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The Numeric Estimate Prediction Market

The prediction markets illustrated so far are designed to predict probabilities, but sometimes it is useful to aggregate individual predictions of numbers that are not probabilities, for example, how many games the New York Mets will win this year or how many people in Love Canal will die of cancer over the next ten years. A very simple solution is to divide the plausible range of numbers into intervals and to calculate the probability of each one. The intervals can but need not overlap. For example, TradeSports featured a set of contracts used to predict how many votes Judge Samuel Alito would receive on the floor of the Senate to confirm him as a justice of the U.S. Supreme Court. The six contracts specified that they would pay off if Alito received more than forty votes, more than fifty votes, more than sixty votes, more than seventy votes, more than eighty votes, and more than ninety votes. An alternative approach would have included contracts corresponding to the cases in which Alito received forty votes or fewer, from forty-one to fifty votes, from fifty-one to sixty votes, and so on.

These approaches are somewhat clunky, for they do not allow for an easy calculation of the average expected result. For example, on January 10, 2006, just after Alito’s confirmation hearings began, the bid-ask midpoint for the “more than sixty” contract was 60.8, and for the “more than seventy” contract the midpoint was 15.2. That suggests that the market estimated a 45.6 percent chance that Alito would receive between sixty and seventy votes but provides little information about what the best estimate actually would be. A partial solution would be to offer additional contracts–more than sixty-two votes, more than sixty-four, and so on–but this, too, becomes cumbersome, in part because there might be few people interested in trading on each of these contracts. The interval approach does have its uses–it is the most straightforward way of determining, for example, the probability that more than senators will vote to confirm–but it is less useful when one is seeking a point estimate of the number of votes that Alito is likely to receive.

There is, however, a simple alternative. The prediction markets we have seen so far are binary–for example, paying off ten dollars per contract if the event occurs or not paying at all. But payouts can range depending on a number that is verifiable ex post. For example, TradeSports might have used this approach with Alito, promising to pay nothing if Alito received no votes, ten cents if Alito received one vote, and so on. Of course, it is particularly convenient that the Senate happens to have one hundred members at this time, making each vote worth a dime. It will similarly be simple to design a prediction market that predicts a percentage. For example, in addition to sponsoring “winner-take-all” markets, the Iowa Electronic Markets sponsors vote share markets. Figure 1.7 shows the vote share market for the 2004 U.S. presidential election. Each penny in closing price corresponds to an anticipated 1 percent of the vote. Aside from a temporary spike in Kerry shares (to which I return below), the anticipated outcome was remarkably stable, providing the appearance of an almost boring election cycle. Of course, the election was not boring, because the anticipated Bush and Kerry shares happened to be quite close at some points in the election cycle. The graph, however, emphasizes that the real fight was about a relatively small number of swing votes.

A numeric estimate prediction market can also be used also to predict numbers that will fall on a closed interval between numbers other than zero and one hundred. One possibility, if the interval is a subset of that range, is simply to use the same approach as the vote share market. For example, TradeSports includes shares that predict the number of games each team in the National Basketball Association will win in a particular year’s regular season. The maximum possible is eighty-two according to the current NBA schedule, but this simply means that no one will rationally purchase a chance of a $10 payout for a price above $8.20. Another possibility is to map the range linearly from zero to one hundred. So, for example, TradeSports might have provided that a tradable contract would pay off 1000/82 cents per win.

More generally, a prediction market can be used to predict any number that will become apparent at some later time. A prediction market could be used for a number that might turn out to be positive or negative. Either the interval can be translated to a more familiar one, such as zero to one hundred, or trading at negative prices could be allowed. If I purchased a tradable contract at minus five cents I would receive five cents from the seller. A prediction market also might be used to predict a number on an unbounded interval, say, from zero to infinity. The only problem is that if very high numbers become plausible, then the prediction market sponsor might be unable to pay off the contract, and individual traders might not be able to afford to engage in transactions. Thus, as a general matter, the trick is to translate a plausible range of numbers into a manageable contract size. The rules can always provide that if the actual number exceeds the maximum, then the payoff will be the maximum. For example, a prediction market might be used to predict how many points an NBA team will score in a season, with every hundred points paying off one cent. The rules could stipulate that ten thousand points or more will pay off one dollar. If this outcome is particularly unlikely, it should have little effect on the pricing.

January 24th, 2008 Market Designs Comments ( 4 )

 

4 Responses to “The Numeric Estimate Prediction Market”

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