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## Even Capped Prediction Markets Can Be Manipulated130

Slashdot regular contributor Bennett Haselton writes "My last article on prediction markets contained an erroneous assumption, one whose implications are far-reaching enough that they deserve their own article. (And if you read to the end, I'm offering \$100 to be split between the readers who submit the best alternative solution or the best counter-argument to the points made here.)" Read below for the rest of Bennett's thoughts.

In my last article, I wrote:

There could be rules and safeguards to prevent abuses of the system (rules that could be imposed by U.S. law, even if they're not enforced by overseas betting markets), such as not allowing individuals to bet more than \$500. (This is already enforced by the Iowa Electronic Markets.) That's small enough to stop individual bettors from trying to manipulate the market through enormous wagers (although they might find ways to do that anyway). It's also small enough that it wouldn't be worth it for any one individual to try and influence a political outcome just to win a bet. You could try to enlist your friends to help you place a collective \$10,000 bet on a single outcome, but the more people you rope into your coalition, the greater the chances of someone (a) turning you in for violating the betting laws, or (b) taking the \$500 you lent them, and then refusing to pay it back if they win their portion of the wager.

There's an error here, but one subtle enough that even all the commenters (with no shortage of the usual snark) missed it. To begin with, consider what happens if two different betting markets are taking bets at different odds for the same event.

Suppose CappedEx, a futures exchange that limits each user to betting \$500, is publishing 4:1 odds of an Obama victory. If you bet \$40 that Obama will win and he wins, you get paid \$10 (from other users on the exchange), but if he loses, you pay out \$40. Meanwhile FreedomEx, an exchange that has no betting limit for any user, is publishing 6:1 odds for Obama winning. Bet \$60 on Obama, and you get \$10 if he wins, but pay \$60 if he loses. On both markets, of course you can bet in the other direction as well.

What do you conclude from this? That the un-capped FreedomEx probably has more accurate odds, and that as James Surowiecki (author of The Wisdom of Crowds) said, betting limits "make [the markets] less accurate" and "real money is what makes it work"? Or that CappedEx, with its safeguards against manipulation, is more reliable, and FreedomEx is being manipulated by someone trying to change the reported odds of their favored candidate winning? Or that there is simply some random fluctuation in the odds as reported by various markets, so they'll naturally diverge at times?

The correct answer is: you should stop wasting time "concluding" things, and get online as soon as possible and make bets in both markets, because if they're allowing bets to be placed at different odds, you can guarantee yourself a profit.

Make a \$50 bet in CappedEx on Obama to win (4:1 odds), and a \$10 bet in FreedomEx on Romney to win (1:6 odds). If Obama wins, you win \$12.50 in the CappedEx market and lose your \$10 in FreedomEx, for a \$2.50 profit. If Romney wins, you lose \$50 in the CappedEx market but win \$60 in FreedomEx, for a \$10 profit. With a little algebra, you can show that any time the two markets allow you to place bets at different odds ratios, you can make a guaranteed profit by picking a ratio somewhere in the middle (in this case, the two ratios were 1:4 and 1:6, so we picked 1:5) and making separate bets in the two markets in opposite directions, for amounts in that ratio. (A commenter on the Marginal Revolution blog describes exactly how he made an almost risk-free profit through this kind of "pure arbitrage play". He said it was "almost" risk free because of other factors like currency conversion fluctuations.)

Now, any time a good is trading for a lower price in market A than it is in market B, and the costs of shifting the good between the two markets is negligible, traders will start to buy the good in market A and re-sell it for a profit in market B (the traditional definition of "arbitrage"). This increases demand in market A (driving the price up) and increases supply in market B (driving the price down) until the price difference disappears. In the same way, any time two prediction markets have different "market odds" for the same event, as arbitrage players lock in guaranteed profits by placing opposite bets in the two markets, the market odds in the two markets will converge toward each other until the gap is negligible. This is true even if one of the markets has a cap on what people can invest or how much they can stake on any particular outcome.

For Intrade, there couldn't be a worse time for someone to be pointing this out, but it seems logically inescapable: As long as there is a prediction market anywhere in the world that allows unlimited wagering on a particular outcome, all other prediction markets (whether they are capped or not) can be manipulated indirectly, by playing a large wager in the non-capped market. I was wrong to say that you would have to "enlist your friends" to place bets in the capped market, building a large coalition of market-manipulators (and hoping that none of them would rat you out for using them to circumvent wager-limiting rules). By placing a large wager in the non-capped market, and shifting the market odds there so that they're different from the odds in the capped market, you can indirectly "enlist" all the users in the capped market, to place arbitrage bets and make a guaranteed profit. When this happens, the odds in both the capped market and the non-capped market will shift, as the gap between them narrows -- which means you have manipulated the market odds in the capped market, without ever going near it yourself.

In this case, why have caps on the amounts wagered in prediction markets at all? (The Iowa Electronic Markets have a maximum investment balance of \$500, and a 2008 paper, "The Promise of Prediction Markets, authored by several prominent economists, advocated the creation of prediction markets with a maximum investment of \$2,000.) Presumably the cap is not to prevent unlucky investors from losing their life's savings, since the law already allows multiple ways to do that, by betting on volatile stocks in the stock market. And it won't stop market manipulation, if the capped market can still be manipulated by using another non-capped market as a proxy. Robin Hanson, Professor of Economics at George Mason University and one of the co-authors of the 2008 paper, candidly told me that the cap was just a matter of selling the idea: "As a practical matter, many people's comfort with such markets increases when there is a cap, so they are more likely to accept the proposal with a cap. So it makes one seem more reasonable to propose a cap, if one can get most of the benefits one wanted from such a system that has a cap, relative to one without it."

So is there a solution to the manipulation problem? Actually, is it even a problem? Robin Hansen and Ryan Oprea wrote another paper arguing that manipulators can improve prediction markets, by subsidizing the existing players in the markets and rewarding them for paying attention. (If a "manipulative" bet causes a sudden shift in the reported odds, opportunistic investors can place bets essentially wagering that the odds will return back to their previous level.) Economist Alex Tabarrok makes the same point here. This opportunism also means that the market shift caused by a manipulative bet usually corrects itself within a few minutes.

Presumably, if more people start to take prediction markets seriously, the incentives to manipulate them would increase. As Tabarrok adds, "prediction markets have truly arrived when people think they are worth manipulating". At the same time though, as more people start to take prediction markets seriously, presumably they'll attract more actual users, and since the amount of money required to shift the market is proportional to the amount already invested by everyone else, this means it will require larger amounts of money to shift the market odds to the same degree.

So these economists all seem to think that prediction market manipulation is a good thing, and that the prediction markets themselves are an even better good thing even when they can be manipulated, but now I'm not so sure. If people do think that market odds are worth manipulating, presumably the point is to create a self-fulfilling prophecy: People think that Romney's chances have gone up, so they become more incentivized to support him and vote for him, and soon his chances actually have gone up (although possibly not to the full extent of the boost in the manipulated market odds, so the manipulator may still lose money). If you can boost Romney's market odds even for a few minutes just by spending a few tens of thousands of dollars, how much would it cost to sustain the higher odds for several hours -- and what if those hours were at a crucial time in the election or in the news reporting cycle?

What if, contrary to my last assumption, people start to take prediction markets seriously enough to be influenced by them, but the prediction markets don't see a proportionate influx of actual investors and money -- so the cost of manipulating them remains about the same? IF prediction markets gain more influence in people's actual voting decisions, BUT those markets don't see an influx of new users, AND an election is close enough that the market odds could make a difference depending on when they're reported, AND someone spends enough to sustain the manipulated odds during crucial periods during the election... Well, that's a lot of assumptions you have to grant, but individually they're quite plausible -- and if all of them hold true, you could change the outcome of a presidential election for just a few million dollars spent on the prediction markets.

And in fact, if you successfully swung the election, you'd actually win all the wagers you had just placed -- which means that now rich manipulators can throw their election to their preferred candidate, and make a bundle. It also means that all those opportunists who usually act to "correct" the market odds deviations, by taking your free money when you start placing manipulative bets, could realize that your bets might actually change the outcome, and would decline to take your money -- which in turn means it would be even cheaper for manipulators to change the outcome, creating a self-reinforcing cycle. If smart bettors see that once a behemoth starts the market moving, the behemoth will probably win, they'll just get out of its way and clear an easier path.

The same kind of trick wouldn't normally work on the stock market -- if you're wealthy enough that you can increase the share price of a stock by buying enough of it to shift the market, then when you try to reap your profits by unloading the stock, the price will drift back down as you're selling it off. (Or if your purchases do manage to create a self-fulfilling prophecy -- your infusion of cash into the company enables them to realize their plans and become a genuine success -- well, then you're just a successful angel investor, more power to you.) But a presidential election prediction market would be analogous to a stock where if you can keep the price artificially inflated for several crucial hours on November 6th, 2012, then the price becomes permanently locked in at that point and you can sell it off for a profit, regardless of the value of the underlying company.

So, according to my own reasoning, this idea that I was so gung-ho about a few days ago, could not only be used to create a type of financial instrument that rewards manipulation more perversely than anything we've ever seen, but could also let a Saudi prince pick the next leader of the free world on a bet.

I'm not sure if there's a solution. I'm not a libertarian so I was never in favor of prediction markets as a matter of "personal liberty"; I was in favor of them because they're useful insofar as they can harness the wisdom of crowds to convey important information. But if they can be manipulated to influence real-world events, is it worth it?

In keeping with the theory that money does motivate people to think harder about such things, I'm once again offering \$100 to be split between the readers who email me the best-argued solutions to this problem -- or the best counter-argument to any point I've made here. Put "prediction markets" in the subject line. If your submission wins a portion of the award, you can either claim the money for yourself, or to be donated to a preferred charity in your name. (I reserve the right to pay out less than the allotted \$100 if there aren't enough worthy submissions, but that didn't happen last time.) Any sufficiently valuable comments are eligible even if they're not strictly counter-arguments or suggested alternatives, and I'll post a follow-up article summarizing what people send in. You can't make as much off of me, as you could have made by taking some market manipulator's intentionally losing bet on Intrade that Romney was going to win the election, but at least it's legal.

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