Game Theory and Democracy

Math 89s

Professor Hubert Bray bray@math.duke.edu

189 Physics Building (919)757-8428 (mobile)

Office Hours: Mondays, 5-7 p.m., or by appointment. Please email me if you are coming after 5:30 p.m. so that I will know not to leave early.

Objectives: What is democracy? For example, given a finite number of choices, how does a group of equals choose the option which “best” reflects the will of the group? With two choices, the accepted answer is “majority rule.” However, in the case of decisions with more than two options, this is an open question in the sense that philosophical notions of “best” are not universally agreed upon.

In this seminar, we will use mathematics and game theory to aid us in our discussion on the meaning of democracy and to examine the pros and cons of different approaches to this question. We will discuss preferential ballot elections (where each voter ranks all of the choices) and cover some of the most common vote counting methods used to determine a winner in a preferential ballot election. We will see how some of the most “obvious” vote counting methods, such as Instant Runoff Voting (used on many college campuses), have some significant theoretical defects. Finally, the seminar will include an introduction to game theory which is an essential tool for predicting how intelligent people with agendas behave given carefully defined rules.

Homework: Students will conduct and analyze surveys and elections. Problems will also be assigned in class.

Essays: Each student will write two essays on the topics of their choice which make connections to game theory and democracy.

Exams: There will be a final exam which will be comprehensive. Students will be tested on the topics covered in the homework and all of the material presented in class.

Grade: The grade for the course will be based on

1) 25%: Homework and Class Participation

2) 25%: Essay #1

3) 25% Essay #2

3) 25%: Exam