454
Opinion of the Court
tricts in any pair of States. Under their test of fairness, a method was satisfactory if, for any pair of States, the transfer of one Representative would not decrease the discrepancy between those States' districts.27 The choice of a method depended on how one decided to measure the discrepancy between district sizes. Each of the five methods could be described as the "best" in the sense of minimizing the discrepancy between districts, depending on the discrepancy measure selected. The method of the harmonic mean, for example, yielded the fairest apportionment if the discrepancy was measured by the absolute difference between the number of persons per Representative. The method of major fractions was the best method if the discrepancy was measured by the absolute difference between the number of Representatives per person (also known as each person's "share" of a Representative).28 The method of equal proportions produced the fairest apportionment if the discrepancy
27 The committee explained the test as follows: "Let the population of a State be A and the number of Representatives assigned to it according to a selected method of apportionment be a, and let B and b represent the corresponding numbers for a second State. Under an ideal apportionment the population A/a, B/b of the congressional districts in the two States should be equal, as well as the numbers a/A, b/B, of Representatives per person in each State. In practice it is impossible to bring this desirable result about for all pairs of States.
"In the opinion of the committee the best test of a desirable apportionment so far proposed is the following:
"An apportionment of Representatives to various States, when the total number of Representatives is fixed, is mathematically satisfactory if for every pair of States the discrepancy between the numbers A/a and B/b cannot be decreased by assigning one or more Representative to the State A and one fewer to the State B, or vice versa, or if the two numbers a/A and b/B have the same property." 1 App. 18.
28 A person's "share" of a Representative is the reciprocal of the population of a person's district. For example, in an ideal district under the 1990 census, each person has a share of 1/572,466 of a Representative.
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