Zocalo is playing a key role at MIT’s Center for Collective Intelligence, where they are investigating a variety of approaches to connect people and computers so that—collectively—they act more intelligently. We’re integrating independent agents into prediction markets with human participants to see what subject areas and what market mechanisms lead to markets in which both people and autonomous software contribute to improved predictions. The project involves several professors from the Sloan School, the Media lab, Cognitive Science, CSAIL, and a knowledgable and capable group of grad students and undergrads. The local Boston press got wind of some of the experiments and wrote it up.

The project is sponsored by MIT with funding from Lincoln Laboratory and the Air Force. No official endorsement from those organizations should be inferred.

It’s actually quite common. The term in the economics literature that includes this is regulatory capture. When there’s a regulatory body specific to a particular industry, it’s very common for industry to be the major source of expertise in the area, and so for the regulators to be reasonably friendly with the businesses. The businesses can work for regulation that limits entry, and cuts down on competition that reduces profits, and they can work together to ensure that public relations problems are addressed in a cohesive way. But cutting down on competition often means fewer choices for consumers by way of tighter controls on what products are offered.

In our case, the thing I worry about is a narrow ruling that only “socially valuable” questions can be asked, and an expensive process for deciding what innovative questions can be posed. It seems likely that some interests will work to ensure that sports and entertainment questions be declared off-limits. The companies that have the strongest interest in fighting that faction are mostly persona non grata in the CFTC’s eyes, since they currently operate outside the law (TradeSports) or outside the country (BetFair).

The narrower the set of approved questions, or the more expensive the process of getting approval, the less chance that markets will be commercially successful. I think the experiments within companies have indicated (though not proven) that a mix of valuable and popular claims is necessary in order to attract continuing participation.

My biggest worry about fighting for CFTC regulation at this point is that they’ll approve something narrow, and this won’t produce enough successes to demonstrate that loosening the restrictions over time would be beneficial. The alternative is to continue to find ways to introduce markets under the radar and demonstrate their value to the academic audience, which could lead to a friendlier hearing in a more distant future after prediction markets have demonstrated social value and little risk of harm.

Of course the other likely outcome is that the novel experiments don’t happen because of the threat of litigation or regulation. But that seems unlikely given the growth in internal markets within companies. I think there’s more likelihood of long-term success without regulation than with it, and we’re better off waiting until the chances that the regulations will provide a broad approval are significantly higher.

(Cross-posted from pancrit.org.)

I’m pleased to be able to say that I have two consulting contracts at this point. I’m working with a group at Chapman University and another university I’m not allowed to mention in public announcements. The Chapman team is led by Dave Porter, who I worked with while he was at George Mason University. Most of the Experimentalists from the GMU Economics department have moved (or are in the process of moving) to Chapman in Orange County, California. Dave has been using Zocalo for economics experiments since 2005, while I was at CommerceNet. He has plans (and budget) to expand Zocalo to support a variety of experiments that he’d like to do. The software continues to be used at George Mason as well.

The other group is probably familiar to most of you, though my contract says I can’t use their name for publicity without approval (which they didn’t give). Suffice it to say, I’m happy to be working with this group; the professor in charge has been working on market-related software systems for almost 20 years.

These consulting contracts support my continued development of Zocalo, and both groups are fully supportive of the open source approach. Having these groups actively working with the software, requesting changes, and reviewing progress will contribute substantially to the usefulness and usability of the code. The fact that one group is working with the experiment configuration and the other with the prediction markets ensures that both will continue to be enhanced and get more robust as they are being used.

This announcement is being cross-posted to my blog: pancrit.org.

The article is written for (and probably only accessible to) people who understand the language of computability and complexity theory. It does review the economic principles underlying prediction market mechanisms beyond call auctions and the double auction, but only sufficiently to introduce them to Computer Science people who are new to this application area.

The chapter closes with a list of open questions, and I’d like to highlight a couple of them:

1. “Are there less expressive bidding languages that admit polynomial matching algorithms yet are still practically useful and interesting?” If someone can find a feasible mechanism that supports an interesting subset of a complete combinatorial or conditional claims, we could run markets that provide answers to much more interesting questions.
2. The idea of betting on outcome permutations is intriguing. (Apparently I missed this paper at the recent conference in San Diego.)
3. “What is the complexity of finding a match between a single new order and a set of old orders known to have no matches among them?” I’m more interested in finding cheap solutions or new ways to pose the problem that are more tractable, but determining the complexity is the first step in the crowd Sami and Pennock are talking to.
4. “The model in Section 1.5 directly assumes that agents bid truthfully. Is there a tractable model that assumes only rationality and solves for the resulting game-theoretic solution strategy?” Wouldn’t proving incentive compatibility be sufficient to establish that rational agents would bid truthfully? I expect LMSR to be incentive compatible, though I don’t know how hard the proof is. I have a vaguer feeling that the Dynamic Parimutuel might also be incentive compatible, though I think the fact that the price isn’t directly a probability makes the link more tenuous.

I hope the inclusion of this chapter in what appears to be a broad work on computability, efficiency, and algorithm design in games, negotiations, markets, and networks will lead to new ideas that will expand the set of alternative market designs we can make use of. (I have linked to the chapter above; if you want to download the whole book, Pennock’s blog contains the password that you’ll need.)

Researchers use scoring rules as a laboratory tool to convince people to reveal their true expectations about some set of outcomes. Participants are asked to give estimates of the likelihood for a set of outcomes, their scores are some function of the value they gave for the actual outcome. Scoring Rules are called “Proper” if they are designed so the participant’s best strategy is to honestly reveal the probabilities that seem most likely. The Logarithmic Scoring Rule (one of the Proper rules) provides a reward that equals the logarithm of whichever estimate turns out to correspond to the actual value. Since the total of all the estimates must be 1, the participant can only increase some probabilities by decreasing others.

Robin Hanson described how an Automated Market Maker (AMM) that adjusts its prices based on a scoring rule can support unlimited liquidity in a prediction market. If each successive participant in the market pays the difference between the payoff for her probability estimate and that due to the previous participant, the AMM effectively only pays the final participant. If the AMM’s scoring rule is logarithmic, participants who only update some probabilities don’t effect the relative probabilities of others they haven’t modified. (This last effect is only valuable for Combinatorial Markets, which I’ll talk about in a later post.)

The change in the user’s payoff is log(newP) - log(oldP) (or equivalently log(newP/oldP)) for each state. For a binary question, the possible gain will be log(newP/oldP), and the cost will be log((1-oldP) / (1-newP)). For the rest of this article, I’ll use gain and cost rather than the log(...) expressions, since there are only these two, and I’ll be using them a lot.In multi-outcome markets, the most common approach is to let the user specify a single outcome to be increased or decreased, and to adjust all the other outcomes equally, but this isn’t the only possibility. This design choice has the useful property that the probabilities of other outcomes will be unchanged relative to one another. Since the other outcomes are treated uniformly, they can be lumped together, which results in the same arithmetic as a binary market. Since those other cases sum to 1-P, the price is cost. It is also reasonable to allow the user to specify either a complete set of probabilities, or particular cases to increase and decrease and how much to change them. Whatever the case, the LMSR adjusts the reward for each outcome to be log(newPi/oldPi). I’ll describe more possibilities in this vein when I cover the Combinatorial Market.

I hope you found all this interesting in an intellectual sort of way, but you may have noticed that this description isn’t applicable to markets in which the traders hold cash and securities. The whole thing is couched in terms of participants who will receive a variable payoff, but they don’t pay for the assets, they merely rearrange their predictions in order to improve their reward.

In order to turn this into an AMM that accepts cash for conditional securities, we have to pay careful attention to the effects of the MSR on people’s wealth. The effects are easiest to describe in the binary case, and every other case is directly analogous, so I’ll start there. In a binary market, the participant raises one probability estimate (call it A) from oldP to newP and lowers the probability of the opposite outcome (not A) from 1-oldP to 1-newP. If the trader had no prior investment in this market, the reward will increase by gain.

In order to reproduce that effect in cash and securities, the AMM charges cost in exchange for gain + loss in conditional securities. Why does the trader get securities equal to the cost plus the potential gain? The effect of this is that if A occurs, the participant has paid cost, and received gain + cost, for a net increase of gain over the original position. If A is judged false, the participant has paid cost with no return, which is the effect we hoped to match.

When an AMM supports a multi-outcome market using the approach I described above, one outcome is singled out to increase (or decrease), while all other outcomes move a uniform distance in the opposite direction. If the single outcome is increasing, the exchange is trivial to describe: we charge the trader cost for gain + cost in securities. The effect looks just like the binary case. The user has spent some money and owns a security that will pay off in a situation the trader thought was more likely than its price indicated.

If the trader singles out one outcome to sell (and thus reduce its probability), the difference among the alternatives I described in the first article in this series on Basic Prediction Markets Formats becomes evident. The trader is betting against something, and the market can represent this using short selling, complementary assets, or baskets of goods. The market might allow short selling (like InTrade), a complementary asset (like NewsFutures and Foresight Exchange), or a basket of securities representing all the other outcomes (like IEM). Since there are distinctly different points of view on this question, different markets will make different choices.

In order to support the short sales model, the trader needs to receive the payment first along with a conditional liability. In our model, the trader would receive gain in cash immediately, and securities that required repayment of gain + cost if the outcome (which the trader bet against) occurs. The platform would presumably require the trader to hold reserves to ensure the repayment.

With baskets of goods, the trader would get the appropriate number of shares of each of the other outcomes. The charge would be cost, and that would purchase gain + cost of conditional assets in all other outcomes.

The complementary assets model would charge cost in currency, and provide gain + cost of an asset that paid off if the identified outcome didn’t occur. The complicated part of this representation is that traders can hold both positive and negative assets. In a 4 outcome market, a trader holding 3 units of A and 2 units of B who sold 4 units of C could be shown equivalent portfolios of either A: 3, B: 2, C: -4 or A: 7, B: 6, D: 4. I think either choice is defensible. The first resembles the transactions the user has made, and so is probably more recognizable; the second provides a more consistent view of possible outcomes. (And looks the same as baskets.) If both positive and negative numbers are shown, the trader has to realize that the negative holdings pay off in all other cases. On the other hand, displaying a portfolio in a 7-outcome market as A: 3, B: 3, C: 3, E: 5, F: 3, G: 3 doesn’t seem as clear as D: -3, E: 2.

I doubt this detail will be of much interest to most users of Prediction Markets. Luckily for them, the trade-off the logarithmic rule makes between cost and reward just happens to produce prices that match probabilities. But if you are implementing Hanson’s LMSR, you should understand the alternatives well enough to verify that your market maker correctly implements the design. Zocalo Prediction Markets support binary and multi-outcome markets with a Market Maker based on the Logarithmic Market Scoring Rule. The design takes advantage of the parallels between the different markets by only implementing the logarithmic rule in one place.

This article is cross-posted from pancrit.org.

Other Articles in this series

• PM intro: basic formats (2005-12-30)
• PMs with Open-ended Prices (2006-01-05)
• Looking at Both Sides (2006-04-17)
• Book and Market Maker (2006-04-28)
• Liquidity in N-Way claims (2006-07-19)
• Continuous Outcomes using Bands and Ladders (2006-09-20)
• Integrating Book Orders and Market Makers (2007-01-10)
• Conditional and Combinatorial Betting (2007-03-06)

One thing that Chris Masse seems to constantly argue is that Prediction Markets on dry subjects need to be accompanied by entertaining questions in order to to keep the audience’s attention. The economists had good reasons for shying away from recommending that sports betting should be included, but there are many other topics that diverse markets could include that give traders a reason to check back in. The range from the obvious entertainment questions (movie earnings and oscar winners) to legislative outcomes (bills passing and control of particular legislative bodies) and introduction and market success of new technologies. While these kinds of questions might be out of place on some single-topic markets modeled after the University of Iowa’s markets on elections, the internal corporate markets that they also mentioned often use them to help maintain interest. The letter’s recommendations that the CFTC “allow contracts that price an economically meaningful risk or uncertainty” unnecessarily limits the kinds of contracts that would be allowed.

Back on the side of supporting the letter’s authors again, I’d have to admit that if the CFTC or Congress acts to implement anything resembling the recommendation it would very likely increase Prediction Market activity greatly, and eventually lead to a broader acceptance. If the initial definition is too narrow, however, questions that don’t have clear economic implications (in the view of Congress and the regulators) might be stuck offshore for a long time to come.

The easiest compound question to pose is a simple conjunction of two others. InTrade had separate markets in whether Bush would be reelected in 2004 (“BUSH”), and whether Osama bin Laden (“OSAMA”) would be captured before the election. Justin Wolfers and Eric Zitzewitz asked InTrade to add a single combined contract that would pay off if both came true. Their paper, Experimental Political Betting Markets and the 2004 Election shows how the prices on these three contracts can be combined to show how one event would be likely to effect the other.

InTrade created three separate claims to cover combinations of the two base questions. They were “Bush wins election” (BUSH), “Osama is captured before the election” (OSAMA), and the combination: BUSH&OSAMA which would have paid out if both the others came true. Wolfers and Zitzewitz estimated the market’s conditional probability by comparing the price of OSAMA with the price of BUSH&OSAMA. If the price levels were rational, the difference between the two prices had to equal the chance that Osama would be captured and Bush would not be reelected. Since the market price of BUSH&OSAMA was 91% as high as the price of Osama, they concluded that that represented the conditional probability. A weakness of this conclusion is that while investors and arbitrageurs have an incentive to ensure that the price of BUSH is correct relative to ~BUSH, (and OSAMA with respect to ~OSAMA), there’s no bet that lets an arbitrageur exploit superior knowledge of the conditional probabilities.

Sometimes investors believe they know how one outcome will effect another, and want to bet directly on that linkage. If you were confident before the election that Osama’s capture would raise the probability of Bush’s reelection to 95% (above the level the the market prices implied), having the conjunctive bets didn’t provide a bet that would have looked beneficial to you. You might think you could buy Bush&Osama (because you believe Bush’s chances are improved if Osama is captured) and sell ~Bush&Osama (because this is the outcome your view says is least likely), but you’d lose both bets if Osama wasn’t captured (which is an outcome your prediction doesn’t specify.)

Conjunctive claims allow observers to deduce connections between claims, but since the investors aren’t directly rewarded based on the conditional probabilities, they have little incentive to ensure that the implicit conditional probabilities reflect their understanding of the connections between the outcomes. In order to evaluate different proposals we have to look at what investors would spend up-front, and then compare the possible outcomes and how the investor’s earnings change in each situation.

If Bush is a 60% favorite to be re-elected, and the market thinks there’s only a 10% chance Osama will be captured before the election, the odds on the conjunctions might be:

If you think Osama’s capture would improve Bush’s prospects to 95%, what should you buy or sell? Your prediction says that the ratio of Bush&Osama to ~Bush&Osama should be 19:1, but doesn’t have anything to say about Bush&~Osama or ~Bush&~Osama. If you buy Bush&Osama and sell ~Bush&Osama, you can make the prices match your beliefs better, but you’ll lose money if Osama isn’t captured. In order to support conditional bets directly, market operators have to find ways to allow traders to buy positions without exposing themselves to risks due to the independent cases.

A contract that acts like a conditional bet directly (written as BUSH|OSAMA, pronounced as “Bush given Osama” or “Bush conditional on Osama”) would pay off if Bush is elected, and return your investment if Osama bin Laden isn’t captured. That gives investors the right incentive.

In order to support betting on conditional probabilities, the bets have to be able to return the investors’ money in particular cases. I know of three detailed proposals that have this property. They are: betting on arbitrary boolean expressions, representing the complete cross-product of possible outcomes (providing a complete set of Arrow-Debreu securities), and using the independent claim as currency for purchasing the dependent claim. There are two additional suggestions that might work, but haven’t been written down in sufficient detail to be sure.

Robin described and implemented Combinatorial Information Markets which represent probabilities and traders assets explicitly for all possible combinations of outcomes. Fortnow, Kilian, Pennock, and Wellman described how you might try to support bets on arbitrary boolean combinations of conditions. Their conclusion seemed to be that solving the general problem would be computationally infeasible. They didn’t describe how to address the problems they found, but I think it’s possible that a market that supported only binary combinations could be designed. And finally, Peter McCluskey built (and released as open source) USIFEX in 1999. It allows the user to use the coupons of the independent event as the currency. This combination allows traders to express conditionals directly. Unfortunately, that system didn’t attract a user base quickly enough, and Peter stopped development soon after the initial release.

For an article on Decision Markets written in 1999, Robin Hanson suggested creating markets using assets that pay off in “units of A if B passes” (and “… if B doesn’t pass.”), and allow traders to trade the assets for each other. The price of A|B in terms of B (which can be built from component assets) expresses the conditional bet. Robin didn’t explain how to set up a market in which people trade assets for assets and didn’t describe how to let the users see how various combination bets would express the conditional claims they might have been interested in. (This is the first of the two incomplete suggestions.)

Robin’s Combinatorial Information Market design uses a complex internal representation and can support arbitrary conditional bets. He built a prototype implementation that allows the user to explore these conditionals by choosing assumptions, and then adjusting probabilities in the resulting hypothetical situations. I wrote a prototype of my own in E. Neither prototype is more than a proof-of-concept that the institution works, and neither has been operated for any general market. The strength of this approach is that users can express conditional connections between arbitrary claims; this aspect has been shown to be effective in a laboratory experiment. Robin ran tests of this market after he proposed its use for PAM, and there were apparently no problems in running it with 6 traders estimating all outcome combinations for 8 events. The glaring weakness is that it doesn’t scale well. It’s not clear how to build a version that would work even with a market with dozens of questions and hundreds of users. I’ll describe this market in more detail in a future post in this series.

Peter McCluskey built USIFEX in 1999. It works quite differently and doesn’t seem to have the performance problems of the other proposals. The primary idea for supporting conditional trading is that you buy units of A|B using units of B as currency when betting on a conditional question. The effect is that when buying A|B, you end up with coupons of ~B as part of the purchase, and that’s what ensures you’ll be repaid if the independent event doesn’t occur. USIFEX is open source, but it hasn’t been maintained since it was released in 2000. The code was resurrected for use in the Swiss MarMix exchange, (AFAICT without making any use of the conditional betting features). The biggest weakness of Peter’s approach, as I recall, was that it would have taken a lot of users to ensure that the conditional markets weren’t extremely thin. A longer description of USIFEX is also in the works.

Todd Proebsting built an implementation of the Hanson design that works without conditionals. Dave Pennock wrote up a description of Todd’s approach, focused on the Market maker. I intend to describe the implications of Todd’s approach for betting on conditionals in a future post. (This is the second incomplete suggestion.) I think it might be straightforward to extend Todd’s approach to support conditional betting without running into the exponential growth of Robin’s solution. The drawback is that the market operator has to separately capitalize and enable every conditional question that you want the system to support, while Robin’s approach enables all of them by default. It’s also possible that Zocalo Open Source Prediction Market software would be compatible with this approach, where it’s clear that Zocalo would require substantial modification to support the Hanson proposal.

Other Articles in this series

• PM intro: basic formats (2005-12-30)
• PMs with Open-ended Prices (2006-01-05)
• Looking at Both Sides (2006-04-17)
• Book and Market Maker (2006-04-28)
• Liquidity in N-Way claims (2006-07-19)
• Continuous Outcomes using Bands and Ladders (2006-09-20)
• Integrating Book Orders and Market Makers (2007-01-10)

Cross-posted from pancrit.org.

Dave Pennock gave a gentle introduction to the Market Scoring Rule invented by Robin Hanson. In the comments, Sid asked for an explanation of how to integrate the MSR with an order book. Dave asked me privately if I’d be willing to tackle that, and this post is the result. Robin’s short note on integrating an order book and a market maker covers a lot of territory very quickly. In Robin’s defense, it was written to clarify some ideas in the midst of a conversation we were having at the time, and hasn’t been cleaned up for publication. I’ll expand on it here so it has a chance of making sense to others. The paper couches things in terms of the MSR, a particular AMM, but none of the implementation depends on which AMM is used.

There’s a working example of the integration we’re talking about in the code for Zocalo. The code that does this is currently in transition since I’m adding support for multi-outcome markets. For the moment, I recommend reading the code for version 375, since the current code is more complex and possibly incomplete. You can either download the complete source code for release 2006.5 of the Zocalo Prediction Market, or browse the code directly using the SVN interface.

The paper starts by giving a very compressed introduction to the idea of a prediction market and market maker (hereafter AMM for Automated Market Maker). Unless you’re very familiar with the details and the formalisms that Robin uses to describe them, you’d be better off reading the original papers (Logarithmic Market Scoring Rules, Combinatorial Information Market Design) than trying to pick anything up from the first four paragraphs of the note.

The fourth paragraph slips into the idea of integrating an order book with the AMM he’s talked about to that point. (“If instead [the AMM price resulting from buying the entire quantity is higher than the user's max marginal price], a portion [...] could be traded with the market maker, leaving a book order for the remaining quantity”). From that point, he talks about how to integrate the two markets.

If new orders get the advantage of any order price overlap

In book order systems, if orders arrive asynchronously, you will often see orders that “overlap”, i.e. orders to buy at a higher price than the best offer to sell, or orders to sell lower than the best offer to buy. The system has to have policy about what price to transact at in these cases. The system could tell each party that they got the price they requested, and pocket the difference; it could use the book order’s price or the new offer’s price; or it could split the difference in the interest of fairness. If any choice is made other than using the stated price of the order in the book, investors have an incentive to carefully submit bids a little at a time (aka “structure” their bids) so they won’t pay more than they have to if new orders should arrive. Robin argued elsewhere (I can’t find the reference at the moment) that you should just transact at the book order price so that people submitting market price orders don’t waste their resources and yours on this optimization.

That choice also simplifies the calculation for accepting new offers. As Robin says, “each book order [...] imposes a constraint on the market maker price”. The AMM should fulfill orders up to that limit, then let trade continue with the book order. This requires a loop, in which you buy from the AMM until you reach the limit imposed by the best order(s), then trade up to the book order’s available quantity, then go back to the AMM until you reach the next book order. You can see the approach in Zocalo’s method Market.buyFromBothBookAndMaker(…). (The method starts at line 237.)

At every step,

• find the remaining quantity q of the new order
• find the price p available from the best existing order
• if the AMM’s price is no better than the book order, trade up to q with the book
• otherwise trade with the AMM to the lesser of p or q

The loop stops either when the new order is fulfilled or the price limit specified by the new order is reached.

That’s the simple version for a one-dimensional AMM. The multi-dimensional version arises if you implement the AMM as described in “Combinatorial Information Market Design”. There are two open source implementations of this approach available for reading by hard-core hackers. Robin built an implementation in Lisp, and I wrote a version in E. Neither is more than a demonstration of how the market engine works, since no serious user interface was written for either one.

Rather than attempt to explain how the approach translates to the multi-dimensional case now, I’d prefer to wait until after I write an explanation of the n-dimensional combination market, and that depends on a gentle introduction to conditional and combinatorial betting which I haven’t written yet. Having someone ask about Robin’s note raises my priority for writing these prerequisites.

Other Articles in this series

PM intro: basic formats (2005-12-30)
• PMs with Open-ended Prices (2006-01-05)
• Looking at Both Sides (2006-04-17)
• Book and Market Maker (2006-04-28)
• Liquidity in N-Way claims (2006-07-19)
• Continuous Outcomes using Bands and Ladders (2006-09-20)