Mathematics of Democracy

Last week, as the Census Bureau organized its 1940 figures, a Harvard mathematician was studying a still unsolved problem in algebra unwittingly posed by the Constitutional Convention of 1787. The Constitution says: "Representatives ... shall be apportioned among the several States ... according to their respective numbers . . . but each State shall have at least one Representative." "This problem," points out Harvard Mathematician Edward Vermilye Huntington, "has worried Congress into a state of great perplexity and bitter debate after every decennial census for over a hundred years." In a 41-page Senate Document he recently tackled the problem.

Everything would be simple if only "fractions of a Representative could be admitted." The number of Representatives is now set by law at 435. So if one State, through population gains, is to gain a seat in the House, another must lose a seat. Losing States must be convinced by a display of clear-cut mathematical theory that their losses are just. Formulas based on unsound mathematics have often led Congress into errors.

A good apportionment formula will:

1) tend to equalize the population of each Congressional district in the U. S.,

2) give each State its fair share of the total 435 Representatives.

Mathematician Huntington's formula discards all formulas except the "test of equal proportions." A seat should not be taken from one State, given to another, unless the percentage difference between the Congressional districts in the two States is reduced.

Example (from the 1920 census): New York had 42 seats, each representing 247,157 people, Vermont had two seats, each representing 176,214 people--a difference between districts of 40%. But if a seat were transferred from Vermont to New York, the difference would be not decreased but increased to 46%. So no transfer should be made. In short, Dr. Huntington aims not to abolish inequalities, which is impossible, but to keep them to a mathematical minimum.

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