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Voting with Rubber Bands, Weights, and Strings


William S Zwicker*
Union College

February 20, 2012
4:30 pm
Bailey Hall 207

Refreshments will be served in Bailey Hall 204 at 4:15


Abstract Suppose each voter ranks three candidates p, q, and r for president. How should we decide the winner? Here is a bizarre voting system: we arrange six points as the vertices of a hexagon, labeled with the six possible rankings. Each voter loops one end of a rubber band around the vertex with their ranking, and the other end around one movable point O. O is released, it achieves an equilibrium position, and the winner is determined by the ranking on the vertex closest to O.

Surprisingly, this voting system is identical to another, well-known rule usually attributed to Jean Charles de Borda (but it’s actually much older).

We’ll address some of the following questions:

  • Can a computer pretend to be a bunch of rubber bands1?
  • How can dishonest voters use their rubber bands to stretch the truth?
  • What happens if we replace rubber bands with strings and weights?
  • How can we count ties, and why do we get fewer ties with weights and strings than with rubber bands?
  • *With co-authors D. Cervone, and undergraduates (from Union and Skidmore) R. Dai, D. Gnoutcheff, G. Lanterman, A. Mackenzie, A. Morse, and N. Srivastava

    1Yes, of course it can. So…BRING YOUR LAPTOPS!

    For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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