## Operations Research and the US Presidential Election

I am in Cork, Ireland, attending the Irish Conference on Artificial Intelligence and Cognitive Science (I gave a talk on sports scheduling and three themes of modern integer programming: complicated variables, large scale local search, and logical Benders constraints). Conversation here (when an American is in the group: presumably without an American conversation is about hurling or something) is on the US Presidential Election. Some of the historical anomalies are a bit confusing. Why is it only now that Barack Obama “accepts” the nomination from the Democratic Party: shouldn’t he have decided on this long, long ago? What if he didn’t accept the nomination?

The most confusing aspect of the election process is our use of the Electoral College to elect the President. Rather than directly electing the President, voters vote for electors, with each state being given a set number of electors. For most states, all of the state’s electors are given over to just one candidate. This makes interpreting the polls quite difficult. One recent poll had Obama (the now-nominee of the Democrats) and McCain (the presumptive Republican) tied at 47% support each. A natural leap was to then assume that the election is a toss-up. But it is really the distribution of support that counts. It is possible to win the election for President of the United States with .00001% of the vote. For instance, suppose only one voter shows up in 49 states, and those voters vote for Obama, and 10,000,000 Republicans vote for McCain in New York, then Obama would lose the national popular vote 10,000,000 to 49 but he would have an overwhelming majority in the electoral college. While the results would never be that extreme, it is certainly possible (and has happened) to win the national popular vote and lose the electoral vote.

Interpreting polls gets more complicated when you try to address the uncertainties in the polls. For instance, the 47% results above are only for those in the survey who had a preference. There are a huge number of “undecided” voters who do not yet have a preference. How should they be handled as we try to figure out who is ahead (I hate this idea of elections as a “horse race”, but if the media is going to see it as a race, they could at least accurately represent the real race)?

Sheldon Jacobson (University of Illinois), Steven Rigdon, and Ed Sewell (both of Southern Illinois University Edwardsville) are addressing this issue by taking the current poll data and determining the probability of winning the election for each candidate. They have a fascinating website that is being constantly updated.

It is worthwhile to read their methodology section.

The mathematical model employs Bayesian estimators that use available state poll results (at present, this is being taken from Rasmussen, Survey USA, and Quinipac, among others) to determine the probability that each candidate will win each of the states. These state-by-state probabilities are then used in a dynamic programming algorithm to determine a probability distribution for the number of Electoral College votes that each candidate will win in the 2008 presidential election.

There is a full paper by the above authors along with Christopher Rigdon.

They point out a few limitations of their approach. Of course, the results are only as good as the poll data: if the poll data is off, then their results are meaningless. Further, they are not (currently) treating Maine and Nebraska correctly: those two states divide their electors by congressional district, while every other state is all-or-nothing.

Currently, they have Barack Obama with an 89% chance of winning, which is pretty high, but down from the 96% chance they had him at on July 31.

1. Stephen Nash | August 29, 2008 at 9:32 am | Permalink

You might want to check out the web site http://www.pollster.com/, which is devoted to polls and polling, with regular posts about how various polling organizations handle “undecided” and “likely” voters and many other issues related to polls. They also give on-going estimates of how the electoral college votes are likely to come out, along with consolidated polling results (running trends based on the outcomes of numerous polls). Perhaps more than any sane person would really want to know. Stephen

2. Ken McFarlane | August 30, 2008 at 1:51 pm | Permalink

I was drawn to your site as a fellow admirer of Pratchett and O’Brien, but am intrigued by the links to the Election Polling site. I can’t offer much comment on the statistical modeling (if that is the correct term). That part of it is above my meager statistics competency, but have a few historical nuggets to contribute.

Their are several reasons for the existence of the Electoral College. When the Constitution was being written, one of the main concerns of the representatives at the Convention, who were men of property and “substance” (read “rich”), was creating a democracy that wouldn’t lead to the domination of the “mob” (read “poor”). Therefore checks were put on voting rights and direct elections. Originally, Senators were not elected by direct elections either, and the President and Vice President still are not. These posts were seen as controls on the populist demagogues likely to spring from the House of Representatives.

Another tension running through the Constitution Convention was between the highly populated and the sparsely populated states. The consequence of direct elections would be to give the interests of states like New York and Pennsylvania more influence than smaller states, such as, Rhode Island and Delaware.

The Big v. Small debate was resolved several ways,including the bicameral Legislative branch and the Electoral College, which gave equal weight in electing the President to the small states as the large.

As a side note, I wonder if the Senate’s elaborate etiquette isn’t a result of its establishment as a type of House of Lords.

Anyway, so much for the light-weight history blurble. Thanks for the link to a interesting site that I have bookmarked to keep an eye on. Also, let’s hope that Terry Pratchett’s health allows him write many more books.

3. Ken McFarlane | August 30, 2008 at 2:01 pm | Permalink

I forgot one thing. Obama accepted the nomination because it wasn’t officially his to accept until the vote of the delegates at the convention. This process predates the insane primary/caucus system we have now. The Convention used to be the place where the politics and backroom deals took place. No one went to the convention (except incumbents) as the “presumptive” nominee.

The primary system was an attempt to democratize the nominating process,which has grown battered and worn and needs a thorough overhaul.

4. Kellie | September 1, 2008 at 7:21 pm | Permalink

Great article! I think many people are confused by the electoral college. You did nice job of explaining it in simple terms. I checked out the recommended site as well and found it to be an easy-to-understand visual.

5. Sanjay Saigal | September 2, 2008 at 12:14 pm | Permalink

The most popular (numerous mentions in the MSM and the blogosphere) statistically interesting predictive electoral analysis is available at http://www.fivethirtyeight.com/. The 538 folks use poll aggregation with (fairly basic – they use normal distributions without any explanation as to why) Monte Carlo Simulation to produce detailed scenario-based predictions. The polls themselves are weighted according to their past success; I’m unclear on whether the weights are dynamic or statically determined.