Deliberative Prediction Markets
When one prediction market is used to predict the outcome of another, participants who have private information in the first prediction market have an incentive to reveal that information to participants in the second. Suppose, for example, that a participant in the two-stage prediction market discussed immediately above were to obtain secret information that the favorite horse had not slept well, lowering his chance of winning from 0.75 to 0.70. Simply entering a prediction of 0.70 in the first prediction market will not be sufficient to profit on the information, because the payoffs in the first prediction market depend on the prediction of the second. The participant might still profit by announcing a prediction in the second prediction market, but if that market has only a small subsidy, the profit from doing that will be small. To maximize profit, the participant will want to reveal the information underlying the prediction to participants in the second market in as credible a way as possible. For example, if the participant can share a video of the horse’s restless night, the participants in the second prediction market will lower their own forecasts of the horse’s probability of victory. If that market results in a prediction of 0.70, then the holder of the private information will have profited by replacing a prediction of 0.75 with a prediction of 0.70. This approach should work as long as no one has the ability to manipulate the second prediction market. This structure thus encourages market participants not only to announce predictions or enter into transactions based on their private information but also to share that information with others and to try to convince others that those announcing the predictions have correctly interpreted the information. In other prediction market structures, such as a probability estimate prediction market or a one-stage market scoring rule, such incentives will be much more attenuated. Sometimes a prediction market participant will reveal information to make it possible immediately to capitalize on a prior trade. For example, in a probability estimate prediction market for a horse race, a trader might buy up shares of a horse that is underpriced. The trader could then simply wait for the race to occur, but might wish to cash in on this information before the race, thus avoiding the inherent riskiness of the race itself. So the trader could reveal the evidence or analysis indicating that the horse is underpriced. By changing other traders’ evaluations, the trader will be able to sell the shares for a higher price. There are, however, two reasons why this incentive often is not powerful enough to lead to disclosure of information in some markets. First, in some circumstances, it makes more sense to keep information secret in the hope of buying more cheaply priced shares and earning a higher profit. If, for example, a trader’s new information suggests that a share is worth thirty cents, the trader should buy as many shares as possible for less than that price, until no one is willing to sell any more. But there is always the possibility that the market price will fall again, particularly if no one else has access to the trader’s information. When that happens, the trader can increase profits by buying up still more shares. Revealing information to the market would block this strategy. Second, revealing information in a form that succeeds in convincing other traders is not costless. Specific pieces of evidence might need to be documented, by photographs, for example, and distributed. Analysis that a particular trader might have done in her head might need to be explained in a way clear enough for others to understand. Information, moreover, must be conveyed in a way that allows it to be absorbed by other traders easily. Even if revealing information does not cost very much, the benefit associated with making it possible to cash out of a market earlier might not be sufficiently great to justify it. Incentives to reveal information are likely to be particularly low in low-liquidity prediction markets in which very few are expected to participate. In markets with a very small number of traders, the danger that any single trader might have information that the rest of the market lacks is particularly high, and there is little reason voluntarily to give up this advantage. We can, however, build on the two-stage market scoring rule design to encourage a greater degree of information revelation.55 That design itself would encourage revelation, but without much hurry. A market participant merely would need to reveal information in time for it to be absorbed by the second prediction market. Participants who hope that their trading will not lead the market implicitly to incorporate the information, thus allowing them to trade further on it, would wait until relatively late to reveal the information. The result is that although the market encourages revelation, the process does not closely resemble a deliberative process, in which participants gradually offer evidence and arguments and respond to those offered by others. Ideally, the prediction market should encourage traders to release evidence and arguments as they become available and to consider the evidence and arguments released by others. A simple way of doing this would be to create a multistage market scoring rule. The profits of predictors in each stage would be determined by the prediction at the end of the next stage. The final stage of the market predicts the event itself, using a strictly proper scoring rule. A possible drawback of this approach is that the market subsidy must be divided among the stages, but it might be difficult to predict in advance which stages will be the most important to subsidize. An alternative approach is one in which each prediction is evaluated on the basis of the market prediction at some later interval. Suppose, for example, that a prediction market will be run continuously to predict the trade deficit at the end of 2015. The market rules might provide that each prediction shall be evaluated on the basis of the prediction made a week later, except that if the market closes before that time period has expired, the last predictor’s profit or loss would be assessed in the usual way. Suppose that the most recent prediction is $500 billion, but a market participant has developed a complex new economic model that can be used to predict trade deficits and, using the information from that model and other existing information, predicts that the trade deficit in fact will be only $400 billion. At the moment when the participant enters the $400 billion prediction, that is the market prediction. Others, however, might enter new predictions based on the information available to them. Suppose that one week later the market prediction is $430 billion. The trader would then be credited 40 points, where each point corresponds to $1 billion in improved prediction, because the $400 billion prediction was $30 billion away from the $430 billion prediction made a week later, and the preceding $500 billion prediction was $70 billion away. At the close of the market, points will be converted into dollars at the rate that uses up the market subsidy. In some circumstances, the market sponsor might want to subsidize certain time periods at a higher rate than other time periods. For example, in the trade deficit prediction market, the market sponsor might want to devote half of the market subsidy to the first time interval and split the remainder among the remaining time intervals. This would especially make sense if the task of developing initial predictions requires more work than the task of changing predictions on the basis of new information. There might be other situations, however, in which initial predictions are easy to produce and so the reverse approach should be taken. Accomplishing either would be straightforward. Points could be multiplied by a weighting factor that changes over time in accordance with a plan announced in advance. In this system the trader will have an incentive to reveal information about his model in an effort to convince others that his prediction was as accurate as possible. Others, meanwhile, will have incentives to scrutinize such information. If a subsequent participant finds that the new prediction was unsubstantiated or that the new information should lead to a different prediction, the participant may enter still another prediction. If someone makes a prediction without any supporting information, other participants will likely assume that there is no such information, and they will move the prediction back to its original level. If the week expires with the prediction at that level, the $430 billion prediction will have produced no profit, even if the model is correct. Of course, someone who does move the prediction back to the original $500 billion level will want to produce analysis supporting that move, because that person will be evaluated based on a prediction yet another week later and will need to convince other market participants of the wisdom of moving the prediction back. There are at least two potential problems with this system. The first is the danger of manipulation. Someone might announce a prediction and then announce another prediction the instant before a full week has passed, and continue to do this every week. If someone could do this successfully–and it might be difficult, given that many different traders would try to enter the last prediction–that person could make substantial profits. One solution would be to prevent a trader from making repeated predictions, but this still does not eliminate the possibility of collusion among two or more traders. A simple solution is to randomize the exact length of the time interval that will be used to identify the later prediction that disciplines the earlier prediction and to keep such information away from predictors. For example, the interval might be a week plus or minus one day. This will give market participants incentives to identify repeated trades and to enter new predictions pushing in the opposite direction. Of course, the exact length of the time interval might vary from one market to another, although it should be enough time so that market participants will be able to consider information offered in support of that prediction. In some circumstances, the interval might change over the course of the market, with shorter intervals in periods in which more information is available or in which information becomes easier to process, for example, toward the end of the market. A further caveat is that the precise time of the end of the market should also be randomized somewhat to prevent manipulation. Second, some traders might seek to profit on information without revealing it by developing a reputation for accurate analysis. Suppose, for example, that a market participant has spent a great deal of time and effort developing a sophisticated model that might help make economic predictions useful in a wide variety of market contexts. That participant might announce that such a model exists, and perhaps allow some individuals who sign confidentiality agreements to consider the model, but not release it. If the model in fact is strong, then over time, other traders will come to recognize that this trader’s predictions tend to be valid, and the trader will have little incentive to release the model. This result is not altogether lamentable, because this strategy will tend to be useful only when information can improve predictions in many prediction markets deployed at various times, and there are strong reasons to encourage the development of such generally applicable models. When such a model is developed, the information that the model results in a particular prediction itself is a valuable kind of information, even if the inner workings of the model are proprietary. The real concern is not that an occasional market participant would want to keep some information a trade secret, but rather that large numbers of participants would decide not to reveal information that has little chance of being useful in a later prediction market. For example, a market participant who has developed a reputation for accurate analysis might simply stop releasing analyses, relying instead on his or her reputation for accuracy. Ordinarily, however, this would not be a sound strategy, because some market participants would be worried that the sudden decision not to release analysis might indicate that no such analysis existed. Those participants would thus move predictions in the opposite direction. It would take some amount of experience before the market accepted a participant’s claims to have secret analysis that supports predictions, and always some skepticism would remain, preventing the participant from earning as much as he or she could earn by revealing information and analysis. So unless revealing information is expensive, market participants will have incentives to reveal it. At least, participants will have incentives to reveal any analysis that they have already prepared in digital form and that does not contain valuable trade secrets, such as algorithms for making future prediction market forecasts. If information retention were commonplace, some remedies might be available, though none is probably ideal. One remedy would be to require that predictions and supporting arguments be entered anonymously. Such an approach should be broad enough to preclude market participants from supporting statements by reference to particular models that they have developed. Enforcing this restriction, however, might require effort and would demand some set of penalties. Another approach, which might be used as a complement to the first one, would be to allow market participants falsely to claim to be other market participants. For example, if Model X has produced excellent predictions in the past, anyone would be allowed to claim to be reporting the results of Model X, thus quickly making claims to be announcing results of Model X worthless. This, too, might be difficult to enforce, however, because market participants who have developed models would have incentives to provide ways of verifying to other participants whether particular statements in fact are their own. Yet it might be difficult to do this without obviously flouting the rule requiring anonymous predictions, so conceivably this regime could be effective. Whether or not it provides perfect incentives to induce revelation of all information, a deliberative prediction market should improve matters, leading to exchange of information and arguments, rather than mere numbers. The approach bridges part of the gap that separates prediction markets from the Delphi Method and its aspiration to structure and facilitate deliberative groups. Deliberative prediction markets will probably do little good where there is a great deal of public information and relatively little private information, such as prediction markets forecasting the outcome of a presidential race; virtually any new piece of evidence in such a market is likely to be a drop in the bucket, and so incentives to release information that is not already publicly available will not be significant. But in prediction markets with few participants in which research and analysis can lead to significant changes in predictions, a deliberative market might help a great deal. The incentive to release information will be greater in this context because any such information will be of greater importance to anyone who might trade subsequently. Ultimately, the release of information can produce greater prediction market accuracy. The simple reason is that deliberation can improve decision making, particularly where participants have financial incentives to guard against some of the pathologies of deliberation, but the point can be elaborated by considering the relations among the pieces of information exchanged in deliberation. First, participants are better able to judge how much weight to give to the opinions of others. In other prediction market designs, participants assign some weight in their own predictions to the valuations of others, as manifested, for example, by the prices at which transactions clear. These earlier predictions ordinarily reflect some information or at least some analysis that the later predictor cannot observe directly but that presumably has some weight. But is be very difficult to assess how much weight without the underlying information or analysis. Second, participants are better able to determine whether information that they possess is truly new private information or is information that others have already traded on. If information in fact is new but a participant estimates that that others may have already traded on it, the participant will not move the prediction as far as the new information will warrant. Third, once information is released, there is no need for other market participants to produce the same information. The result is that the market subsidy will not be wasted on redundant acquisition of information by multiple parties, and it should thus produce more information, leading to greater market accuracy. Deliberative prediction markets might be particularly useful in contexts in which prediction markets otherwise might affirmatively discourage information release. In the absence of prediction markets, an individual might possess information that has no financial value, and he or she might release that information to advance his or her reputation as someone who has developed and identified important information. With prediction markets, however, that same information suddenly now will have financial value, and so individuals may conceal information that they otherwise would have disclosed to maximize their ability to trade on the information. Once there is a reward for information, what would have been released in the absence of a reward might suddenly be more valuable if kept secret. Prediction markets thus sometimes aggregate information at the expense of nonrelease of analyses that might allow observers better to assess particular problems. Deliberative prediction markets encourage not only information aggregation and production but also information release by providing a reward for convincing others that one is correct.
Leave a Reply