Math Department (Thesis/2007-08)

Monotonicity properties of voting rules

Under the direction of: William Zwicker

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Dear Students,

I've found that it is very helpful for students to get a head start by doing some background reading before the official start of a thesis. If you will be working with me, please get in touch as soon as you know - in particular, at least 2 weeks before exams for Spring term 2007. Drop by my office (Bailey 200B) or send e-mail: zwickerw@union.edu.

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A function of the kind we study in Calculus (such as $f(x) = x^3 + 3x + 17$) is monotonically increasing if it has the property that any increase in the value of the input number $x$ yields an increase in the output number $y = x^3 + 3x + 17$. This idea has been generalized to many different settings, and voting is one of them. Suppose an individual changes her vote (think of her vote as the input) in a way that appears to favor a certain candidate $X$ in the election. The voting rule is "monotonic" if such a change never damages $X$'s finish in the election. Well, the problem is that this definition is pretty loose. What do we mean by "appears to favor"? Or by "damage"? These ideas can be made precise in more than one way, so there are a number of possible definitions for "monotonic" voting rule. We'll explore various notions of monotonicity in voting, perhaps coming up with some new ones.

Math Department web pages Created: 25 Apr 2007 Last modified: Apr 25, 2007 6:15:08 PM Comments to: math@union.edu

2007-2008 Thesis Form Thesis Topics for 2007-2008 Thesis Topics - W. Zwicker