Up: Student Seminars for 2006
Top: Math Department Student Seminars

Huygens’ Theorem and the Theory of Voting

by

William Zwicker
Union College

February 13, 2006
4:30 pm
Bailey Hall 201

Pastries and drinks will be served at 4 pm in Bailey 204

Abstract:

Here are three general methods, each of which can be used to create a variety of specific voting systems:

Scoring rules: Each voter assigns points to each candidate. The winner is the candidate with the most points.

Mean proximity voting: Each voter is identified with a point in space. Each candidate is identified with a point in space. The mean position \$g\$ of the voters is calculated. The candidate closest to \$g\$ wins.

Distance-to-unanimity voting: The outcome of any election is clear when the vote is unanimous. When a vote is not unanimous, the winner corresponds to whichever unanimous choice is “closest” to the actual vote.

In what ways are these three general types of voting different? We use a theorem of Huygens to prove that the three classes are exactly the same.

Christiaan Huygens (1629-1695) was a Dutch scientist, mathematician, and astronomer known for important work on optics, telescopes, and pendulum motion, and for his close association with many important researchers of his time: Descartes, Pell, Wallace, Newton, Hooke, Mersenne, and others. One of his theorems concerns sums of squared distances to the mean location (or center of gravity) of a set \$S\$ of points:
These distances satisfy \${d_1}^2 +{d_2}^2 +{d_3}^2=3f^2 +({e_1}^2+{e_2}^2+{e_3}^2)\$, if \$g\$ is the mean location of \$s_1, s_2\$, and \$s_3\$.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.
Up: Student Seminars for 2006
Top: Math Department Student Seminars

 Union College Math Department Home Page Comments to: math@union.edu Created automatically on: Tue Oct 23 08:04:58 EDT 2018