# 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.

(Bold numbers could be clicked upon. To increase the number, click to the right of its vertical center line. To decrease it click to the left of the line. Dragging the mouse near the center line will accomplish the same task, but faster.)

### This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

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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, 5th 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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