In a bit more detail, almost all the simulations begin with polls in the so-called battleground states and use them to estimate the probability of one candidate or the other (either will do, but most use Obama as a base) winning each of these states. If, for example, Obama leads McCain 52 percent to 48 percent with a margin of error of 4 percent in a given state X, then standard statistics might tell us that his chance of winning the state is roughly 85 percent. (That is, because of sampling error there's an 85 percent he'll get at least 50 percent of the vote in state X.)
If there are other polls in the state or sources of relevant demographic data, they are averaged in, with more consideration given to recent data and polls as well as to those that have been more accurate in the past.
These computations are done for all states, and then a computer runs thousands of virtual elections in which Obama has an 85 percent chance of winning state X, McCain has a 60 percent chance of winning state Y, and so on for all the other states. The various ways that Obama can attain at least 270 electoral votes and hence win the election are determined, and then the overall likelihood of his winning is calculated.
The state probabilities can be combined in this way to yield a probability of winning the election as a whole since, if the election took place today, there's little reason to believe that sampling errors in the various states would be correlated. But things do happen, and this is not the case if what we want is a prediction of the November result and not the September result.
Some states tend to shift together over time, but more importantly and more generally the polls are particularly volatile during the two to three months before an election. There are the two conventions, the four debates, the inevitable gaffes and scandals, the advertising campaigns (the despicable but effective Swift Boat smear, for example), and external events, each of which can change the electoral total by 10 to 50 votes and which together can change it by much more.
So unless one candidate or the other is ahead by more than the algebraic sum of these anticipated swings, a prediction now is much less reliable than today's latest simulation, poll of polls, or online market might suggest. Combining the uncertainty of these various swings increases the overall uncertainty. In probability-speak, variances add. As we near the election, the opportunity for sudden swings in sentiment declines, and polls, simulations and markets become much more predictive of the actual result.
Finally, much has been written about the crucial importance of, and extreme interest in, the 2008 election. This is a welcome bit of news. It can, however, also be seen as an indication of how far from constitutional government we've come. If Congress had asserted itself more forcefully in recent years and occupied its rightful place as a co-equal branch of government, it would matter less which presidential candidate wins since he would not have quasi-imperial powers. Nevertheless, the races for the House and the Senate are also extremely important this year.