Game Theory and Democracy
Math 89s, Fall 2014
Hours: Mondays and Wednesdays, 4:30 - 5:30pm, or by
appointment. Please email me if you
are coming after 5pm so that I will know not to leave early.
As the trend towards democracy continues, the question of determining
what democracy actually means becomes increasingly important. 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
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 three 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%: Class Participation
2) 50%: Homework and Essays
3) 25%: Final Exam