Imagine a baseball reporter charged with covering the sport for his weekly newspaper. How long would he last if he gave the total number of runs produced by each team in the league during the week, but seldom gave the number of games won and lost by each team?
Now imagine a political pollster charged with providing weekly updates on the electoral prospects of the candidates. How long would he last if he gave the percentage of voters nationally favoring each of the candidates, but seldom gave the percentages in the important battleground states?
It seems to me that the questions are quite analogous, but the baseball reporter would be viewed as a joke while the political pollster wouldn't be. Why? Especially in a close race, who wins the World Series of politics depends crucially on who wins the games in the individual purple states — those that are neither blue (Democratic) nor red (Republican), but somewhere in between.
But this is only marginally related to my topic this month. The question I want to consider is how there have come to be large contiguous regions of the country that are red or blue and only relatively small regions that are purple. Some light may be shed on this question by an abstract model introduced in 1999 by Joshua Epstein of the Brookings Institution (Learning to be Thoughtless: Social Norms and Individual Computation).
Imagine that arrayed around a big circle are millions of people who are asked each day whether they intend to vote for George Bush or John Kerry. Assume that these people have an initial favorite, randomly choosing Bush or Kerry, but that they are very conformist and decide daily to consult some of their immediate neighbors. After polling the people on either side of them, they adjust their vote to conform with that of the majority of their neighbors.
How many people each voter consults varies from day to day and is determined by the fact that they are "lazy statisticians." They expand their samples of adjacent voters only as much as necessary and reduce them as much as possible, wishing always to conform with minimum exertion.
There are various ways to model this general idea, but let's assume the following specific rule (which can be made more realistic). If one day a voter, say Henry, polls the X people on either side of him, the next day he expands his sample to the X+1 people on either side of him. If the percentage favoring the two candidates in this expanded sample is different than it is when he polls only the X people on either side of him, he expands his sample still further.
On the other hand, if the percentage favoring the two candidates is the same in the expanded sample as it is when he polls only the X people on either side of him, Henry decides that he might be working too hard. In this case he reduces his sample to the X-1 people on either side of him. If the percentage favoring the candidates is the same in this smaller sample, he reduces the sample still further.
Every voter updates his or her favorite daily and interacts with other voters according to these same rules.
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.