A lot of bloggers (e.g. the indefatigable Stephen Green) have been posting electoral maps and trying to anticipate who is going to win based on the latest and greatest polling data. But Green, who had posted many such maps over the past few months, finally threw in the towel on Tuesday, declaring:
Say it with me now: It’s all a bunch of crap.
The polls all suck, for reasons gone into by people way smarter than I am. The predictions all suck, because everybody is working from the same assumptions, based on voting patterns from the last election.
… And yet everyone – myself included – still bases all their predictions on a tight race? I don’t know how this thing is going to pan out. Neither do you. But right now, I feel as though the electorate is going to play all of us pundits – amateur and professional – for fools.
And I think he’s 100% right about that … coloring states red or blue based on poll results is of limited use when there are so many conceivable outcomes, when we have such a hard time extricating sampling biases from polls, etc. Here is one possible way out of the dead end – instead of thinking deterministically and trying to project a winner in each state, let’s look at everything probabilistically, and run a Monte Carlo scenario to see each man’s chance of winning.
For this exercise, I assumed:
- that each candidate’s probability of carrying a state was equal to the current selling price on TradeSports.com. For example, if the price of “Bush carries Iowa” is quoted at 58, then Bush has a 58% chance of carrying Iowa in any given trial.
- No third-party candidates had any chance of carrying a state.
- Colorado and Maine are treated as all-or-none propositions.
- no “faithless electors” shun their commitment to vote for their candidate.
- all 51 events (50 states + DC) are independent.
I ran 10,000 trials, and this is what I got, based on today’s TradeSports prices:
Bush averaged 279.99 electoral votes to Kerry’s 258.01. The standard deviation of the vote was 30.78 electoral votes.
Bush got a majority of the electoral vote in 6283 trials; Kerry got a majority of the electoral vote in 3583 trials, and 134 times the race finished in (gulp) a dead heat, 269 electoral votes to 269.
In 10,000 trials, the most electoral votes Bush got in any one trial was 419; the most Kerry got was 357.
This approach is not perfect either, because it is not true that all 51 events are independent. If Bush’s 6% chance of carrying California comes through, he is probably going to win everywhere else in the country too. It would be possible to build some positive correlation into the model, but I have no idea what the correlation coefficients might be, and just saying that they round down to zero probably isn’t unreasonable.
What I find really interesting is that right now there appears to be greater than a 1% chance that this thing will finish in a tie. (In that case, the House of Representatives breaks the tie, of course, and would presumably re-elect George W. Bush, since the House has a Republican majority. My understanding is that the House vote would take place BEFORE the new Congress was sworn in, so that lame duck Reps who had already lost or retired could cast a vote to determine the presidency.)
If anyone finds this line of thought remotely compelling, I will update this (with current prices from TradeSports) a few times between today and election day.
UPDATE: An astute reader points out that the new Congress would cast the vote in the 269-269 tie scenario … the new (109th) Congress will be sworn in on 1/4/2005, and we need a new President by 1/20/2005, so there’s a two week window of opportunity there. A few of you also noted (correctly) that the House vote goes by state — the California delegation gets one vote, the Wyoming delegation gets one vote, etc. Right now, there are 31 states that have more GOP Congressmen than Democratic Congressmen … and everything is so gerrymandered now, I just cannot see that number changing much no matter what happens on election day. Of course, GOP Congressmen would be under no obligation to vote for Bush.
There has been one instance in US history where no candidate received a majority of the electoral vote and the House had to pick the next president — the election of 1824. But we have come close a few other times — in 1968, for example, if Wallace had carried one or two more southern states, Nixon might well have been unable to get the needed 270 electoral votes. Since the House had a huge Democratic majority at that time, they would have elected Humphrey even though Nixon had more popular and electoral votes.
A few of you asked a question that I had thought of myself — the individual state prices on TradeSports suggest that Bush has a 62%+ chance of winning, but you can buy a “Bush is elected” contract for about 60 or 61. So is there an arbitrage opportunity? In an ideal world, you could buy a Kerry contract for all 51 states and buy 51 Bush Wins Overall contracts, and you could expect to make money, net-net, off that, except of course that transaction costs would certainly render that unprofitable.