# 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,

- Compute the divisor D = (Total population)/(Number of seats)
- 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

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

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