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Election Monte Carlo

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.

22 comments to Election Monte Carlo

  • Excellent scenario. One quibble: Nebraska can split its electoral votes, though the likelihood is near zero.

  • Foobarista

    One thing: there has been suspicions that a certain palindromic billionaire has been gaming Tradesports to try to influence those who look to it for clues about what the “pros” are doing. In particular, some suspicious trades (ie, a massive sell at 10% probability of a Bush win, some wierd trades just after the debates, etc) have the handiwork of someone used to gaming currency and other markets.

  • drscroogemcduck

    I wonder if it’s possible to exploit a difference of odds between the Bush contract and the contracts for the states. Your Monte Carlo simulation has the odds at around ~0.63 and the current price is around ~0.60. It may of been easier when funny things were happening to the Bush contract assuming it wasn’t also happening to the State contracts.

  • Robert

    Concerning the House and ties.

    Yes, the Republicans have a majority in the House but they don’t cast individual ballots. Rather, they vote collectively on a State by State basis.

    http://www.law.cornell.edu/constitution/constitution.amendmentxii.html

    I’ve also been under the assumption that the new COngress gets to make the choice, but I could be wrong.

  • Jacob

    “The polls all suck, for reasons gone into by people way smarter than I am. The predictions all suck” ….

    If you are still interested in posting your predictions, go ahead …. It won’t hurt anyone.

    It’s like all prominent economists who, at each year-end, post their predictions of economic indicators for the next year. A review of past predictions shows they never get anything right. Still they repeat the ritual every year. Seems that predicting the future gives one an aura of wisdom, regardless of results.

  • Christopher: That is a good piece of analysis. Please do repeat it a few times before election day.

    Robert:

    >Rather, they vote collectively on a State by State basis.

    Can someone tell me how they do this. Does the congretional delegation of a state get together, take a vote, and then vote as the majority of the delegation dictates? Or something else? And what happens if the delegations consists of an equal number of democrats and republicans?

  • Does anybody have any idea how many bets are placed on spread betting sites for events such as the Presidential Election? Is it tens, or hundreds or many thousands? It would be interesting to know. If the numbers are large then I imagine that the predictions are far more likely to be right than any poll or pundit.

  • there has been suspicions that a certain palindromic billionaire has been gaming Tradesports to try to influence those who look to it for clues about what the “pros” are doing. In particular, some suspicious trades (ie, a massive sell at 10% probability of a Bush win, some wierd trades just after the debates, etc) have the handiwork of someone used to gaming currency and other markets.

    Donald Luskin doesn’t know what he’s talking about, on this or any other issue for that matter. If any market were vulnerable to manipulation, it would be the much shallower IEM, not TradeSports. It’s virtually mathematically impossible for market manipulation of the sort Luskin is baselessly spreading paranoia about to be carried out successfully; for more on this, see here.

    I find it strange that a libertarian should have so little faith in the resilience of the market.

  • I heard that Tradesports is certainly turning over £10m+ on the Presidential race alone. UK bookies reckon they will take £5m in bets from the UK.

    I punt these things regularly and I’m pissed off that I missed out on whomever it was selling Bush down to 10% probability. The market retraced pretty quickly, before I could buy it till it bleeds… so people probably checked Bush wasn’t assassinated / choked on a pretzel and jumped back in.

    Whomever is doing it is not behaving rationally unless he ‘knows’ Kerry is going to win. If the person was doing it for profit he would not have made a speculative attack but would have sold Bush down slowly rather than trying to overwhelm the Bush backers. Frankly if some Kerry backing plutocrat wants to give crazy odds I’m willing to take ‘em.

    See politicalbetting.com for good commentary.

  • David Hecht

    >>Rather, they vote collectively on a State by State basis.

    >Can someone tell me how they do this. Does the
    >congretional delegation of a state get together, take
    >a vote, and then vote as the majority of the
    >delegation dictates? Or something else? And what
    >happens if the delegations consists of an equal
    >number of democrats and republicans?

    It’s been a long time since it happened, but basically the procedure will be that each state delegation is polled, and the majority will determine for whom their state’s vote is cast.

    In the case of evenly divided delegations, their vote is not counted. However, since representatives are not bound by party in their votes, this doesn’t necessarily signify: I remember, for instance, Connie Morella, a GOP congresswoman from Maryland, saying she’d follow her district (meaning Gore) in voting…which would have made Maryland 5-3 in favor of Gore and given him an extra delegation.

    I haven’t looked at the current makeup of the House, but after the last Presidential election, there were 28 states whose delegations were controlled by the Republicans, 18 by the Democrats, and four divided. I’d be very surprised if there had been a lot of swing since then.

  • Sorry, wake me up when the average margin of victory for either candidate falls outside one standard deviation. Not to denigrate your work here, but your analysis isn’t really any more sound than the polls or election markets. I’ve been monitoring both and have thrown in the towel along with Steven — this one could go either way. (I personally think it will go for Bush, but I don’t justify that on anything more firm than my own intuition.)

  • flaime

    There is a Professor Sam Wang of Princeton who is doing a statistical analysis of all polls to develop an idea of how the election might turn out that is interesting. But it’s still basedon polls. Search for ‘Meta-Analysis of State Polls’ on google.

  • “be greater than a 1% chance that this thing will finish in a tie”

    Why is that surprising? What 1% means is that the US could expect to have a tie on average every 400 years.

  • If the Presidential election gets thrown into the house because of an electoral tie, or for any other reason, the decision will be made by the new house.

    The Presidential election process is defined by Article II. Section 1 of the US Constitution and Us Code Title 3 Chapter 1. The Congressional election process is defined by Article I Sections 2-5 of the US Constitution and US Code Title 2 Chapter 1. This might all make useful reading given the way the election may go this year.

    The new house is seated on January 3rd and the process of counting electoral votes starts on January 6th. Therefore it is the new house that does it. In particular from 2USC7 “The Tuesday next after the 1st Monday in November, in every even numbered year, is established as the day for the election, in each of
    the States and Territories of the United States, of Representatives and Delegates to the Congress commencing on the 3d day of January next thereafter.” And from 3USC15 “Congress shall be in session on the sixth day of January succeeding every meeting of the electors…”.

  • Shawn

    It seems to me that the big unknown in this election is going to be the size of the turnout. I suspect (no real evidence as such) that the turnout will be high, perhaps historically so.

    Traditionally a large turnout favoured the Democrats. But whether this remains true this time is hard to say, in part because the Republicans are, for the first time, mounting a serious ground war in the last days of the election, and in part because a large turnout of the hard left to get rid of Bush may be nullified to some degree by a larger than usual turnout of the Christian Right in his favour.

    There are just to many unknowns, what ifs, and unique historical circumstances in this election to make a prediction.

  • Interesting stuff Chris. Please post more.

    I do agree that there are some weird things happening with the numbers there sometimes but it’s probably no worst than regular polling data the experts use.

  • does numbers for a living

    Ummm …. actually, the scores at Tradesport (even if not manipulated) don’t equate to probabilities of winning. So your simulation, while fun, really doesn’t show what you suggest it shows.

  • Yes, Does Numbers, of course the scores at TradeSports don’t represent a probability that a candidate will win — they represent what the market, right now, is willing to pay for a contract that pays a fixed amount if a certain event takes place, and it’s a leap of faith to assume that the current price is a reasonable estimate of probability.

    If I was selling a contract that paid $100 if an honest die came up “six,” it would be rational to pay any amount up to $16.666… for that contract. If traded in a competitive market, the price of the contract would come very close to representing the probability of a die coming up six (the price might be a bit lower because of risk premium, or time value of money if the roll of the die was a ways off, etc.) But it should be close.

    That’s a totally different scenario than a political race, because of course nobody has any idea what is going to happen, or what probabilities to assign to the possible events. People are just making guesses as to what a reasonable price would be to pay for an uncertain payout. But the dominant factor in what you would be willing to pay for a TradeSports contract is your best estimate of the probability that the underlying event will occur. Other things could influence the price, and of course it’s a leap of faith to assume that those other factors round down to zero.

    In the currency markets, if one currency sells at a forward discount (i.e. the futures price is lower than the spot price) this could be assumed to mean that the market thinks the currency in question will inflate more than the currency in which the contract was denominated. It doesn’t mean that anyone KNOWS there will be more inflation in one currency than in another, but rather that the market is factoring “inflationary expectations” into the market prices of currency contracts. You could think of the price in a TradeSports contract as representing a “probabilistic expectation.”

  • Larry Hughes

    The state-by-state vote in the House also occurred in 1800, not just 1824. In 1800 Hamilton threw New York state to Jefferson because while he disagreed with his policies, he preferred Jefferson’s character to that of Aaron Burr, who, as runner-up, became Vice-President. It wasn’t too many years before everyone agreed Hamilton had made the right choice.

    Last time, in 2000, it was felt by the Supreme Court and many others that our enormous government could not wait until January to make its Presidential decision, owing to the enormous complications of “transition” periods from one regime to the next. New appointees must be given security checks, and many other details take time. Yet, I think they would follow the 19th century procedures if the electoral votes should result in a tie again, provided the courts had cleared up the inevitable lawsuits–on an expedited basis–and the electoral vote was still even. (Don’t expect ithis to happen, however. Bush seems to be pulling ahead enough to avoid all argument).

  • Actually, Larry, that isn’t right … it’s true that the election of 1800 ended in a tie, but at the time there was no provision for the House of Representatives to break the tie. The electors just had to keep casting ballot after ballot until somebody finally prevailed; as a result of that election, we got the 12th Amendment, which provided for the House to break ties if nobody got a majority of the electoral vote. So 1824 is the only time the House elected a president.

    I agree with you on the last point, though — it’s hard to imagine a smooth transition taking place if the House picks a new president just a week or two before he’s supposed to be sworn in.

  • David Gillies

    Can you post the code? I’d like to play with this but I don’t want to duplicate effort.