Math Colloquium September 23, 2009 - The Apportionment Problem

The U S Constitution requires that the seats in the House of Representatives be apportioned to the States according to their populations. But Representatives come in whole units while population proportions don't. "So, what's the problem? Just round off! It's third-grade mathematics." Well, no, it isn't. Though the Founding Fathers apparently didn't realize it, there are intractable difficulties in coming up with a "fair" apportionment scheme. This talk will explore various methods that have been used or proposed, along with what's wrong with them. The contribution of mathematics is to establish that there is no "perfect" method.