(With four days left before Election Day, I foresee see five possible scenarios. Each day leading up to Election Day, we’re going to explore one of the scenarios. This post is the second installment of the series.)
I am going to offer a couterintuitive: this scenario is based on the average of the polls, and yet I regard it as the least likely result.
Let me begin with a short stroll down Geekery Lane. The central limit theorem holds that, even for a non-normal distribution, repeated measurements of the population will cluster normally about the mean. That’s nerd-speak for the idea that an average of averages will on average give you a pretty good guess of the result. The central limit theorem is the entire basis of the Real Clear Politics average which, in the recent past, has given us a pretty good estimate of how most elections turn out.
Jay Cost has done a great job laying out the case that thes year’s poll results are bimodally-distributed. There aren’t enough observations to test the hypothesis of non-normality with any degree of certainty, but the shape of the curve is sufficiently “odd” that it makes one think that the RCP Average is giving us screwy results.
I should probably also describe what a bimodal distribution is. I’ll start first by describing what it is not: it is not normal–in both the statistical and usual sense of the word. Most measurements are normal; there is an average about which the results cluster and a decreasing number of observations away from the center. A bimodal distribution is different; it has two peaks. An example of a bimodal distribution is the starting salaries out of law school. In 2008 the “average” was about $72 thousand a year, but there are two peaks: one at about $45k and another $160k (see below). In the case of a bimodal distribution of salaries, the average is worse than meaningless; it is misleading. If a law grad was not in the sub-population of law students who goes to be an associate at a big name, large city law firm, where starting salaries (until recently) were about $160k, the grad was likely to earn well under the average result.
As is sometimes the case with bimodal distributions, it is as a result of there being two very different populations in the overall group (big firm lawyers vs. other lawyers). In the 2012 election, we apparently have two different sampling methodologies giving us this odd result. One methodology assumes a 2008-like electorate; the other assumes an historical average. While it is possible that the truth is somewhere in the middle, I suspect that it is not. And lest you think that this is a dig at Real Clear Politics, here is how Sean Trende, RCP’s lead statistician characterizes his own results:
“We have enough national pollsters consistently saying one thing, and enough state pollsters saying another, that I’m fairly sure the “right” answer won’t be in the middle. It really is a “two men enter, one man leaves” situation.”
All that being said, what does the scenario look like? In one word: Ohio.
This is the nailbiter that isn’t over in one night. Think 2000. Mitt Romney wins the popular vote by almost one-percent. Most states break along partisan lines. Slightly Republican Florida, North Carolina, and Virginia go with Romney. His one-point national number is enough to push him just barely over the edge in Colorado, Iowa, and New Hampshire, but he falls short in Paul Ryan’s native Wisconsin by just a few thousand votes. Ohio is razor-thin close. With a shifting number of tens of thousands of uncounted absentee and provisional ballots hanging out there, the Buckeye result isn’t known for days. There are enough reported shenanigans in Mahoning and Cuyahoga counties that hundreds of lawyers (the expensive big firm kind) have employment for months. In the end, Barack Obama wins Ohio by a fraction of a percent, giving him an electoral lead with 271 to 267, as he loses the popular vote 49.9% to 49.0%.
In down-ticket races the results are divided as well. Republicans pick up senate seats in Missouri, Montana, Nebraska, and North Dakota, while losing two in the Northeast for a net gain of a couple, but not enough to give them control of the chamber. In the House, Republicans lose a net of just a few districts, allowing them to retain control with about 235 seats.
Going forward with the slimmest of victories and deprived of the oxygen of a campaign, the re-elected Obama can’t escape the nation’s economic difficulties and he begins a steady decline into a long four-year period of lame-duckdom. This scenario is the least likely (I hope) and gives our nation the least desirable result.
See all the scenarios:
Scenario 1: Nate Silver is right
Scenario 2: RCP is right
Scenario 3: Rasmussen is right
Scenario 4: Gallup tracking poll is right
Scenario 5: Gallup electorate poll is right
And the prediction is . . .