Four Voting Methods

The applet below helps practice and gain insight into four voting methods: Plurality, Borda, Plurality with Elimination, Pairwise Comparison. The instructions for using the applet are available on a separate page and can also be read under the first tab directly in the applet.

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, download and install Java VM and enjoy the applet.

What if applet does not run?

(This applet was created to accompany Excursions in Modern Mathematics, Seventh Edition, by Peter Tannenbaum © Pearson Education. Reproduced with permission. An earlier version of the applet is still available online at


  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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  • Fair Division: Method of Sealed Bids II
  • Fast Power Indices
  • Five Methods of Apportionment
  • Hamilton's Apportionment Method
  • Huntington-Hill Apportionment Method
  • Jefferson's Apportionment Method
  • Method of Markers II
  • Shapley-Shubik Power Index Calculator
  • Voting Methods and Social Choice
  • Webster's Apportionment Method
  • Weighted Voting and Power Indices
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