Learn about different voting methods and fair division algorithms, and explore the problems that arise when a group of people need to make a decision.Preview Lectures
Much of our daily life is spent taking part in various types of what we might call “political” procedures. Examples range from voting in a national election to deliberating with others in small committees. Many interesting philosophical and mathematical issues arise when we carefully examine our group decision-making processes.
There are two types of group decision making problems that we will discuss in this course. A voting problem: Suppose that a group of friends are deciding where to go for dinner. If everyone agrees on which restaurant is best, then it is obvious where to go. But, how should the friends decide where to go if they have different opinions about which restaurant is best? Can we always find a choice that is “fair” taking into account everyone’s opinions or must we choose one person from the group to act as a “dictator”? A fair division problem: Suppose that there is a cake and a group of hungry children. Naturally, you want to cut the cake and distribute the pieces to the children as fairly as possible. If the cake is homogeneous (e.g., a chocolate cake with vanilla icing evenly distributed), then it is easy to find a fair division: give each child a piece that is the same size. But, how do we find a “fair” division of the cake if it is heterogeneous (e.g., icing that is 1/3 chocolate, 1/3 vanilla and 1/3 strawberry) and the children each want different parts of the cake?
No background is required; all are welcome!
Suggested readings will include a selection of articles and other material available online.
The class will consist of lecture videos, which are between 8-15 minutes in length.
Each video will contain 1-2 integrated quizzes. There will also be standalone quizzes that are not part of the video lectures and a (not optional) final exam.
Will I get a Statement of Accomplishment after completing this class?
Yes. Students who successfully complete the class will receive a Statement of
Accomplishment signed by the instructor.
What resources will I need for this class?
For this course, all you need is an Internet connection, copies of the texts
(most of which can be obtained for free), and the time to read, write, discuss,
and think about this fascinating material.
What is the coolest thing I'll learn if I take this class?