Analyzing epistemic gains, and robustness of prediction markets

9 Mar

Since at least James Suroweicki’s “Wisdom of the crowds”, a multitude of scholars involved in the field of epistemic democracy have taken to theorizing epistemic utility of tools like “Prediction Markets”, and even the “Wikipedia” model. Cass Sunstein, a Professor of Law at University of Chicago, has in particular been effective in advocating the idea through a stylized analysis that cherry picks successfully working corporate prediction markets and ignores problems like the current morass of InTrade. Here below I analyze the conditions under which predictions markets can deliver their theorized epistemic gains, and test their robustness to violation of optimal conditions. I however start with analyzing a comparison that political scientist Josiah Ober makes between Ostracism and Prediction Markets and in doing so lay out some of the essential features of markets.

Josiah Ober and Learning from Athens

Ober has been a keen exponent of the idea that ancient Athens had institutions that ably aggregated information from citizens, and fostered “considered” judgments. In his Boston Review article, he strangely argues that the decision to build hundreds of warships, prodded by Oracle (!) and now known deliberate misinformation by Themistocles, led to an ultimately ‘right’ decision by the assembly to build warships and not say distribute the windfall from the silver mines to the average citizen. There are two problems here – one is epistemological with its reliance on Oracles for signs, and the other is use of manipulative information ala Cheneyesque. It is impossible to answer whether Persia attacked because they felt inklings of a threat due to the huge armada of ships that Athens had built.

At another place, Ober has compared the first step of Ostracism proceedings – the Demos taking a vote to determine whether to hold ostracism or not – with Prediction Markets. He argues that the vote to hold Ostracism or not aggregated individual level information or predictions about whether there is “someone” whose presence is pernicious enough so as to merit Ostracism. There are three pitfalls to such comparisons and I will deal with them individually. Firstly, Ostracism didn’t provide people with direct private economic incentives to reveal private information or seek “correct” information, and something which economists believe is essential (it is also born out in experiments). To counteract this argument, Dr. Ober argues that the manifest threat of making a “wrong” decision was large enough to impel citizens to gather the best information. There are two problems with this argument – penalties for making wrong decision fall on a continuum and are rarely either prosperity or annihilation (certainly the case in Themistocles and Persia), and secondly even in presence of immanent threats (something not quiet true in this case as the threat is defined vaguely as “wrong decision”- which is a little different from the most informed decision) to groups “collective action problem” prevails – albeit in an extenuated form.

In ancient Athens, decision to hold Ostracism or not was made through a vote. Vote is a deeply impoverished aggregator of private information for with each dip you get only a yes or a no. This impoverished information sharing also exerts enormous pressure on distribution of “right” information among the population for a small minority of “right” voters can easily be silenced by a misinformed majority. The only way in fact a Voting system can reliably aggregate information (if choice is binary) is if each dip –on average -has more than 50% chance of being correct. (Condorcet’s insight) Markets on the other hand provide for information to be expressed much more precisely through price. (We will come to the violations of this tenet in markets later.)

Unlike in voting, markets deter information (and misinformation unless strategically) sharing although price does send cues (information) to the market. (Of course strategic players fudge investments so as monetize their investment maximally) Suffice it is to say however that voting systems are more prone to aggregating disinformation, than market systems where incentives for gaining “right information” increase in tandem with people investing with “wrong information”.

Markets, Betting Markets

I will deal with some other issues including assumptions about distribution of private information later in the article. Let me briefly stop here to provide an overview of markets and betting markets in particular.

Markets, when working optimally, are institutions that aggregate all hidden and manifest information and preferences and express it in a one-dimensional optimally defined parameter, price. Since all individual preferences are single-peaked with reference to price, markets are always single-peaked, avoiding aggregation issues and Condorcet’s paradox. Markets aggregate not only information about demand, and supply but also the utility afforded by the commodity to each individual consumer, and such aggregation optimizes the “allocative efficiency”. And apparently all this is done magically – and in Adam Smith’s coinage at the beckoning of the famous “invisible hand”.

Prediction markets – also known under the guises of “information markets” or “idea futures” among others – tie economic gains to fulfillment of some prediction. The premise is that possibility of economic gain will provide people to reveal hidden information – or more precisely bet optimally without revealing information. Prediction markets are quiet different from regular markets for trading is centralized against a bookmaker that decides the odds after aggregating bets. This type of architecture puts significant constraints on the market than say the architecture of a share market, which is essentially decentralized. I will come to the nature of the constraints later but suffice it is to say that it avoids some of the “variances” and “excesses” and “excess variances” of the decentralized system – the kinds which made Robert J. Shiller turn to behavioral economics from playing with math and monkey wrench models.

Expanding on the nature of prediction markets – “A prediction market is a market for a contract that yields payments based on the outcome of a partially uncertain future event, such as an election. A contract pays $100 only if candidate X wins the election, and $0 otherwise. When the market price of an X contract is $60, the prediction market believes that candidate X has a 60% chance of winning the election.” (Prediction Markets in Theory and Practice -2005 Draft, Justine Wolfers and Eric Zitzewitz) A more robust description is perhaps necessary to explain how bookies come to know about these odds. In much of sports betting, bookies commence betting by arriving at consensus that reflects expert opinions of a small group of professional forecasters. “If new information on the relative strengths of opposing teams (e.g., a player injury) is announced during that week, the bookie may adjust the spread, particularly if the volume of behavior favors one of the teams. In addition, since the identity of the bettors is known, bookies may also change the spread if professional gamblers place bets disproportionately on one team. To make these adjustments, the bookie moves the spread against the team attracting most of the bets to shift the flow of bets toward its opponent. Shortly before game time, the bookie stops taking bets at the ‘closing’ point spread. Like securities prices at the end of trading, closing spreads are assumed to reflect an up-to-date aggregation the information and, perhaps, biases of the market participants.” (Golec and Tamarkin, Degree of inefficiency in the football betting market, 1991, Journal of Financial Economics: 30). There are other ways through which a similar arrangement can be executed. For example, computerized software now continually adjust the odds depending on bets. The danger is that you can quickly short the system if you solely rely on anonymous betting data. I will come back to his later. One additional point to finish the description – Given the nature of the commodities or assets traded, we can only get results on questions that have binary answers, and not say discovery questions unless discovery questions can be split into innumerable binary questions.

Before we analyze the betting market efficiency, I would like to present a short list of the previously theorized (and proven) betting market failures or “instances where the operation of the market delivers outcomes that do not maximize collective welfare.” There are several forms of market failure:

  • Imperfect competition – where there is unequal bargaining power between market participants;
  • Externalities – where the costs of a particular activity are external to the individual or business and imposed on others (e.g. Assassination Markets);
  • Public goods – where there are goods for which property rights cannot be applied; and
  • Imperfect information – where market participants are not equally informed.

* Taken from Objectives of Betting and Racing Legislation (doc)

*As always, penalties follow some function of the extent of violation. Most effects are non-linear.

Let’s analyze the epistemic dimension of the market as in its capability to deliver information that is somehow better. The supposition in a prediction market is that people aren’t revealing (or finding information) for they have inadequate incentives to do so. So betting is merely a way to incentivize the discovery process. It is important to note that merely the fact it assumes that people have private reserves of information (generally amounting to knowledge that other people aren’t smart) severely limits the role of the prediction markets in areas where there isn’t such knowledge. Certainly I can’t think of a lot of public policy arena where it is the case. (It is also important to keep in mind that most policy decisions have a normative dimension aside from some fully informed preference dimension.) Otherwise betting markets merely try to aggregate – and don’t do so well – public information cues. Simon Jackman in his forthcoming paper that analyzes betting behavior in political markets in Australia has found that betting markets essentially move following the cues of opinion polling results. There is no information source outside of what is already publicly accessible that people rely on to make their bets. So the idea that somehow prediction markets will deliver better results even where privately held reserves of information are low or zero is ludicrous and easily empirically disproved.

More importantly, betting markets – even sophisticated ones like the sports betting markets – are incurably biased – proven statistically multiple times over – they underestimate home field advantage, and all too often “go with the winners”. The bias is supported by two intertwining psychological biases – “safe betting” and “betting on favorites” – and it is a bias found in nearly all betting markets.

Betting markets behave best if there is complete adversarial betting – which is never the case for most of the price is set by investment by small players following the elite herd. This has defined by Sushil Bikhchandani, David Hirshleifer and Ivo Welch, in a classic 1992 article, as “information cascades” that can lead people into serious error. Shiller recently wrote about this while explaining how the housing bubble (essentially banks betting on loans) stayed under the radar so long. He quotes the paper at length –

“Mr. Bikhchandani and his co-authors present this example: Suppose that a group of individuals must make an important decision, based on useful but incomplete information. Each one of them has … information…, but the information is incomplete and “noisy” and does not always point to the right conclusion.

Let’s update the example…: The individuals in the group must each decide whether real estate is a terrific investment… Suppose that there is a 60 percent probability that any one person’s information will lead to the right decision. …
Each person makes decisions individually, sequentially, and reveals … decisions through actions — in this case, by entering the housing market and bidding up home prices.

Suppose houses are really of low investment value, but the first person to make a decision reaches the wrong conclusion (which happens, as we have assumed, 40 percent of the time). The first person, A, pays a high price for a home, thus signaling to others that houses are a good investment.

The second person, B, has no problem if his own data seem to confirm the information provided by A’s willingness to pay a high price. But B faces a quandary if his own information seems to contradict A’s judgment. In that case, B would conclude that he has no worthwhile information, and so he must make an arbitrary decision — say, by flipping a coin to decide whether to buy a house.
The result is that even if houses are of low investment value, we may now have two people who make purchasing decisions that reveal their conclusion that houses are a good investment.

As others make purchases at rising prices, more and more people will conclude that these buyers’ information about the market outweighs their own.

Mr. Bikhchandani and his co-authors worked out this rational herding story carefully, and their results show that the probability of the cascade leading to an incorrect assumption is 37 percent. … Thus, we should expect to see cascades driving our thinking from time to time, even when everyone is absolutely rational and calculating.

This theory poses a major challenge to the “efficient markets” view of the world… The efficient-markets view holds that the market is wiser than any individual: in aggregate, the market will come to the correct decision. But the theory is flawed because it does not recognize that people must rely on the judgments of others. …

It is clear that just such an information cascade helped to create the housing bubble. And it is now possible that a downward cascade will develop — in which rational individuals become excessively pessimistic as they see others bidding down home prices to abnormally low levels. “

Betting markets like all other markets are “sequential” with each investor trying to parse tea leaves and motives of prior investors. The impulse to do original research is counterveiled by the costs, and by the fear that others know something that they don’t.

The other intersecting psychological factor that complicates markets is complete blind betting. Time and again even as information and probabilities converge, some bettors hold out for a miracle.

It is also important to keep in mind the following tenet that governs prediction market behavior– “Garbage in, garbage out… Intelligence in, intelligence out…” So prediction markets – to the extent that they rely on speculation are remarkably likely to follow any information that is likely to give them a leg up. While misinformation theoretically incentivizes procurement of good information, it never pans out empirically for major investment by another is seen as an informational cue, more powerful than whatever access you may have. This is an important point – for the competitor has no way of knowing your information for all s/he has access to is the investment that you make on it, and the space for conjecture about the veracity of the competitor’s information is immense. This is a market based on never revealing information, and that diminishes the efficiency considerably.

Betting markets merely rely on the fact that you are less misinformed than others, and that gradient can be built through strategically spreading misinformation (quiet common in betting circles) or through some theorized virtuous cycle of increasingly good information.

Betting markets can be easily shot by someone willing to lose some money. Asymmetry in finances can hobble the incentives for betting market and information discovery process.

Lastly, laws against insider trading limit the kind of information bettors have access to. They limit information discovery process severely. Relatedly, information – for it to be monetizable – has to be brought into the system privately so bettors may try to sabotage release of public information. Not only that, they have to be strategic in how they send cues to the market so that they earn the most money from their bets. If done en masse or rashly, it will almost certainly short their bets. So not only do betting markets have only one way of expressing information – price/investment- bettors go to great lengths to hide that cue especially if they know how the cues are being aggregated.

In summary, the above list of problems with betting markets underscores the analytical and empirical evidence against the naïve ill-substantiated unbridled faith in the epistemic prowess of the betting markets.