Aggregation of Estimates When Decision by Majority is Not Possible
The Open University of Israel Research Institute for Policy, Political Economy and Society Working Paper No. 2/2011
38 Pages Posted: 10 Sep 2011
Date Written: September 9, 2011
The majority principle is a basic rule for reaching a decision in many legal systems. The principle dictates such procedural rules as creating panels consisting of an odd number of judges to ensure a majority opinion, and in some legal systems, a mandatory debate to guarantee that the majority has considered the minority opinion and rejected it. Nevertheless, decision rules are also needed for cases in which no opinion can muster a majority. The issue we analyze in this article debated between the years 200-600 C.E. by the sages of Jewish law, and it appears likely to challenge the 21st century scholars as well. The topic deals with determining the value of an asset as an aggregation of three different appraisals by professional assessors. According to the majority principle, it is clear that if two of the assessors agree on one value with the third one disagreeing, the decision follows the majority opinion. The problem arises when each of the assessors quotes a different value. For cases in which three assessors who appraise an asset specify values of 80, 100, and 120, three Tannaim suggested various methods of aggregation.
In the first part of the article, we sought to discover the meaning of the others’ opinion, which appears to be an interesting one and poses a challenge to understand it. We recommended three ways of understanding this method, only one of which appears to be consistent with the course of the Talmudic discussion. The three proposals are based on three different principles: the midrange, cluster analysis, and the measure of average deviation.
In the second part of the article we showed that the controversy of the decisors about the “middle course” (milta metziata), whether it refers to the midrange or the median, is also present in another context surrounding the wages of laborers, which also involves the aggregation of various values. Our conclusion is that Maimonides, consistent in his method, prefers the midrange, whereas the schools of Rashi and Rashbam prefer the median. We showed that each method has its advantages and disadvantages, based on which loss function we wish to minimize.
In the last part of the article we raised the question of the generalization of our topic to values that are different from those brought in the baraita, although we noted above that in this article we do not discuss the generalization of the ruling to a general number of assessors.
The implications of this topic for other cases that involve the aggregation of various values should be handled with caution. We have shown at the outset of the article that the understanding of the aggregation in our case as an “estimate” is clear in light of the legal halakhic status of the assessors as expert witnesses, as opposed to judges and witnesses. In other cases it may not be possible to rely on estimates, and the present Tannaitic controversy may not apply.
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