# Capstone Proposal

Posted on: November 13, 2010

The time has come for me to submit the proposal for my Capstone Senior Project. I have decided that I would like to explore the complexities of voting, including the paradoxes and problems that can arise when there are three or more candidates (or issues) on the ballot. There is a rich history of voting analysis that dates back to 1770 with French mathematician JC Borda, who, concerned with the outcomes produced by plurality voting, developed a weighted voting system called the Borda Count. A decade or so later, the Marquis de Condorcet attempted to discredit the Borda Count by demonstrating flaws in the procedure, and presented his method based on pair-wise counting, which had some problems of its own.

Then in the 1950’s, Kenneth Arrow, perhaps unaware of this 18th century conflict, analyzed similar problems with voting. He began by defining basic conditions that should be met in a voting procedure, and then attempted to find a voting method that satisfied these conditions. His conclusion was that with three or more candidates, the only procedure that satisfies all the conditions is a dictatorship! So if we are left to choose “between a dictatorship or a paradox” (per Donald G. Saari), what are we to do? Saari uses mathematics to show that there is a more reasonable option, and in fact shows mathematically that the Borda Count is the most reasonable option. I would like to study this centuries-long debate, the issues and “solutions” as they were presented, as well as Saari’s analysis that leads to a reasonable resolution. As has been suggested, since Saari uses linear algebra in his analysis, it would be interesting to run a few elections with fellow students and manipulate the outcomes using linear spaces. I would also like to investigate the reasons why plurality voting is still widely used, even though its flaws are fairly obvious.