The geometry of voting and Arrow's impossibility theorem

Speaker Name: Ryan Gantner (rgantner at sjfc dot edu )

Speaker Afiliation: St. John Fisher College

Abstract: In this talk, we'll look at some of the peculiarities which can arise when more than two candidates seek election to a position. As an amusing example to illustrate the basic ideas, we'll specifically examine the 1998 Minnesota gubernatorial election in which ex-professional wrestler Jesse Ventura was elected as a third-party candidate. In this example and other examples, we'll build a geometric representation of one particular family of voting schemes and see how the geometry can help us understand the paradoxes which arise. Finally, we'll talk about Arrow's impossibility theorem, which gives a grim conclusion about the possibilities of running a "fair" election.

Target Audience: In this talk, we'll use a few concepts related to 3-dimensional plotting and projection, along with parameterizations of line segments. However, these concepts are fairly easy to pick up on the fly, so really the only math required is a basic knowledge of algebra.