Mathematics and the Law: Apportionment of the U.S. House of Representatives

Since the founding of the United States, the decennial ritual of apportioning representatives among the states to the House has generated controversy.  Four distinct methods have been tried and more have been suggested.  It has been the subject of political feuds, mathematical feuds, legal challenge and perorations to God. It is also an excellent example of how mathematics can illuminate the law and how law can motivate mathematics.            

In this talk I will give a crash course in the theory of apportionment. I will discuss the different approaches to apportionment and how they relate to each other. After some discussion of the history of the apportionment of the House, I will show how developments in the law point to new methods of apportionment that have never been employed and the surprising implications they have for the make-up of the House.