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Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.

Mathematics, Queen and Servant of Science, New York, 1951, p 164.

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# Apportioning Representatives in the United States Congress

## Jefferson's Method of Apportionment

Fair enough?  Not necessarily.  When the bill reached the desk of President Washington for his signature, there was a great division of opinion among his Cabinet members (one of whom was Alexander Hamilton, the Secretary of the Treasury).  After listening to their opinions, Washington issued the first presidential veto in U.S. history.  He objected that the bill unconstitutionally resulted in House members representing fewer than 30,000 persons, and that there was not a single divisor that could have resulted in the final apportionment.  See http://gwpapers.virginia.edu/documents/presidential/veto.html for the text of the President’s veto message to Congress.

Ten days after the veto, Congress passed a new method of apportionment, now known as Jefferson’s Method in honor of its creator, Thomas Jefferson.

The “D” here is the same as it was for Hamilton.  By decreasing D by some value d, Jefferson lowers the value of the denominator of the State Quota, thus raising the quota.  Eventually the total of all State Quotas, rounded down, will match the predetermined number of House seats.  The method therefore addresses one of Washington’s two objections:  a single divisor will produce the apportionment.

To address the other concern, the Congress changed the number of House seats from 120 to 105.  Thus a divisor of 33,000 was sufficient to produce the apportionment, and no state had a “persons to Representative” ratio of less than 30,000.

This method was approved by the President and was used to apportion the U.S. House from 1792 through 1842.  But how different is it from Hamilton?  If Hamilton’s method had been applied in 1792 to a House of size 105, 13 of the 15 states would have been assigned the same number of Representatives they received under Jefferson.  It was Virginia that benefited under Jefferson (surprise!), while Delaware would have gained a seat under Hamilton that it instead lost to Virginia.

See the spreadsheet 1792 Jefferson for an illustration of the actual Jefferson apportionment of 1792 and a comparison with Hamilton.

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Caulfield, Michael J., "Apportioning Representatives in the United States Congress," Loci (November 2008), DOI: 10.4169/loci003163