This site is a repository for interesting mathematical diversions. I'll add a new item each month (or so)—something more involved than a simple puzzle. There are now fourteen topics in this site and they are very diverse. I try to choose "real" problems from everyday life. Contributions are welcome (both new problems and solutions to problems that I post).

U.S. Presidential Election

The U.S. Presidential Election is determined by a college of electors. The electors are chosen in 51 different contests conducted in each U.S. State and the District of Columbia. The plurality winner in each state receives all of the electors for that state. Different states have different numbers of electors ranging from a minimum of three to a current maximum of fifty-five. (This is an oversimplification in the case of Maine and Nebraska. Rather than being conducted as a single election in those states, an elector is chosen in each Congressional District, and two electors are chosen on a statewide basis. As a result, the U.S. Electoral College is really chosen in 54 elections, rather than just 51.)

This arrangement creates some interesting mathematics, since different combinations of states can form a winning arrangement of 270 electors necessary to gain a majority in the Electoral College. Polling data in individual states is used by the campaigns to understand which states are "in play" in each election. Combining the random and systematic errors in polling data with systematic changes in voter sentiment results in an overall uncertainty about the state-by-state results.

Campaigns need to decide where to put their resources in order to maximize the return on their investment, and it is not always obvious which states are the most critical at any given time. I've written a Presidential Election Predictor to combine state-by-state projections into an overall statement about the probability of the outcome of the U.S. Presidential Election. The program is written to take state-by-state probabilities, such as those provided by a political futures market, and provide an overall probability of victory by each candidate. By adjusting the inputs, it is possible to see which states are likely to have the biggest effect on the outcome of the election. I've also written a page discussing the methodology of this analyisis.