…Governor Kathleen Sebelius of Kansas. A bridge-builder to Republicans in pursuit of progressive goals - fits Obama’s message. Read here for more.

There are so many other possibilities: Biden, Hillary, Richardson, Kaine, Webb, Clark, Bayh… here are some tea leaves from Obama himself.

The meta-analysis, which is probabilistic and therefore takes into account the uncertainty of polls, gives a current median outcome of Obama 280 EV (95% CI 251 to 320 EV), McCain 258 EV, Meta-Margin 0.94%. So it appears that the more likely winner today, by a hair, is unchanged. However, a change could still happen.

[Thanks to reader Jeff for the correction above. By the way, you may mock pundits for merely averaging polls state by state, but in 2004 they weren't even doing that. Small steps...]

First let’s review what a jerseyvote is. In 2004, I said that in a close election, resources were best deployed in states where the outcome is uncertain, with win probabilities between 20% and 80%. That campaign was quite closely fought, as evidenced by a plot of median EV estimate:

Meta-analytic EV estimator for 2004 Kerry-Bush race

For most of the campaign, neither Kerry or Bush spent much time outside the 95% confidence band. The exceptions were a few weeks in August (when Kerry was definitively ahead, between the Democratic convention and the Swift Boat Veterans for Truth attacks) and September (when Bush was definitively ahead, between the Republican convention and the first debate). Therefore both candidates had a vital interest in the same battleground states, any of which could be critical to their efforts.

I pointed out that the disparity of influence by different voters could be quantified using the Meta-Analysis. I defined the “jerseyvote,” a measure of the power of an individual voter on influencing the election outcome, relative to a voter in New Jersey (me, for instance). By this measure voters in Pennsylvania, Ohio, and Florida had thousands of times as much power as I did. This suggested that activists should try to get out the vote in those states, and campaigns should advertise there - which they did.

This year, the dynamics are different. Until recently, Obama has spent the post-primary season clearly ahead of McCain:

Meta-analytic EV estimator for Obama-McCain race

For most of the last two months, Obama’s 95% confidence interval has been entirely above the magic 269 EV threshold. For this reason I had to redefine voter power since when the race is not close, individual voters don’t have much power anywhere. I redefined it as the amount of power that voters have if the race swings sufficiently to make either candidate’s win probability 50%. The results are in the right sidebar. You’ll see the expected suspects: Ohio, Virginia, New Hampshire, Nevada, and so on. These match the places where McCain is spending the most money. What this tells me is that the McCain campaign is assuming that if they win, it will be tight. Therefore they are running a “Kerry/Bush” campaign, in which the goal is to get just over the threshold. They are not expecting a blowout; they just want to win.

In this same light the Obama campaign’s spending suggests a more optimistic view. Their pattern of expenditures makes sense if they are assuming that they have many opportunities to win. In this scenario, voters in many states can potentially contribute to an electoral victory, and are worth pursuing. This pattern of behavior is seen in candidates who expect substantial victories; they will even go so far as to campaign to help downticket races, in the hopes of winning more Congressional seats to build a larger caucus on their side.

Last week the fact that my jerseyvotes calculation (as previously defined) identified non-battleground states seemed like an error. But it gave the expected results for a race that is less close - and evidently that’s what the Obama strategists are expecting, despite Obama’s recent slippage to near-parity. In summary, the Obama campaign’s spending makes sense if they believe that the recent decline in their candidate’s fortunes is transient, and the advantage they enjoyed in July will return in the fall. To put it another way, they are acting as if they have enough eggs to put into multiple baskets.

At first glance, there are two reasons you might be less interested in the Meta-Analysis this year:

1. In 2004, the suspense was greater. Although Bush was in trouble for most of the summer, the success of the August Swift Boat attacks tightened the race considerably. In 2008, many people have been expecting a less eventful campaign.
2. The Meta-Analysis has a lot of competition. In 2008, polling sites have grown in number and in sophistication. Four years ago the stars were the data accumulators: RealClearPolitics, electoral-vote.com, Race2004.net, and others. There was modeling, but it had a certain cult-ish quality. This year, the advent of the highly popular predictive site FiveThirtyEight.com has made poll geeks a mainstream phenomenon.

But think again.

The race is currently closer than I was expecting. McCain and his campaign are pursuing their best option, to attack Obama repeatedly and relentlessly. The result is clear, as you can see in the graph on the right: a decline in Obama’s electoral vote expectations. To state the obvious, your degree of certainty in the fall outcome has almost certainly decreased in the last few weeks.

This brings me to the second reason. Whichever way you care about the outcome, you are probably watching polls, both national and in key states. What you may wish for is a way to look at all current polls at once to get a general picture. I believe that this site is a good stop for you.

But first let me describe some of the better sites, and why you might want to come back here.

• For relatively raw data, Pollster.com is an excellent source for all US races, and provide us with a direct data feed. They have excellent display tools and expert commentary on the ins and outs of polls. Mark Blumenthal and Charles Franklin are, in particular, incomparable. There is also RealClearPolitics, which has been around longer and is less polished. They are right-leaning but when it comes to data they shoot straight.

• Another site worth watching is Electoral-vote.com. Its host, Andrew Tanenbaum, author of the MINIX operating system and former teacher of Linus Torvalds. You can’t get better geek credentials than that. On his site he gives the most recent nonpartisan state polls using a simple averaging algorithm. His site provides a form of today’s snapshot. He also provides past data, a useful geek resource.

• For modeling, you have many choices. The best known this year is FiveThirtyEight.com, run by fantasy baseball guy Nate Silver. His approach to polling analysis is heavy on numerical analysis and simulation with lots of trend fitting. In particular, he makes a projection into the future. The projection is done plausibly, but is very uncertain since the range of possible movement is large. Nonetheless his grasp of polling data is excellent, as is his commentary. There are many other hobbyists, just a few of which I list here: [1] [2] [3] [4] [5]

What you get here at election.princeton.edu is a pure snapshot of the freshest available state polls. Using simple statistical estimation tools, I give you the median outcome of an election held today using the populations sampled by the pollsters. The methods take into account inter-pollster and sampling variability and calculate a probability distribution of all possible outcomes. Finally, I give the Meta-Margin, an estimate of how much the margin would have to change to flip the outcome.

Simplicity is important for several reasons. It allows me to make the code open-source so that you can play around with it yourself. More importantly, the more elaborate adjustments done by hobbyists elsewhere reduce transparency - and might not increase accuracy. In my view, complexity is only warranted if it adds significantly to accuracy and is justified by both logic and data. The Meta-Analysis isn’t perfect (see my earlier post on its biggest flaw). But I think it’s the best available tool for synthesizing currently available state polls at a single glance.

My bottom-line recommendation to you for following the national race is what I do myself. First, I look at the national average margin between Obama and McCain, for which new data appear frequently. Second, I look at the median EV estimator at the top of this page, which is slower but more precise. Together, these two measures give you an excellent picture of what’s happening.

As currently implemented, the Meta-Analysis uses recent polls to generate a high-precision estimate of the outcome of an election held today. It calculates the probability distribution of EV outcomes. By Election Eve, this snapshot should be a good predictor of the final outcome.

However, August is a slow polling month - despite the fact that August 2004 was when the Swift Boat Veterans for Truth attacks began. In the last seven days, Electoral-vote.com reported only 24 new polls, meaning that fewer than half of the states were updated. Compare that with the 2004 database from later in the season, which showed 60-100 polls per week starting in mid-September and 264 polls in the week immediately before to the election. Look for the response speed of the Meta-Analysis to improve quite a bit in September.

In Ohio, a key state, the three most recent polls ended 15, 20, and 22 days ago. This implies that it will take several weeks for us to see the impact of a major political event. For example, it took about two weeks to respond fully to Hillary’s withdrawal on June 7th (see history graph).

So where are things today, really? Using the last week of available polling data from Electoral-vote.com, the median EV estimate is Obama 294, McCain 244, with a +/-1-sigma band of Obama [279,310] and a 95% confidence interval of Obama [267,325]. In this calculation, the most recent Michigan poll is 3 days old. As of today the race is fairly close.

In 2004, a very close race, I used NJ voters as the measure - the “jerseyvote.” However, jerseyvotes are worth little and fluctuate wildly. Also, 2008 is politically rather different, at least for the moment: measuring voter power makes the most sense if there is an overall swing nationwide so that local changes make a substantial difference. Remember the goal: to identify where local resource allocation (such as GOTV) will have the most effect.

Today I’m making some changes to the MATLAB and python scripts to reflect the discussion. Assuming they stick (which is chancy, I’m soloing today), they will be:

1) Voter influence is now calculated under the assumption that overall, state polls have shifted by a constant amount, one that makes the win probabilities 50-50. This change is equal and opposite to the Popular Meta-Margin, i.e. a swing of approximately 3% toward McCain. It’s equivalent to assuming that some large-scale campaign event occurs in the very near future to make things a toss-up. (This is one case in which taking non-independence among states may affect the result.)

2) Voter influence is now normalized to the day’s most powerful voters - today, Nevada. What to call the units - centinevadas?

Today I’d like to outlline the basic contrasts between this calculation and a popular resource, FiveThirtyEight.com. That site, run by Nate Silver, a sabermetrician, is a good compendium of information and commentary. However, both our goals and methods differ on several key points. The biggest difference is that this site provides a current snapshot of where polls are today, while he attempts a prediction using many assumptions, including an enormous uncertainty about what will happen between now and November. This is a fundamental difference in what we provide. His approach does have some structural problems…

The first step in estimating Electoral College outcomes is to estimate the state-by-state win probabilities. Silver’s approach is to use current polling information as well as a slew of other factors, including past reliability of individual pollsters and informed guesses about how much future change may occur. My approach is to take the last three polls only, giving a current snapshot. Therefore his site is future-oriented, while mine is focused on the here and now. To some extent this is a matter of taste (though what I provide is far more easily interpreted).

The second step is to combine these probabilities into an estimate of the likely overall outcome, measured in electoral votes (EV). Silver’s approach is to carry out thousands of simulations, then tally the simulations. That method reflects the fantasy baseball tradition, in which individual outcomes are often of great interest. However, such an approach is intrinsically imprecise because it draws a finite number of times from the distribution of possible outcomes. The Meta-Analysis on this site calculates the probability distribution of all 2.3 quadrillion possible outcomes. This can be done rapidly by calculating the polynomial probability distribution, known to students as Pascal’s Triangle.

To illustrate what a difference this makes, let’s consider some recent data. Fivethirtyeight lists win probabilities for the 50 states and the District of Columbia. That site’s tabulation of 10,000 simulated outcomes looks like this:

These simulations are drawn from the true distribution corresponding to fivethirtyeight’s figures, which looks like this:

This true distribution takes the form of a bell-shaped curve, as expected given the large number of states and Silver’s cautious future projections. In contrast, the distribution of simulations is highly irregular, probably because of inadequate sampling. The undersampling may account for an error in his top-line EV estimate, Obama 303, McCain 235. I calculate the true estimate from his probabilities as Obama 308, McCain 230. In fact, because of the smoothness of the distribution this result could be obtained without any simulation at all, simply by adding up all the states’ EV, weighted by probability. To put it bluntly, his simulations are not only imprecise but also unnecessary.

Now let’s look at today’s snapshot of polls on this site:

The distribution looks spiky because recent polls give fairly extreme single-state probabilities. For example, if the election were held today, an Obama victory in Washington state is near-certain, but in November less so because of unknown future events.

The Meta-Analysis is also precise because it uses dozens of polls from states in contention, and over 100 polls in all. Today’s Meta-Analysis gives an EV estimate of Obama 331, McCain 207, with an effective margin of error (MoE) of 35 EV. This MoE is equivalent to a little bit less than 1.0% - better than you will find at any other resource on the Web.

Such high precision is useful for tracking movement in the race from day to day. The estimator’s history shows only one major swing this year: Hillary’s withdrawal in early June, which was followed by a sharp jump in Obama’s performance against McCain. No other event provided nearly as large a change. Indeed, for the last three weeks there has been virtually no movement.

I’ll end with a caveat. Individual states are polled less frequently than the nation as a whole. Therefore the Meta-Analysis may respond more slowly to changes than national averages. But it responds far more accurately.

So - to relieve your anxiety at the vagaries of individual polls, come back again!

Averaging is an excellent way to see past variation in individual data points. A standard measure of how well you know the true average is the standard error of the mean (SEM), which can be thought of as a multiple-poll version of the famous Margin of Error. Today, the SEM of the last 6 polls is 2.3%, a fairly typical value.

But the Meta-Analysis uses dozens of polls at any given moment from states in contention, and over 100 polls in all… Look at today’s Meta-Analysis, which gives an EV estimate of Obama 329, McCain 209, an EV margin of 120 EV. The Popular Meta-Margin is 3.36%, which gives a linear conversion of 120/3.36=36 EV per percentage point. (Remarkably, linearity is not a bad assumption, as seen in past election data.) Our 95% confidence band is 70 EV wide. Typically, such a confidence band is about 4 times the SEM, making our equivalent SEM 18 EV. This converts to about 0.5% - less than one-fourth the SEM of the Pollster.com average.

An important caveat is individual states are polled less frequently than the nation as a whole. Therefore the Meta-Analysis responds more slowly to changes in opinion. But since it is so much more accurate, it’s still likely to be a better way to detect swings. I can’t prove that - not yet, anyway…

We’ll also do more than just report on polls. The reason is simple: compared with 2004, this area has blossomed (here are several great resources). We will also provide a forum for Princeton-based election analysis spanning many disciplines: computer science, politics, statistics, psychology, and neuroscience, to name a few. I’ll be inviting professors and other researchers to provide commentary. The result will be a group blog that is richer than anything I could do by myself. It’s a work in progress - stay tuned!

And now, back to the polls. In 2008, different (and perhaps more) states are in play than in 2004. I have decided to extend my calculation to all 50 states and the District of Columbia. My statistics will be based on the full probability distribution, covering 2,251,799,813,685,248 permutations - nearly 2.3 quadrillion. (Note that it’s the exact distribution, not repeated simulation as you’ll find on other sites. But that’s a topic for another day.) The results will be “clean,” reflecting polls only - no inferred outcomes from pre-2008 data, no special assumptions about undecided voters.

Our graphics aren’t quite up yet, so here are today’s unadorned results. Based on 137 polls (up to 3 per state), the current median outcome is Obama 306 EV, McCain 232 EV (95% confidence intervals Obama [275,327], McCain [211,263]. The Popular Meta-Margin is Obama +3.1%. For an explanation of what these quantities mean, see the old site.