Introduction to the Chances of Presidential Victory

Almost two weeks ago, Barack Obama led the 2012 general election for President of the United states with a virtually unassailable advantage in the most important swing states:

1. Pennsylvania
2. Ohio
3. Wisconsin
4. Colorado
5. Virginia
6. Florida
7. North Carolina

On October 3rd, Obama met his Republican challenger, Mitt Romney for the first of three Presidential debates. While one's judgement of the winner of these debates is greatly influenced by personal perspective, Mitt Romney was declared the victor by the media. In the subsequent 10 days, we have seen Mitt Romney surge from roughly 44.5% support among likely voters to close to 48%. At the same time, Obama's support has fallen from over 48% to nearly 46%. A difference of about 1.5% separates the candidates today (Saturday 10/13/2012).

More importantly, Romney now leads in Colorado, Virginia, Florida, and North Carolina. With leads in these states, Mitt Romney's easiest path to victory is to take all four of these swing states along with three in which Obama leads: Nevada, New Hampshire, and Iowa. To say that Obama "leads" in these latter three states means that Obama has a better chance to win these states than Mitt Romney. Here's the breakdown as of today:

• Nevada : 16% chance of Romney winning
• New Hampshire : 16% chance of Romney winning
• Iowa : 12% chance of Romney winning

(These chances come from Pollster.)

Clearly, for Mitt Romney to win the Presidency, he must overcome all these poor chances at once. To calculate Romney's chance of winning these three states we just multiply these three probabilities together to get an 0.3% chance. Here's the math:

     0.16 * 0.16 * 0.12 = 0.003072

As you may recognize, 0.3% is a very slim chance. You might be thinking: "Clearly, that's not Romney's chances for winning this election. After all, he is leading the national polls by about 1.5%."

Indeed, this thinking is correct because there are other ways for Romney to win the Presidency. He could simply win Ohio where he has a 5% chance of victory. If Mitt Romney wins all the swing states in which he has better chances and if he also wins Ohio, then Romney will win the general election. The reason is that Ohio is worth 18 votes in the Electoral College while Nevada, New Hampshire, and Iowa are worth 16 votes in aggregate.

It's obvious that there are many paths to victory for both candidates, so calculating the chance of victory for a candidate requires one to calculate the chances for all paths to his victory.

Using this approach, here are the chances for the candidates if the election were held today:

• Obama: 96.25% chance of winning
• Romney: 3.75% chance of winning

Additionally the most likely electoral vote count would be:

• Obama: 290 votes
• Romney: 248 votes