Webster's Apportionment Method

Daniel Webster proposed his apportionment method in 1832.It was adopted by the Congress in 1842, and then replaced by Alexander Hamilton's in 1852. It was again adopted in 1901 and reconfirmed in 1911. Finally, it was replaced by Huntington-Hill's method in 1941.

(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.


What if applet does not run?

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 Webster,

  1. Compute the divisor D = (Total population)/(Number of seats)
  2. Modify D by an amount d, that could be negative, such that when state allocations {(State population)/(D + d)} are rounded in the customary manner, they add up to the exact number of seats.

(One of the applets at this site combines Webster'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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  • Jefferson's Apportionment Method
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  • Shapley-Shubik Power Index Calculator
  • Voting Methods and Social Choice
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