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.