, and this effects the probabilities. Another principle plays a role as well. In cases where the classification is not clear, there is an inclination on the part of the Rabbis to decide on the basis of clear rules, and not to allow for distinctions.
*This lecture was delivered in Yeshivat Har Etzion in the framework of the series, "The Sacred and the Profane." This summary was not reviewed by Prof. Aumann.
 In similar fashion, it is possible to argue that if he came to her, perhaps she had acted in a provocative manner, and once again, the chances applying in this particular case do not match the general rules of probability. As stated above, however, Chazal decided the law in accordance with a clear-cut rule: If the interested party is passive, we rely on pure probability; if he is active, we are concerned about moral hazard and leave the uncertainty in place.
 This law is based on the principle regarding a doubtful case of ritual impurity: if it arose in the public domain, it is ritually pure, and if it arose in the private domain, it is ritually impure.
(Translated by David Strauss)