Epstein's model showed that the result of all this consulting is a little surprising. After several days of this sequential updating of votes, there are long arcs of solid Bush voters and long arcs of solid Kerry voters and between these there are small arcs of very mixed voters. After a short while, voters in the solid arcs need consult only their immediate neighbors to decide how to vote and almost never change their votes. Voters between the solid arcs need to consult many people on either side of them and change their vote quite frequently.
Although Epstein didn't apply his model to voting but to more automatically followed social norms, the idea of extending it to voting is seductive. People do tend to surround themselves with others of like mind and generally only those at the borders between partisans, the so-called swing voters, are open to much change. His major point, which I'm distorting a little here by casting his model into an electoral framework, is that social norms, often a result of nothing more than propinquity, make it unnecessary to think much — about what to wear, which side of the road to drive on, when to eat, etc.
To the considerable extent that voting is — at least for many — an unthinking emulation of those with whom they associate, the model helps explain the near uniformity of the political opinions of their friends. (Rush Limbaugh's depressingly telling phrase "ditto heads" applies to many on both sides of the political spectrum.)
When there's some sort of shock to the system, Epstein's model suggests something else rather interesting. If a large number of voters change their vote suddenly for some reason (say a terrorist attack or environmental catastrophe), the changed voter preferences soon settle down to a new equilibrium just as stable with solid Bush, solid Kerry, and mixed border areas, but located at different places around the circle. The model thus shows how political allegiances can sometimes change suddenly, but then settle quickly into a new and different segmentation just as rigidly adhered to as the old.
Returning finally to my introductory point, I note that unless there is some cataclysmic change in the presidential race, the only polls that count are the ones in Ohio, Florida, and the relatively few other contested states.
Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books, including Innumeracy and A Mathematician Plays the Stock Market. His Who’s Counting? column on ABCNEWS.com appears the first weekend of every month.