Ranking Ranking Rules

In the next section, we discuss more general forms of rules.

Talmud, Babylonian (3rd–5th c CE) and Palestinian (3rd–4th c CE), is the collection of rabbinic materials of various genres – rulings, discussions, interpretations, stories, morals, and other literary forms. The Talmud is arranged as comprehensive interpretation to the Mishnah, the basic and authoritative collection of old rabbinic oral instructions edited circ. 220 CE. The Mishnah is composed of 60 tractates ordered in six “orders” (sedarim). Each single paragraph of the Mishnah is also called a Mishnah.

The discussion in the Talmud is purely theoretical as by the time the issue was discussed the Jerusalem temple was destroyed for more than 200 years. This does not prevent the rabbis from analyzing the question as they maintained that the study of the old laws is culturally and spiritually important, regardless of their actual relevance.

A sacrifice made for the atonement of an unintentional sin or ritual fault. As the Hebrew name ḥattat means also “purification” (see Milgrom, 1991-2001:758-759), sin-offering is obligatory in specific rituals even when no sin is committed, like after childbirth or after recovery from leprosy.

An animal sacrifice which is entirely consumed by fire on the altar. Burnt-offering may be brought either as public or individual sacrifice. In the latter case, it can be obligatory, for certain rituals, or voluntary, as an act of piety.

A voluntary individual offering, usually brought as thanks-giving offering or for the purpose of a feast. Except for some inner parts of the animal, the flesh of the peace-offering is eaten by the priests, the donor, and his family.

A tenth of the newly born cattle. Animal tithe is given each year to the priests, who has to sacrifice and ritually eat it.

Lev. 12:6. Another example is that of a nazirite, who is required to bring, when accomplishing his vow, a group of three animals: a sin-offering, a burnt offering, and a peace-offering (Num. 6:16–17). A very common group is the pair of birds – a sin-offering and a burnt-offering – brought by the poor person who cannot afford the regular cattle offering (e.g. Lev. 5:7, 12:8, Luke 2:24).

The old (3rd c CE) rabbinic commentary to Leviticus, attributed to the school of R. Akiva, the 2nd c CE mishnaic scholar.

Sifra (1988, 18:5–6:189). Italics added.

Through an exegesis to Lev. 5:8: “And [the priest] shall offer that which is for the sin-offering first.”

Actually, the only example for such a combination is the set of offerings brought by a mother after giving birth (Lev. 12:6). See Talmod Bavli (1961:Zev.90a, s.v. ha’of). For Rashi, see footnote 2(')@ below.

A similar solution is offered in the Talmud Yerushalmi (1982-1994:Hor.3:7, 48a) to a similar question, based on a different set of rules and sacrifices.

The Babylonian’s wording alludes to the formula used by the Mishnah to postulate the precedence of tithe to birds: “The tithe precedes the bird-offerings, since it is an animal-offering” (1933:Zev.10:3).

Observe that the language of the Talmud is very clear – the question relates to a choice function, which is to select one out of a set of options. The question is not what is the right order at which the animals will be sacrificed, although eventually this question too will be answered.

R. Shlomo b. Yitz ḥ ak (northern France, d. 1105), preeminent commentator to most parts of the Bible and the Babylonian Talmud. In this article, reference is made to Rashi’s commentary printed on the inner margins of the traditional editions of the Babylonian Talmud.

Although this is not the topic of our paper, we should mention here that Rashi’s interpretation of the Palestinian solution essentially claims that the Independence of Irrelevant Axiom (IIA) must be violated. According to this axiom, the ranking of two options does not depend on the existence of other alternatives. See Naeh and Segal (2009) for a further discussion of the Talmudic analysis of this idea.

In this context, means “has a priority regarding the title of the good.”

In most legal systems, a good-faith purchaser for value may gain title even though the intermediate seller’s title is voidable (e.g. Section 2–403(1) of the UCC, “[a] Person with voidable title has power to transfer a good title to a good faith purchaser for value”). In some legal systems a good-faith purchaser for value may gain title even if the intermediate seller’s title is void (under the “market-overt” rule) (e.g. Medina (2003)).

According to the standard set by the Equal Employment Opportunity Commission (EEOC), a test that is implemented to select candidates is considered imbalanced when it results in a selection rate of a specific race (that is, the ratio of those qualified out of all candidates of this race) which is less than 80% of the selection rate of the race with the highest selection rate. 29 CFR 1607.4(D) (2008); Watson v. Fort Worth Bank & Trust, 487 U.S. 977, 995–96, n. 3.

According to the prevailing (although not self-evident) approach, it is illegitimate to grant preferential treatment to an individual or to a group because of the race of such individual or group even if such treatment is aimed to insure a fair representation of this race.

In Ricci v. Destefano, 557 U.S. 557, 585 (2009), the Supreme Court held that “once … employers have made clear their selection criteria, they may not then invalidate the test results. Doing so, absent a strong basis in evidence of an impermissible disparate impact, amounts to the sort of racial preference that Congress has disclaimed, and is antithetical to the notion of a workplace where individuals are guaranteed equal opportunity regardless of race.”

See Ricci v. Destefano, 129 S. Ct. 2658, 2676 (2009), in which the Court held that “[e]xaminations like those administered by the City create legitimate expectations on the part of those who took the tests,” and invalidated the City’s decision to discard these tests.

Note that in our example although c wins in the first comparison (where Rule 3 is applied for the pair {a,c}), c is not the best policy overall as it is defeated by b.

See, e.g., Local 28 of the Sheet Metal Workers, Int’l Ass’n v. EEOC, 478 U.S. 421, 479 (1986) (upholding an affirmative action plan in part because it “did not require any member of the union to be laid off, and did not discriminate against existing union members”); Wygant v. Jackson Bd. of Educ., 476 U.S. 267, 283 (1986) (emphasizing the importance of “not disrupting the settled and legitimate expectations of innocent parties”). See also Zamir (2012), Vars (1996:79), and Ayres and Vars (1998:1617).

For instance, the right of the United States to pursue an independent action to recover from tortfeasor for reasonable care and treatment is not subject to any state statute of limitations (sometime 2 years), but only to the 3 years limitations set at the MCRA (U.S. v. Gera 409 F.2d 117 (3d Cir. 1969)). The government is also released from state doctrine of inter-spousal immunity which may prevent the injured from recovering from the injurer (e.g., United States v. Moore, 469 F.2d 788, 790 (3d Cir. 1972)).

Kalai et al. (2002) introduced the concept of rationalization by multiple rationales, where the set of strict preferences over a set S thus rationalize a choice function if for every there is such that is -maximal in T. The Babylonian solution does that and goes a step further by ranking the partial preferences . The rules are applied one at a time until a complete and transitive order is created. Naturally, it may happen that not all rules are used.

Even if disagrees with . In such a case c is overruled by .