Apportionment: Jefferson's method

The apportionment method suggested by future president Thomas Jefferson as a competitor to Hamilton's method. Jefferson's method was the first apportionment method used by the US Congress starting at 1791 through 1842 when it was replaced by Webster's method.

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The given total number of seats (23 in the applet) is to be apportioned between several (3 at the ouset) states proportionally to their populations. To accomplish that task according to Jefferson,

1. Compute the divisor D = (Total population)/(Number of seats)
2. Decrease D by an amount d such that when state allocations {(State population)/(D - d)} are rounded downward, they add up to the exact number of seats.

(One of the applets at this site combines Jefferson's and four additional methods of apportionment under a single umbrella.)

Reference

1. For All Practical Purposes by COMAP, 5^th edition, W. H. Freeman & Company, 2008 (8th edition)
2. G. Szpiro, Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present, Princeton University Press, 2010.
3. P. Tannebaum & R. Arnold, Excursions In Modern Mathematics, 7th edition, Prentice Hall, 2009

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