Rosalie J. Carlson
Harvey Mudd College Mathematics 2013
| Thesis Proposal: | Voting in Interval Societies |
|---|---|
| Thesis: | Voter Compatibility in Interval Societies |
| Thesis Advisor: | Prof. Francis Edward Su |
| Second Reader: | Prof. Michael Orrison |
| E-Mail: | rcarlson@g.hmc.edu |
Voter Compatibility in Interval Societies
In an interval society, voters are represented by intervals on the real line, corresponding to their approval sets on a linear political spectrum. I imagine the society to be a representative democracy, and ask how to choose members of the society as representatives. Following work in mathematical psychology by Coombs and others, I develop a measure of the compatibility (political similarity) of two voters. I use this measure to determine the popularity of each voter as a candidate. I then establish local "agreeability" conditions and attempt to find a lower bound for the popularity of the best candidate. Other results about certain special societies are also obtained.