Fair Division in Theory and Practice
[CSE/Poli Sci 245A (Spring 2015)]

Course Information

The concept of fair division is a central tenet in the design of procedures aimed at generating equitable social outcomes and mitigating conflict. At the national level, such procedures include systems of apportionment, voting, and legislative districting, to name a few. On a smaller scale, these procedures could govern how assets are divided in a divorce, or how to divide a cake.

While "fairness" in theory is indisputably a good thing, in practice the courts, politicians, and even mathematicians have grappled with the question of what it means for a procedure to be fair. An illustration is the 2004 case Vieth v. Jubelirer, in which a plurality of the Supreme Court ruled that claims of political gerrymanders (the drawing of district lines to advantage one political party over another) were not capable of being decided by a court. Interestingly, the Court unanimously agreed that severe gerrymanders are unconstitutional and incompatible with democratic principles of fairness. But neither the Court nor the appellants could agree on a principle of fairness that could be applied to all such cases. Absent such a principle, Justice Scalia wrote "'Fairness' does not seem to us a judicially manageable standard."

This course will examine algorithms and applications of procedures that aim to divide or allocate resources fairly. Some of these procedures were developed by mathematicians looking for formulas that satisfy mathematical properties such as envy-freeness and equitability. Other procedures emerged through historical debates concerning issues like federalism and voting rights. Still others emerged as solutions to ethical and practical problems such as how to fairly allocate kidneys, or match students to schools. All of the procedures we consider will be examined in terms of the fairness goals they aspire to achieve, the mechanisms they employ to achieve those goals, and the shortcomings of the procedures.

Students taking this course should be familiar with basic programming and able to write simple programs.
Teaching Assistants
What When Weight for final grade
Exams Two exams will be given: one at midterm (27 February 2015) and one at the end (17 April 2015).

The end exam may or may not be cummulative, depending on how people do on the midterm exam.

20% each
Homework No homework will be graded, but questions will be posed throughout the semester and you get credit for submitting your solutions. 5%
Labs and Studios At times you will study a given approach or technique by performing analysis, programming, and writing a short document of your findings. 20%
Project You must find some fair division problem to which you will apply a technique we study this semester. The problem can come from your life, from campus life, from greek life, from the region, the state, the nation, or the world.

You will be required to propose your project in the first few weeks of the semester, and reports on your progress may be required periodically during the course.

  • Asking or answering questions in class
  • Course evaluation

Academic Integrity
Anyone found cheating will on any graded assignment will receive an F for this course; other action may also be taken.

Last modified 12:47:15 CST 16 January 2015