Each state is guaranteed how many seats in the house

While that approach may seem straightforward, later experience would show that it was fraught with difficulties. In the s debate, Jefferson prevailed over Hamilton—not because Congress recognized its mathematical subtlety, but largely because it gave one more seat to Virginia, which at that time was the most populous and most politically important state.

Like Jefferson, Webster began with a common divisor, but instead of dropping the fractional remainder, he argued that fractions should be treated in the usual way: rounded up if the fraction was more than one-half, rounded down if it was less. To see how this can happen, consider the hypothetical three-state example described in figure 2 and suppose that the House size were increased from 21 to 22 seats. The quotas would be as follows: state A, Since the state with the smallest remainder is B, it must be the one rounded down.

In other words, in a seat House, state B receives only two seats, whereas in a seat House, it would receive three seats. It could be argued that, since the size of the U. House of Representatives is currently fixed at , the Alabama paradox is no longer relevant. But are there any more reliable methods? All of them are based on the principle of the common divisor invented by Jefferson. Using this method, each state population is divided by an adjustable divisor to obtain a quotient.

The quotients are then rounded to whole numbers and one adjusts the divisor until the rounded numbers add up to the required number of seats. Any such rule is called a divisor method; the only issue is how to round the quotients to whole numbers. In addition to the methods of Jefferson and Webster, three other divisor methods have been proposed over the course of U. John Quincy Adams argued in that all quotients should be rounded up instead of down, no matter how small their fractional parts.

Conveniently, this would have saved a couple of seats for New England, his constituency. Otherwise, he said it should be rounded down. The harmonic mean of two numbers is their product divided by their average. So if a quotient is 2. Joseph Hill, a Census Bureau statistician, suggested an equally bizarre alternative in that was later refined by Harvard mathematician Edward Huntington, and which the House uses to apportion seats today.

They argued that a quotient should be rounded up if it exceeds the geometric mean or square root of the product of the two nearest whole numbers. Congressional delegation—two votes for its senators in the U. Senate plus a number of votes equal to the number of its Congressional districts. Under the 23rd Amendment of the Constitution, the District of Columbia is allocated three electors and treated like a State for purposes of the Electoral College.

Each State which includes the District of Columbia for this discussion decides how to appoint its electors. Currently all States use the popular vote results from the November general election to decide which political party chooses the individuals who are appointed.

This fulfilled the promise of the American Revolution: taxation with representation. The latter amendments, however, did not alter congressional apportionment. Congress has capped the number of Representatives at since the Apportionment Act of except for a temporary increase to during the admission of Hawaii and Alaska as states in As a result, over the last century, congressional districts have more than tripled in size—from an average of roughly , inhabitants after the Census to about , inhabitants following the Census.

Census Bureau. Department of Commerce. Eagles, Charles W. Farrand, Max, ed. The Records of the Federal Convention of The Federalist Papers. New York: Penguin Books, Reid, John Phillip. Chicago: University of Chicago Press, Rossiter, Clinton. New York: Macmillan, Tate, Katherine. Princeton: Princeton University Press, Featured Search Historical Highlights of the House.