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Why swing voters matter
« on: 2004-08-24 10:27:15 » |
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title: Regarding Henry
author: John Allen Paulos
dated: Thursday August 19, 2004
source: The Guardian
vector: Jonathan Davis
Voters look to their neighbours to determine their decision. John Allen Paulos explains why a few swing states of borderline electors will settle the US presidency
In recent years the US electorate has become highly polarised. Large contiguous regions of the country (the red states) favour the Republicans, other large contiguous regions favour the Democrats (the blue states), and relatively small regions in between (which we might label purple) constitute the so-called battleground states.
There are many reasons for this dichotomy, but some light may be shed 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 around a big circle are millions of people who are asked daily whether they intend to vote for George Bush or John Kerry. Assume that they have an initial favourite, randomly choosing Bush or Kerry, but that they are very conformist and decide daily to consult some of their immediate neighbours. After polling those on either side of them, they adjust their vote to conform with that of the majority of their neighbours.
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, wishing always to conform with minimum exertion.
There are various ways to model this general idea, but let's assume the following specific rule. 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 favouring 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 favouring 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 he may be working too hard. In this case he reduces his sample to the X-1 people on either side of him. If the percentage favouring the candidates is the same in this smaller sample, he reduces that sample further.
Every voter updates his or her favourite daily and interacts with other voters according to these same rules. (At the cost of complicating the model we can allow voters to consult an acquaintance network rather than only their immediate physical neighbours.)
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 them, small arcs of very mixed voters. After a short while, voters in the solid arcs need consult only their immediate neighbours 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 applied his model 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 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 - for many - an unthinking emulation of those with whom they associate, the model helps explain the near uniformity of their friends' political opinions. (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.
In any case, unless there is some cataclysmic change in the presidential race, the crucial races are those in Ohio, Florida, and the relatively few other contested purple states.
· John Allen Paulos is a professor of mathematics at Temple University, Philadelphia, and bestselling author of Innumeracy and A Mathematician Plays the Stock Market. www.math.temple.edu/paulos
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