The Theoretical Case for Prediction Markets
Risk and transactions costs might affect not only the amount that individuals will be willing to pay at auction but also their bid and ask prices in the subsequent market. But there is a strong theoretical reason to believe that prices derived from market activity will provide more reliable probability estimates than prices derived from the result of auctions. In an auction, sentimental considerations might easily bid up the marriage tradable contract, but such sentiment is unlikely to last over the long term in a market. If some market participants are merely unsophisticated sentimentalists, then more sophisticated players will bet against them, placing them at a disadvantage. Even if the sentimentalists have purchased all the Jolie-Pitt shares, the market could allow a third party to offer to sell additional shares. Such a third party would merely need to show the ability to pay one dollar per new share if in fact the shares are redeemed. Eventually, the unsophisticated parties will run out of money or, more likely, reach the limits of their celebrity affection. It is one thing to lose a few dollars, another to pour one’s life savings into a bet against eager speculators. The result is that after a while, the bid and ask prices are increasingly likely to be determined by the actions of informed, rather than uninformed, parties. This reflects a key aspect of prediction markets. Prices do not simply reflect an average assessment by a group but also reflect the degree of confidence that different members of the group have in their estimates.11 Simply taking the average estimate of a group may work well for some problems but not for others. For example, Francis Galston studied a competition in which contestants guessed the weight of an ox; the average guess of the 787 contestants, 1,197 pounds, was only one pound short of the actual weight.12 But when Cass Sunstein, a law professor, asked his colleagues to estimate the weight of the fuel that powers space shuttles, they gave a median answer of two hundred thousand pounds, far short of the actual answer of four million pounds.13 People may on average systematically misestimate certain numbers, and even if a few people in a group know the correct answer, those people may have only a small impact on the average. Because no one is forced to participate in a prediction market, those who participate tend to be those who have information relevant to the particular prediction or at least those who can obtain the information at low cost. Among participants, individuals who have the most information should be willing to place the most money at risk. It will not always work out this way, of course. Sometimes, someone who has relatively little information or erroneous information might nonetheless be bold and wager a great deal of money on a particular position. For example, someone might invest heavily after overhearing a conversation in which Pitt refers to Jolie as his wife, when others who heard the conversation realized that Pitt and Jolie were merely discussing their roles in the movie Mr. and Mrs. Smith. Other market participants might surmise wrongly that this trader has some valuable information and change their own initial probability assessments on the basis of this individual’s trading. Meanwhile, someone with excellent information will face some constraints on liquidity. For example, suppose a friend learned that Pitt and Jolie had agreed that they would flip a coin to determine whether to marry. Assuming the reliability of this information and the fairness of the coin, the friend could be sure that the correct probability is 0.5. This friend would probably want to purchase some no-marriage shares for thirty cents, and gradually that would move the price toward fifty cents. But unless the friend can credibly reveal the information to the world and liquidate the resulting financial position, this strategy is not guaranteed to produce profit. A purchase of the no-marriage share for thirty cents produces a 50 percent chance of a seventy-cent profit and a 50 percent chance of a thirty-cent loss. A risk-averse individual might take this deal but decide to stop buying once the no-marriage share reached forty-five cents. Willingness to invest depends both on a trader’s assessment of the quality of the trader’s information and on the trader’s liquidity, so mistaken self-assessments and liquidity constraints can lead market prices astray. The case for a probability estimate prediction market thus cannot be that it will somehow produce perfect information. Such a market cannot tell us for sure whether Pitt and Jolie will marry. And we cannot even be sure that the probability estimate that the market produces will be the best one possible based on existing information. Theory suggests, however, that a probability estimate prediction market can serve as a relatively simple technology for aggregating individual probability assessments. Self-assessments of information quality seem likely to be at least correlated with actual information quality, and so a prediction market in effect provides a mechanism for weighing the estimates of a group of individuals based on the information that members of the group possess. The financial incentives of prediction markets ensure that forecasts will reflect genuinely held beliefs. Prediction markets reflect the intuition that when someone puts his money where his mouth is, he has greater credibility than when he does not. The question remains: How good a technology for producing probability estimates is the probability estimate prediction market? There are, after all, competing approaches. One could seek to identify a group of individuals who might have relevant information or who are experts in the field and survey them. Perhaps a few phone calls to friends of Pitt and Jolie would produce more accurate estimates. Of course, a prediction market participant might make such calls, but there is no guarantee that the market prediction will take this information into account to the optimal degree. Even if prediction markets are superior to alternatives such as surveying experts, another prediction market design might be preferable to the probability estimate prediction market. If Us Weekly ever were to accept such markets, they would likely need to become far more commonplace, but for this to occur, there must be empirical evidence that the probability estimates that they produce are accurate. Generating reliable evidence about the accuracy of probability estimate prediction markets, however, is not easy. The occurrence of an event cannot show that a probability estimate of that event was correct or incorrect. Suppose, for example, that the Pitt-Jolie market predicts with 99 percent confidence that they will marry. If they do marry, that provides some reassurance, but perhaps the result is a mere coincidence. And if Pitt and Jolie do not get married, that might appear to cast substantial doubt on the market. But it could be that the 99 percent estimate was reasonable based on information available at the time, and the l 1 percent possibility has come to pass. Probability estimate prediction markets are not able to miraculously anticipate that events that would seem unlikely to anyone with the relevant information in fact will come to pass. The best hope for them is that their probability estimates will be better than alternatives’. We can only reliably gauge the accuracy of probability estimate prediction markets after much experience with them.
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