Condor Options

You can make a Dutch Book against the Presidential prediction contracts at Intrade.com:

Step 1: Sell an identical number of contracts of each of the three active Presidential contracts – Obama, Clinton, and McCain.  Hit the bid.

Step 2: Wait until the election is over.  You’ll pay out the maximum loss on the contract that won, and keep the premium on the other two.  You’re guaranteed a net profit, while a buyer of all three is guaranteed a net loss.

Let’s say that McCain wins.  As the graphic above shows, assuming a 300-lot allocation, you’d pay out $1944.  But if the Obama and Clinton contracts expire worthless, you’ll make $2007, for a net gain of $63. Let’s say that Obama wins.  You’ll pay out $1071, but make $1134.  Same deal with Clinton.  Actually, you could add on some other peripheral contracts – the other names trading with a bid above 0.1 are Romney, Gore, Biden, and Other.

Why is this possible?  Because if a set of events are mutually exclusive, then their probabilities must be additive.  But Intrade has these contracts priced at 64.3% (Obama), 35.1% (McCain), 2.6% (Clinton), and that totals 102% (103.8% including the other guys).

So why not plunk down a huge bankroll and exploit this arb?  As it turns out, transaction costs are high enough to eat up any real edge, so we wouldn’t suggest doing this with actual money.  Specifically, the fee on the ITM expiring contract will more than eat up your gains.  Plus, we don’t know what the legal situation is, as Intrade is based in Ireland.

But the trade isn’t the point, actually.  The reason that everybody has heard of Intrade is that they get a fair amount of attention from media outlets (we’re guilty, too, sort of) who want a quick quote about somebody’s electoral odds.  But any epistemologist will tell you that if you hold a set of beliefs, and a Dutch book can be made against your wagers on those beliefs, then the set of wagers isn’t coherent.  Frank Ramsey explained the impact of this incoherence: someone who is susceptible to a Dutch Book is willing to price identical wagers differently, depending on how those wagers are described.  In other words, they’re in a fundamentally irrational position.

Does that mean the Intrade percentages are wildly wrong?  Maybe not.  But excluding other sources of information, we’d have no way to know: it’s kind of hard to evaluate a universe that doesn’t conform to the basic axioms of probability.  In any case, http://www.fivethirtyeight.com/ does a better job on the elections.