MAT 3940 - VOTING THEORY

credits: 3.0
When elections are conducted using the standard method of plurality voting, problematic and counterintuitive results can occur. Historically, this had led to many proposals for more fair systems of voting. In the 1950’s Kenneth Arrow investigated these systems in the light of a number of fairness criteria and eventually proved that, under a certain set of assumptions, a completely fair voting system is impossible. In this course we will study these voting procedures, apply them to specific elections and model them using geometric methods such as the Saari Representation Triangle. We will also consider paradoxes that can occur, various fairness criteria and prove a number of impossibility theorems including Arrow’s. Other topics will be discussed if time permits. Objectives: A) Be able to identify and use various voting systems, such as plurality voting, instant run-off voting, approval voting and the Borda Count and distinguish between positional and non-positional voting systems; B) Be able to discuss different fairness criteria and prove whether particular voting systems demonstrate these criteria; C) Be able to discuss Arrow¡¦s Impossibility Theorem and prove other impossibility theorems; D) Be able to use geometric methods such as the Saari Representation Triangle to analyze the results of an election across multiple voting methods; E) Have improved their ability to work with, understand and communicate higher level mathematics; F) Be able to define mathematical concepts precisely and use these definitions in writing proofs; G) Be able to construct their own original proofs and write these proofs in a logically correct and clear way. Method of Instruction: Lecture and in-class activities. Method of Evaluation: Grades and Assignments will be broken down as follows: In Class Assignments 50 points, Homework 100 points, Midterm Exam 100 points, and Comprehensive Final 150 points.

Prerequisite(s): MAT 2100 - DISCRETE MATHEMATICS