Social Choice

Social Choice theory studies the ways of mapping individual preferences expressed by preference ballots, i. e. ordered lists of alternatives, (columns in the applet) into a selection of one or ranking of several such alternatives.

The applet presents four methods: Plurality, Borda, Plurality with Elimination, and Pairwise Comparison of alternatives.

(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. Small triangles in the upper right corner of the cells allow swapping adjacent cells contents, thus adjusting the ballots.)

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?

(A newer version of the applet is also available online at The later version has no direct way for method comparison, but has the advantage of letting on follow the progress of each method setp by step.)


  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

Related material

  • The Constitution and Paradoxes
  • Student's Social Choice
  • Adams' Apportionment Method
  • Banzhaf Power Index Calculator
  • Fair Division: Method of Lone Divider
  • Fair Division: Method of Markers
  • Fair Division: Method of Sealed Bids
  • Fair Division: Method of Sealed Bids II
  • Fast Power Indices
  • Five Methods of Apportionment
  • Four Voting Methods
  • Hamilton's Apportionment Method
  • Huntington-Hill Apportionment Method
  • Jefferson's Apportionment Method
  • Method of Markers II
  • Shapley-Shubik Power Index Calculator
  • Webster's Apportionment Method
  • Weighted Voting and Power Indices
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