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Predicting the presidency: Divorced women, regression modeling, or coin tossing? A mathematician’s take
Rebecca Goldin Ph.D, October 9, 2008
We now have dozens of political scientists telling us that their formulas will predict the winner. But they all face one rather big problem.

The prediction market is filled with political scientists, economists, investment bankers, professors, and... my neighbors. Everyone I know is either living in a state of anxiety about what will happen with the election, or touting a theory that explains why he or she knows what will happen.

To get a sense of how valuable this game is, take a look at Intrade, an online trading company by which people can bet on who will win. At this moment, the last sale of 2008.PRES.OBAMA was 74.7 while 2008.PRES.McCAIN sold at 25.7. In other words, if you listen to the market of those who think it’ll go one way or the other, approximately three quarters of people are thinking that Obama will be the 44th president of the United States.

Then there are those who are trying to isolate the demographic which will, by itself, determine the presidency. The Miami Herald found a “generation expert” who says that divorced women could pick the next president. Alternately, blacks, women in general, Hispanics, young people, and even cell phone users have been claimed could determine the election. Though of course, such categorizations lead one to wonder, how could anyone win an election without significant support from all major groups (though McCain gets hardly any support among black voters and Obama gets hardly any among the Christian right). Why should success be attributed to one demographic and not all the demographics that voted in favor of that candidate?

A quick foray into the blogosphere finds predictions abound. Even psychics are weighing in on the matter. But most of the time, the predictions are made by “serious” people who have thought about an assortment of issues, and are making their thoughtful conclusions public to their readers. Most of the time, they have no particular science to their predictive arts, though they could be based on performance at the most recent debate, or a Gallup Poll (which currently shows Obama in the lead).

Last week, Jeremy Mayer, a George Mason University professor in the School of Public Policy gave a public lecture on the “endgame” of the presidential election. He pointed to several number-crunching models (typically obtained through regression analysis) involving information such as the unemployment rate, median income level, whether the previous party has been in power for eight years or more, and other measurable data.

Some of these formulas have been able to predict the presidency with accuracy – well, except for maybe a few elections. Mayer himself seemed to have designed his own formula (involving opinions about important issues such as stem-cell research and abortion, plus the “strength of feeling” about abortion) to give probabilities that particular individuals will vote for McCain or Obama.

Alan Abramowitz of Emory University is one of the heroes in this field, having designed a simple model that has a high percentage of success. His 1988 article is called “An Improved Model for Predicting Presidential Election Outcomes” and it shows remarkable accuracy in predicting previous presidencies, back to 1948. What was impressive was not just the “who won” question, but how close the percentage predictions were to final votes, typically within 1 percent. By running this formula for today, Mayer (and dailykos.com) pointed to an Obama win.

But this model is just what he says: an improvement on previous (and less accurate) formulas for predicting the presidency. Such equation-editing has continued, and we now have dozens of political scientists telling us that their formulas will tell us who will win. The number of possible correlates to a presidential win of one party or the other is staggering. As history marches on, these equations are tweaked and tweaked until they have a complicated series of coefficients and inputs that will be a best match for (previous) presidential outcomes. We can only assume that they will give us an accurate picture of what the future holds – right?

Well... here’s a math perspective on the issue. Suppose I have a coin -- and it’s magic. I only flip it every four years. If it comes out heads, that means a Republican will be elected, and if it comes out Tails, a Democrat will be elected. You probably wouldn’t believe me; a coin will only give a “random” answer to the question of who will be president. But if this coin – under my artful flipping technique – has correctly predicted the presidency in all but two elections for the past 68 years, you might be impressed! Not including the 2008 election, that’s 17 presidencies, and the coin got 15 right. A quick calculation finds that the likelihood of the coin doing this by chance alone is just over 0.1 percent; in other words, it almost couldn’t have been by chance. It certainly sounds like my coin is rather impressive, and could well have something to say about Obama and McCain.

But now suppose that I chose my coin by going into a room of 100 people flipping coins – each person flips his or her coin 17 times, one for each presidency in the past 68 years, and writes down whether the flip corresponded to the outcome or not. I then choose the most accurate coin. It turns out that there is about an 11 percent chance that one of the coins will get 15 or more elections correct. And if the room had 1000 people, each with a coin, there would be an almost 70 percent chance that someone would have ended up with a magic presidency-predicting coin. Now the existence of a magic coin no longer seems a feat of magic.

Let’s go back to the regression models. Given that the models can be altered by changing a digit in a coefficient in the equation, and that they are designed to model the past correctly, it’s not much of a surprise that they do a good job on modeling the past. And if they are as good as a coin toss, I might still see accurate behavior in the past by the way I selected the model (i.e. I choose the model that has the most previous accuracy). This doesn’t exactly give me confidence in modern political science.

It’s not that regression analysis can’t contribute to accurate predictions and models about the future. It’s that there just aren’t that many presidential elections to predict. When it comes to chance, accuracy has to be established over large numbers.

Instead of regression modeling, you might be better off turning to school children. The Scholastic Election poll has correctly predicted the general election since 1940, with the exception of 1948 and 1960, and even picked Bush over Gore in 2000, as did the Supreme Court but contrary to the popular vote. Their final vote will be tallied on October 10.

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