By John Considine
My guess is that most economists would have heard of Kenneth Arrow and have some idea of the work for which he was awarded the Nobel Prize in Economics. For example, he is known for showing the difficulty combining individual attributes into a common measure (apologies for the generality). My guess is that fewer would know that Arrow was influenced by a paper by a Harvard mathematician with a keen interest in cross-country running. Gordon Tullock has documented how Arrow acknowledges the influence of E.V. Huntington's 1938 paper "A Paradox in the Scoring of Competing Teams".
Today, while looking for an excuse to take a break from grading students' work, I read this very short paper again. It is two pages in length. Huntington opens the paper with a brief discussion of scoring teams of students and cross-country runners. Because individual times were not usually available, the scoring of the running teams has to be done by the rank method. By contrast, the student marks can be aggregated directly. Huntington then presents six cases where teams, comprising of three students per team, are scored using the aggregation of their marks and the ranking method. In all six cases, Team A scores 268, Team B scores 267, and Team C scores 266. However, the rank method give six different rankings: ABC; ACB; BAC; BCA; CAB; CBA.
There is a touch of understated class about the following two lines from Huntington. "In many practical cases it will make no difference which method is used. Nevertheless, the question has a certain theoretical interest which seems to be worth discussing."
Today, while looking for an excuse to take a break from grading students' work, I read this very short paper again. It is two pages in length. Huntington opens the paper with a brief discussion of scoring teams of students and cross-country runners. Because individual times were not usually available, the scoring of the running teams has to be done by the rank method. By contrast, the student marks can be aggregated directly. Huntington then presents six cases where teams, comprising of three students per team, are scored using the aggregation of their marks and the ranking method. In all six cases, Team A scores 268, Team B scores 267, and Team C scores 266. However, the rank method give six different rankings: ABC; ACB; BAC; BCA; CAB; CBA.
There is a touch of understated class about the following two lines from Huntington. "In many practical cases it will make no difference which method is used. Nevertheless, the question has a certain theoretical interest which seems to be worth discussing."
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