# Electoral Analysis

The polls are clearly much tighter now than they were this summer, but it can be difficult to make sense out of so many polls across so many races.  So, I built a little model to synthesize all of the data.  This is what it comes up with (click image to enlarge):

There are three sections in this graphic.  On the left are probability distributions for the number of seats to be held by Democrats in each chamber of Congress.  Democrats have an even chance of maintaining the Senate, and the single most likely outcome is that they will hold 51 seats, down from 53.  Their chances in the House are much less favorable.  The single most likely outcome is that they will increase from 191 seats to 201, but they’re very unlikely to win the 218 needed for a majority.

In the center section are each of the states.  The size of each bubble corresponds to the number of electoral votes that each state controls.  They are arrayed horizontally based on how likely they are to vote for President Obama.  The vertical axis shows how likely each state is to have voted for the winner, whether that be Obama or Romney.  It’s a measure of which states could sway the election on their own, whether because they’re swing states or because they have so many electoral votes.  Taking both axes together, the more important a state is electorally, the closer to the center-top of the graph they will be.

On the right, I’ve plotted the joint probabilities of winning the Presidency, the Senate, and the House.  A Romney win is shown above, where the sum of the four bubbles total to 49%.  An Obama win is shown below, totaling 51%.  In each box, the chances of Republican and Democratic control of the two chambers of Congress are split out.

##### The Model

To be fair, little of this actually qualifies as a model.  The calculations for control of the Senate and the Presidency are almost straight representations of the Real Clear Politics polling averages for each race.  I make assumptions about the standard deviation of the polls, I draw inferences where the sum of the state polls differ from the national polls, and I assume that Angus King would caucus with the Republicans only if they would control the Senate.  In all of the particulars, this analysis is vastly inferior to Nate Silver’s, who assesses each poll individually based on its sample size, methodology, recency, and historical accuracy, among other factors.  If you’re going to place bets, use his predictions, not mine.  For comparison, he currently puts the chance of an Obama victory at 79% and of a Democratic majority in the Senate at 91.3%.

But Silver doesn’t project anything for the House, and there aren’t very many consistent polls of the individual seats.  So, I had to get a little more inventive with my model.  I looked at the historical partisan voter index of each district, favored incumbents who were running for reelection, and factored the effect of redistricting based on which parties controlled the state legislatures and governorships.  Onto this I graft the average polling for the generic congressional ballot.  The Republicans, in short, have an enormous built-in advantage in the House.

Most importantly, I couldn’t find anyone who was modelling all three sets of elections all together.  This is something that deserves more attention, because Obama’s second term will look very different if he is facing a unified Republican Congress.  A Romney Presidency paired with a Democratic Senate could look nothing like one with a Republican Senate.  So, I forced some of the random variation to be shared between the 519 different races, representing a national coattails effect.  I also forced some of the random variation to be shared among all of the races in each particular state.

##### Drawing Conclusions

So, it may not be wise to put money down on any of the individual predictions of this model, but I think that the joint probabilities are illustrative.  The type of national swing required for Romney to win would likely bring along a unified Republican Congress.  There’s almost no way the Democrats could win the House without also holding both the Senate and the Presidency.  And if Obama wins, he will likely still be dealing with Speaker Boehner.

If you’d like to make comparisons between the outcomes of my model over time, see below for the output of previous months.

## 3 thoughts on “Electoral Analysis”

• Trevor says:

That’s an awesome find, Matt. Thanks for sharing! I love his line towards the end of the post: “Don’t like the outcome resulting from the polls you input? Think those polls are “skewed”? Strap on your tinfoil hat, put in whatever numbers you like and see what happens.” Ha!

1. Trevor says:

Addendum: I thought I would clarify the biggest reasons why my calculations diverge from Nate Silver’s. There is a discrepancy between the state-level polling and the national polling. When I sum the product of each state’s current polling and average past voter turnout, it gives Obama a wider popular vote lead than is predicted by the national polls. Nate Silver doesn’t have to resolve this problem, because his model can integrate the results of all the polls in a sophisticated way. I solved the problem by proportionally adjusting all of the state polls halfway to meet the national polls. This had the effect of pushing some of the closest states (like VA and CO) into the Romney column, probably erroneously.

The second biggest reason why my calculations will prove inaccurate is, as I mentioned above, that I assumed a larger standard deviation than the individual polls’ sampling error would otherwise advise. This means that the rare long-shot events are more likely than they should be in my calculations.

Good luck at the polls today! Go Vote!