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Frank Morgan's Math Chat - The Winning Voting System


July 6, 2000


In last time's little survey among the following voting systems:


  • Plurality (whoever gets the most votes wins)
  • Runoff (between two highest vote getters)
  • Approval voting (voter votes for all acceptable candidates)
  • Ranking (voter ranks the candidates from 1 to n and smallest sum of rankings wins)

ranking got the most first-place votes, but using the ranking system, runoff won. But using the runoff system, approval voting won. But using approval voting, runoff won. So I guess perhaps runoff is the winner, although no method won under its own system!

Watch for the complete story in the article by Dana Mackenzie in the November issue of Discover magazine.

Old Challenge. Design your own voting system.

Winning Answers. Joseph DeVincentis suggests a version of approval voting in which each voter has three choices: approval (+1), no opinion (0), or disapproval (-1), and the highest sum wins.

Justin Smith would count votes plus IQ minus the amount of money spent.

New Challenge (Matthias Weber). How can two people determine which is older without revealing their ages? No outside help is permitted. You may assume that their ages are different.

Math Chat is now available directly at


Send answers, comments, and new questions by email to, to be eligible for Flatland and other book awards. Winning answers will appear in the next Math Chat. Math Chat appears on the first and third Thursdays of each month. Prof. Morgan's homepage is at

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Copyright 2000, Frank Morgan.