Making Better Group Decisions: Voting, Judgement Aggregation and Fair Division

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.

About The Course

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? 

Frequently Asked Questions

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?

      In addition to learning about the many different types of voting methods that
      can be used the next time you are running an election, you will also learn
      the best way to cut a birthday cake!  

Why do some lectures have an asterisk (*) next to them? 

      If a lecture is labeled with an asterisk (*), then this means that the lecture is 
      considered an "advanced" lecture.   These lectures will discuss somewhat
      more advanced topics and go into a bit more detail than what is found in
      the regular lectures (for instance,  I may give a proof of a theorem discussed
      in other lectures).   These lectures are part of the course and everyone is
      encouraged to view them; however, you will not be tested on this material. 

Do I need to watch the supplemental lectures?  

      The supplemental lectures are intended to be general introductions to some of the
      mathematical notions that  come up  in the course.   These lectures are not
      intended to be watched one after another.   They are there to supplement my
      regular lectures (for example, if you find that I am using some mathematical notion
      or some notation that you are unfamiliar with).    One of my goals in this course is
      to try to pitch the material (some of which can get quite technical) to a general
      audience (many of whom may not have a background in math).    There are a
      variety of resources on the internet that can be used to supplement these
      lectures.  For instance, it may be useful to consult the following
      Wikepedia pages:   
  • https://en.wikipedia.org/wiki/Table_of_mathematical_symbols 
  • https://en.wikipedia.org/wiki/Naive_set_theory              

Recommended Background

No background is required; all are welcome!