The following article written for the Crimson by Professor E. V. Huntington '95 of the department of Mathematics in the University deals with the proposed Federal Reapportionment in Congress, a question now before the House of Representatives and upon which a vote is scheduled to be taken sometime today. Professor Huntington has devoted much study to this matter and is considered one of the leading authorities of the nation on this subject.
The apparently simple arithmetical problem of computing the proper assignment of a specified number of representatives to the forty-eight states in proportion to their populations was an unsolved problem in Congress for over a hundred years. Up to 1921, no scientific tests of a good apportionment were known; a variety of empirical methods were tried and later discarded, and the decennial debates in the House were often bitter. On one occasion, after a long speech by Daniel Webster, the Senate reversed the action of the House on purely mathematical grounds. If the House is to be kept at its present size of 435 members, any gain for one state will necessarily mean a loss for some other state, so that the need for a sound and fair method of apportionment is an urgent one. Cases can occur in which the use of a wrong method would affect half the states in the Union.
In 1921 a method called the Method of Equal Proportions became available, which provides for the first time a simple and obvious test of a good apportionment--that is, a test which shows at once whether each state is as nearly as possible on a parity with every other state in the matter of representation, as the Constitution intended.
If the "disparity" betwen two states is defines as the percentage by which the congressional district in one state exceeds the congressional district in the other state, then an apportionment made according to the Method of Equal Proportions is one which cannot be improved by any transfer of a representative from any state to any other state; that is, in such an apportionment, any proposed transfer will be found to increase, rather than decrease, the "amount of disparity" between the two states.
This is all that any Congressman needs to know about the mathematics of apportionment in order to protect himself and his state against any injustice in the matter of representation. There is a short-cut process of computation used by the experts in the Bureau of the Census to turn out, in two or three hours, a correct apportionment of any number of representatives on the basis of any given populations of the states; but this is a matter of technical detail. The result is the important thing, and the result can always be checked up, in case of any dispute, by a direct and straight-forward application of the test.
There is a vigorous discussion in Congress between these favoring the Method of Equal Proportions, which pats all the states on an equal footing, and those favoring an older method called the Method of Major Fractions, which gives a marked advantage to the larger states. For example, the 1920 population of North Carolina is 2,559,123 and of Vermont 352,428. Under the Method of Equal Proportions, North Carolina receives 10 and Vermont 2 representatives, and the "disparity" betwen the two states is 45 percent. Under the Method of Major Fractions, North Carolina receives 11 and Vermont 1 representatives, and the "disparity" is increased to 51 percent. The Method of Major Fractions is obviously unfair to Vermont.
The most recent account of the mathematical theory of this problem is in the Transactions of the American Mathematical Society for January, 1928: a non-technical paper on the subject formed part of the program of Section K of the American Association for the Advancement of Science at its New York meeting on December 28