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...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.
"The Essence of Mathematics" in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Apportioning Representatives in the United States Congress
Apportionment and Presidential Elections
The 1870s saw a new twist in the apportionment wars, one that spilled over into a Presidential election. In the apportionment of 1872, the House size was set to 292. Hamilton’s method was legally in place. Yet the actual apportionment approved by Congress differed in four states from the Hamilton apportionment. New York was assigned 33 seats in 1872, Illinois 19, New Hampshire 3, and Florida 2. But Hamilton’s method would have given New York 34, Illinois 20, New Hampshire 2, and Florida 1. Whatever Congress may have intended, the apportionment they approved is one that would have been given by Dean’s method for the Census of 1870.
Why is this such a big deal, outside of those four states? Because in the closely contested election of 1876, Samuel Tilden won the state of New York while his opponent, Benjamin Harrison, won the other three. Harrison beat Tilden in the Electoral College by a vote of 185 to 184. Had Hamilton’s method been followed, the count in the College would have been reversed and Tilden would have been elected! See the spreadsheet 1876 apportion for an illustration of the Hamilton calculation as compared to the actual apportionment and for a tabulation of the electoral votes in the election of 1876.
So in 1876, Hayes won under a Dean apportionment but would have lost under a Hamilton apportionment, even if no other factors had changed. Now let’s jump forward to the Presidential election of 2000. In the Electoral College, George W. Bush defeated Al Gore by a tally of 271 to 266. (Gore should have had 267 votes, but one of his electors from Washington, D.C. abstained.) Had the Congress used Jefferson’s method to apportion the House after the 1990 census, Gore would have garnered 271 electoral votes and become the President. Even more intriguingly, had Hamilton’s method been in place, the Electoral College vote would have been tied at 269 and the election thrown to the House of Representatives for resolution. Methods of apportionment do have practical consequences!
Caulfield, Michael J., "Apportioning Representatives in the United States Congress," Loci (November 2008), DOI: 10.4169/loci003163