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Self-Resolving Prediction Markets

Normative prediction markets can be used to make virtually any type of decision, but so far they are not autonomous. They can function only by predicting some normative decision to be made in the future or at least one that might be made. We have seen that prediction markets can forecast the outcomes of other prediction markets, but in the models discussed so far, eventually some prediction market must be forecasting a number to be determined in a way that is extern to the market. We have even seen that a prediction market can give participants incentives to anticipate what the same prediction market’s forecast will be at some later point (see Chapter 4), but in this case also we assume that eventually one or more predictors may be affected by external assessments.

It is possible, however, to have a prediction market that is entirely self-resolving, that is, in which there will never be a need for the sponsor to resolve the market payouts by reference to a number derived outside the prediction market itself. A simple change to the deliberative prediction market accomplishes the trick. As described above, if the market ends when a prediction has not been resolved by a later prediction, then the payouts for the unresolved prediction are determined on the basis of the actual event being predicted. An alternative is to resolve payouts for any unresolved predictions at the close of the market based on the market-closing consensus forecast. Recall that the exact time at which the market ends will not be known, so it will not be possible to ensure profits by promising to make a particular prediction just before the market closes. This market is self-resolving in the sense that the payout for each prediction is resolved on basis of the market consensus prediction at some time.

That it is possible to create a self-resolving market does not mean that it would be useful to do so. At first glance, it might appear that the market would not produce useful information. After all, the market is entirely circular. In effect, the market rewards market participants for predicting numbers that other participants might predict still other participants might predict, and so on. The instructions for the market might provide that participants should forecast interest rates, but participants might decide that they would rather forecast the results of a baseball game. Or different market participants might forecast different things. Perhaps many market participants would in effect enter random numbers, and the prediction market would produce nothing but random noise.

There are reasons, however, that this might not happen. Suppose that you stopped a stranger on the road and asked the stranger to forecast the high temperature for the next day and promised to compensate the stranger for making the forecast. Because you might not ever see the stranger again, you told this stranger that you would then ask another stranger to make the same forecast, and the closer the first stranger’s forecast was to the second stranger’s, the more you would pay the first. You promised that you would continue this process recursively until someone refused to make a forecast, in which case the prior forecaster would receive no compensation. Perhaps the stranger will be smart enough to recognize the recursive nature of the problem, but the stranger will still be better off making a prediction of the next day’s weather than announcing an effectively random number. The reason is that if the second stranger announces a number, there is some chance that it will be a temperature forecast and some chance that it will be effectively random. The first stranger’s incentive, like the incentive of every subsequent stranger, is thus to announce a temperature forecast.

In the language of game theory, the participants in the self-resolving prediction market and in the weather poll are playing a “tacit coordination game.” Thomas Schelling described a game of this type in The Strategy of Conflict: “You are to meet somebody in New York City. You have not been instructed where to meet; you have no prior understanding with the person on where to meet; and you cannot communicate with each other.”8 In an empirical test, a majority of respondents, residents of the New York metropolitan area, picked the same place and time, Grand Central Terminal’s information booth at noon. Both the time and place serve as “focal points,” and someone trying to coordinate with someone else will choose a focal point.

The game would produce more successful coordination if Schelling had told participants where to go. For example, if he told each of two people that they would win large sums of money if they met the next day and that he would recommend the top of the Empire State Building as a meeting place at noon, it seems almost inevitable that they would meet there. Even if Schelling had referred less directly to the place where Tom Hanks would find love in Sleepless in Seattle, the participants, perhaps after asking friends or doing research, would succeed in meeting each other atop the Empire State Building. It seems highly unlikely that one of the two would decide instead to go to a random intersection instead of the Empire State Building. The person might recognize that the tacit coordination game is circular, yet there is some reason to go to the Empire State Building and no reason to go to a random intersection.

The prediction market is much like the version of the Schelling game in which the participants are instructed where to go. The instruction for the prediction market serves as a very strong focal point, and each market participant seems likely to act on the assumption that the next market participant will be seeking to improve on an estimate of whatever the prediction market specified. It is possible that on occasion there will be alternative focal points, such as the number 0 (or, for a probability estimate, 0.5). But market participants are unlikely to pay attention to them, for the same reason that market participants who receive the recommendation to go to the Empire State Building seem unlikely to choose the Grand Central Terminal information booth instead. The instruction makes the original focal point far more inviting.

This analysis admittedly does not guarantee that some other focal point will not occasionally dominate. Imagine, for example, that Schelling gave each of the two players an extremely difficult math puzzle that could be used to derive the longitude, latitude, and altitude at which to meet the other player, but that each player can provide only an imprecise answer to the puzzle, so imprecise that he or she cannot deduce that the answer is the Empire State Building. One or both players might then decide to go to the information booth. Or, alternatively, each player might calculate the location with a very generous round-off. It seems unlikely, however, that the instructions for prediction markets will often be so arbitrary or subjective that participants look for alternative focal points.

Perhaps on rare occasions someone other than the market sponsor could somehow change the problem and thus the focal point. As a general matter, however, this strategy seems unlikely to work. If a market participant could make money by announcing a new instruction and seeing the focal point change accordingly, then market participants would do this repeatedly, and only the original instruction from the market sponsor would differentiate itself. It is possible, however, that market participants might find a particular alternative instruction attractive for some reason. For example, some might argue that participants should not make the prediction requested by the market sponsor but instead should make the prediction that will lead to the most good for the world. This might create an alternative focal point.

The challenge of the self-resolving prediction market is that some criterion other than that recommended by the market sponsor will somehow become focal. General moral and economic reasoning may provide shared modes of analysis and thus provide alternative focal points. Where this is not what the market sponsor intended, however, it is difficult to see why these alternative focal points should defeat the intended one. There will often be many alternative focal points, based on different methodologies that might be used to resolve the market payouts (philosophy, economics, theology, and so on) and different groups whose interests might be relevant to these analyses (the predictors themselves, the citizens of a particular nation, everyone in the world). The one focal point that ordinarily will stand out most prominently will be the one corresponding to the instruction of the market sponsor.

That does not mean that self-resolving prediction markets should not be used to make moral or economic assessments. Perhaps we would be better off if prediction markets did sometimes deviate from their sponsors’ intent for the greater good. The question is simply one of fidelity, and ultimately, if self-resolving prediction markets are faithful, they can be harnessed to engage in moral or economic reasoning. The sponsor of the market, after all, might specify a relevant principle for evaluating a particular question: What should be the minimum income the government should guarantee under a Rawlsian theory of justice? Or what should be the optimal toll price for the George Washington Bridge under general economic theory? Similarly, the sponsor could specify whose interests the market participants should and should not take into account or whose ideology should be the basis of reasoning.

Any question, of course, will involve some degree of ambiguity. Market participants can be expected to look to focal points for resolution of particular ambiguities. Suppose, for example, that the market sponsor did not specify whose interests should be taken into account. Then market participants might seek to identify focal weights for the interests of different groups, including the market sponsor. Or, if there are competing interpretations of a specified theory of justice, then market participants would presumably seek to determine the relative strength of different theories. In the end, this may not be very different from what market participants would do in a normative prediction market. In that case, they would anticipate what proportion of individuals would subscribe to particular approaches, whereas in the self-resolving market, participants would seek to identify the approaches’ inherent appeal.

January 17th, 2008 Market Designs Comments ( 1 )

 

One Response to “Self-Resolving Prediction Markets”

  1. Noam Danon Says:
    January 18th, 2008 at 4:50 pm

    Very interesting article. It raises an issue that we’ve been struggling with for a long time at Qmarkets, when talking to customers (companies).

    It becomes very clear that it is needed, for instance, when using prediction markets to provide a company’s sales forecast for the next year.

    On one hand, you don’t want the market participants to wait until the end of the year until they get their payoffs, so choosing the market price at an arbitrary date before the company’s budget is determined would make sense.

    Problem is, that in this case, the market is actually trying to predict something else - it predicts what participants will predict, or what management will pick as the year’s budget - and not the actual result at the end of the year.

    The alternative, of course, is to keep it open for the entire year, but then it is too far…

    I think the best approach is to combine the two - close the market at beginning of the year, as described in this article - and then open a new market, that will remain open until end of year - and naturally, take the starting prices from the old market.

    Question is - regarding the first market, that actually “predicts the prediction” - will its results still be reliable?

    Noam Danon,

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