The mode of 342

It's striking how likely 342 electoral votes is for Obama in the Election Day histogram. The reason that this particular number comes up a lot is that it's relatively easy for Obama to win the Kerry states plus {NV, NM, CO, AR, MO, IA, OH, FL} with just a modest nationwide shift (about half a percent) from where he stands today. However, after those seven states it takes a good deal more movement for him to pick up anything else. AZ would probably be a swing state if it weren't McCain's home state. People have talked about VA being a possible pickup (and the one small poll conducted recently in VA does show Obama up), but my best estimate is still that Obama is about two points lower in VA than in FL, his next-worst state. Of course, if more polls come out showing Obama doing well in VA, then I bet the mode will climb to 355.
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Obama by 3%

Popular vote estimate:

(Darker red means more votes for McCain, darker green for Obama.)

Prediction if the election were today

• Probability of electoral victory: over 99%.
• Expected value of electoral votes: 319.
• 95% range of electoral votes: 289 to 347.
• Probability of electoral college tie: .1%.
• Probability of popular victory: over 99%.
• Expected popular vote: Win by 3%.
• Swing states:
  • PA 46%.
  • OH 34%.
• Electoral vote distribution (electoral votes vs. probability):
• Confidence map (states sized by electoral vote, darker red means higher confidence that McCain will win, darker green for Obama):

Prediction for Election Day

• Probability of electoral victory: 79%.
• Expected value of electoral votes: 309.
• 95% range of electoral votes: 189 to 405.
• Probability of electoral college tie: .6%.
• Probability of popular victory: 76%.
• Expected popular vote: Win by 3%.
• Swing states:
  • OH 84%.
  • PA 84%.
  • MO 71%.
  • NH 65%.
  • NJ 61%.
• Electoral vote distribution (electoral votes vs. probability):
• Confidence map (states sized by electoral vote, darker red means higher confidence that McCain will win, darker green for Obama):

One extra thing: The Electoral College advantage

It's well known that in 2000, George Bush had an advantage from the Electoral College, winning a majority of electoral votes while failing to win a plurality of popular votes. By contrast, in 2004, John Kerry had an advantage from the Electoral College: With slightly more popular votes across the country, he would have won Ohio (and therefore the Electoral College) while losing the popular vote.

This year's election looks more like 2004. In my simulations, the two candidates have an equal chance of winning when McCain wins the popular vote by about 0.5%. The following chart shows election-day popular vote along the x-axis and probability of Obama victory on the y-axis.

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"Race to 270" is back!

I dug up my old code a couple weeks ago, and, after a thorough re-write, I'm back to making predictions. Lessons learned:

1. Always comment your code. No matter how obvious something seems when you write it, it's not going to make any sense three to four years later. Once I do comment my current code, I'll post it somewhere.
2. I was handling the exceptional cases of Maine and Nebraska in a really dumb way back in 2004 (I honestly can't quite figure out what I was doing, but it looks really dumb), and now I'm handling those cases in a way that fits much better into the theoretic framework I'm using. As a side-effect of understanding this better, I also know how to incorporate data from nation-wide polls into this analysis.
3. My handmade cartograms are a little hokey and too time-consuming. I'd like to use slick Mapresso-made images (like in a recent post of mine to MyLeftNutmeg), but I'm having a surprising amount of trouble finding a shapefile of the 50 US states (let me know if you have one). Once I have this working, it'll be a lot easier for me to make maps quickly.
4. Nobody has this 2008 election in the bag. It might turn out to be a nailbiter, or it might not; but anybody who says they know what'll happen is full of it.
5. The technique I use right now deals well with two sources of error: sample error (i.e., the fact that each poll only surveys a small number of people), and the fact that popular opinion changes over time, so that an old poll has less information now than when it was taken. There's another source of error that I'm not catching yet: Some percentage of people in each poll are undecided, and it's unclear how they would actually swing. I have some ideas about how to handle this, but so far I keep calculating into variance matrices that fail to be positive definite. Ouch--I clearly need to think about this issue more.
6. Another problem I'm having is best described by this simplified situation: A nation is divided into two parts, X and Y. Two polls come out with low alleged margin s-of-error. A poll in part X shows a 5% decline for the Democratic candidate, a national poll shows a 1% decline for the Democratic candidate, and there is no poll in part B. The algorithm will then infer that the Democratic candidate has gained somewhat in part Y. This is the right thing if the pollsters' margins-of-error are accurate and the input correlations between states are correct. However, some weird results (for example, Obama doing worse in Florida than in Georgia) are coming up with my current assumptions, so I think I'm going to have to increase my assumed correlations between states.

So far I've only had time to input data for one candidate pair. I've chosen Obama vs. McCain since they're leading their respective races both in delegates and on the major betting websites. All the probabilities here should be considered conditional on those two candidates winning their nominations.

Another note: Since Democrats now control a majority of state delegations in the House, I now consider a 269-269 tie to be a Democratic victory. There is less than a 1% chance of this happening.

Stats and Maps

If the election were today...

• Probability of victory: 52% +- 1%.
• Expected number of electoral votes: 269 +- 3.
• Expected popular vote: 49% +- 1%.
• Break-even popular vote: Unknown, but probably around 48%. (This means the popular vote margin at which both candidates have an equal chance of victory. I haven't written the small amount of code necessary to measure this, but it should be easy to do.)
• Swing states (measured by correlation between the winner in the state and the winner nationally):
  • OH 67%
  • PA 65%
  • MO 48%
  • FL 41%
  • NJ 38%
  • WI 35%
  • AR 30%
  • ME-2 26%
  • NV 24%
• Electoral vote distribution (electoral votes vs. probability):
  
• Confidence map (states sized by electoral vote, darker red means higher confidence that McCain will win, darker green for Obama):
  
• Expected vote map (darker red means more votes for McCain, darker green for Obama):
  

Map Key

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