Even Capped Prediction Markets Can Be Manipulated

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.

Comments

Poker advice applies to all betting

[SirGarlon]

I forget where I read this, but it still rings true. "When you sit down at the poker table, look around for the sucker. If you don't see one, it's you."

Put in more concrete terms: the existence of exploits like this means there will be winners and losers. If you didn't find the exploit, you're not the winner. So why would I want to wager in a market that I can't guarantee is fair?

Re:Poker advice applies to all betting

[CdBee]

If you have a pension plan you are already wagering in a market of unknown fairness.

Re:Poker advice applies to all betting

[HornWumpus]

If you're in American SS you are already wagering in a market of known unfairness.

Re:Poker advice applies to all betting

[Maxo-Texas]

If you are alive, in any country in the world, you are wagering in a market of unknown fairness.

And it's probably unfair.

Re:Poker advice applies to all betting

[booyoh]

I forget where I read this, but it still rings true. "When you sit down at the poker table, look around for the sucker. If you don't see one, it's you."

I know that it's a quote from the movie "Rounders".

Re:Poker advice applies to all betting

[Archangel Michael]

When I sit at a poker table, and I see an sucker (not me), it is boring. Taking money from suckers is not my idea of fun, and poker is a stupid way to let a sucker depart from his cash. No, I'd much rather be the sucker at the poker table, because at least i can learn from the experience.

That phrase is over played and nuanced in ways that most people over playing it don't really understand. When I sit at a table, and I don't see a sucker, I know I'm in good company, even if I am the sucker.

So...

[M0j0_j0j0]

Money is power, to rule, to have, and to change the future.

But back to the piece i can give you an example of a system protecting itself with a cap. If you go to a Casino, you cannot use Martingale, the roulette caps you to protect the house.

WTF?

[HornWumpus]

Ether the market is large, possibly a decent predictor and more or less manipulation proof due to volume or it's small, a crappy predictor and easy to manipulate. Thinking there are enough people who just want to vote 'for the winner' and will look to a betting line for their vote is just stupid. They will vote the same as their peer group.

Also note: everything said in this manifesto also applies to futures markets. See the Hunts and Silver (or Trading Places and FCOJ) to see what real markets do to big money that thinks it's big enough to move markets for profit.

See also penny stocks to see what relatively big money does to thinly traded stocks. But nobody places any value on the 'predictions' implicit in penny stock prices.

This dude is onto a 'solution' in search of a problem.

Second Foundation

[gmuslera]

Is risky to predict something that you can affect if you know the result of that prediction. Specially if there are more players with the same tools.

Misunderstanding of stock markets

[scheme]

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.)

You have a misunderstanding of how the stock market works. Namely, if you buy company X's stock, company X will probably not get any actual money from the purchase. You're almost certainly purchasing the stock from another investor so you wouldn't be an angel investor. A company can take advantage of a rise in it's stock price by selling it's own stock or by using stock to purchase another company or something like that but that is a side effect of someone pushing up stock prices.

If the author doesn't understand a simple thing like that about financial markets, then I don't have much faith in his ability to talk cogently about markets in general.

Re:Misunderstanding of stock markets

[scheme]

[I]f you buy company X's stock, company X will probably not get any actual money from the purchase.

No, but you will raise the value of the company, which has the same effect.

Not quite, the market valuation of the company increases but that doesn't translate into money that the company can use. The company would have to either sell stock into the open market or use it as collateral or something similar in order to get money. It's just as if you owned a home and the value of the home increased after you bought it. The increase in value doesn't do much for you unless you do other stuff (refinance, get a home equity loan, etc.) to take advantage of the that increase.

Re:Misunderstanding of stock markets

[ceoyoyo]

If you raise the price of a certain company's stock by a significant amount through manipulation, that company can and probably should sell more stock, so they will get money. Essentially, you're offering the company money. You're right, they do have the option of declining, but they may very well accept.

Not really a problem...

[clong83]

Not disputing that two sites might have different odds. Just curious as to why it would be considered a problem? The disparaity should be self-correcting in at least the folloiwing two ways:

1) Savvy bettors will help even it out. If the odds are different, as you point out, a risk-free gain can be made by clever wagering. With free money on the table, people will write automated scripts to detect this sort of thing. They will bet as much as they can when this scenario happens, because hey, why not? This will in effect bring the odds closer together.

2) Typical bettors will help even it out. Suppose you think Obama is going to win. You're pretty sure of it. You check the two sites, and and see odds of 4:1 and 6:1, respectively. Why on EARTH would you place a bet on the 6:1 site? If you only have $100 to bet, it will go further on the 4:1 market. When this situation occurs, the average Obama bettors will flock to the 4:1 site, while the Romney bettors will go to the 6:1 site. The odds will converge.

If, in a scenario where someone has money to burn and continually manipulates the market, then these markets lose their predictive value, yes. However, in that case, there is easy money to be had... Might as well stop complaining and ride that train.

Re:A couple of problems in your reasoning

[nedlohs]

A higher share price (for the same number of shares, obviously) makes it easier for the company to get more money though. They can issue new stock or more likely be able to borrow more money. Though the statement you quote does seem to imply a direct transfer of cash which certainly isn't the case.

Huh?

[mcmonkey]

I'll start by admitting there's a lot of that I didn't understand. I think that's because a lot of it is gibberish.

There are some strange ideas as to what constitutes "manipulation". If I go to a store and purchase an item, I've decreased the inventory of that item at that store. That's not manipulation, that's using the market as designed. If I make a bet and the odds adjust to encourage betting against me, that's not manipulation. That's the way the system is designed. Unless the game is fixed, the house doesn't care who wins. The odds are calculated to encourage equality in wagers, so the losers pay the winners and the house takes the vig, no matter what the outcome. Changing odds isn't manipulation.

To think a prediction market would influence the outcome of a presidential election--what, because no money depends on election results now? You've been reading too many comic books or seen too many Bond films if you're worried about a US election being affected by a villain looking to win a bet. How about a villain looking to win a defense contract, get foreign aid, get a military base relocated to/from his country?

You don't have issue with a Saudi prince picking the next president of the US, but do have issue if the pick is to win a bet in a prediction market? How is that any better or worse than a Saudi prince picking picking the next president of the US to keep arm sales to the Middle East flowing, or keep aid going to Israel?

I think the above ramblings fit in to the "navel gazing" category. That you wrote about two markets with different prices for the same wager/good and didn't immediately address the opportunity for arbitrage makes me think the odds for an insightful conclusion are low.

Presupposition

[Chuckstar]

This analysis presupposes that movement in the prediction markets will cause movement in the actual election. This is not obviously true, to this humble observer. Frankly, the most recent election tends to contradict that entire line of reasoning. The overwhelming media analysis matched what was on the prediction markets (very close election with maybe Obama slightly favored). Meanwhile, it really wasn't close at all, at the end of the day.

In my opinion, it's a little silly to believe that billions in advertising, direct mail, social media, etc. was unable to close the gap, but manipulation of the Intrade trading range could swing the whole thing. (I'm not trying to claim those billions had no effect. I'm only claiming that with all the noise in the election, the signal from any manipulation of the prediction markets would likely be swamped.)

What predictions become self-fulfilling?

[roystgnr]

Systems don't generally exist in locally-unstable equilbria, because if perturbations generate their own positive feedback and if the system isn't carefully protected from even the slightest perturbation, then it will have already left the unstable equilibrium.

So, although it sounds cynically wise to claim that "people want to vote for whoever they think will win the vote", any such effect must not be very strong. The first partisan victory would have tilted the scales toward a partisan landslide which would have set up a partisan shut-out, and we'd shortly be laughing about "second-party voters who throw their votes away" the way we talk about "third-party voters" (where plurality counting really *does* create such positive feedback) today.

Re:my eyes glazed over after the third paragraph

[codewarren]

And you could have earned even more than that in the time it took you to learn all the stuff that allows you to make $100 in that amount of time.

I could have made thousands of dollars digging ditches in the time it took me to learn everything that I needed to know in order to make $100/hr, but that wouldn't have made it worth while in the long run.

I also could have made thousands of dollars in the time it took me to read some philosophy books that never netted me any money directly, but that wouldn't have made it worth it either.

Sometimes it is just worth it to learn a new concept or think in a way you hadn't thought before.

I hear this a lot from shoddy engineers (my field, but equally true in other fields) who can't be bothered to learn anything new unless it's on the company's dime because their time is somehow worth too much to take the time to learn more.

This pervasive attitude that only what makes you the most money in the here-and-now is all that's worth doing is a real problem.

Re:You can always make huge bets.

[skids]

This. And that's not the least of what worries me about this betting. Consider this scenario:

Some bigwig figures he can get a financial break from a candidate worth 10x a political contribution, based on whatever happens in a smoke-filled-room, if the candidate receiving the contribution wins.

He then spends that 10% of the desired return on campaign contributions, and then goes over to e.g. Intrade where, early in the election, odds are fairly even. He takes a bet out on the opponent of the guy he just supported of equal value to the campaign contribution.

If his campaign contribution works and the favor is curried, he's up in cash by virtue of the politician's kickback being worth more than the bet he placed. If it doesn't then he has no loss -- the money he won betting on Intrade covers the cost of the dud political contribution.

This amounts to risk-free bribery on the financial plane. (As to the risk on the legal plane for having such a conversation in a smoke-filled room, that's another matter.)

Re:You can always make huge bets.

[WaywardGeek]

Brilliant proposal. In September, when Obama was at 80% on Intrade, I asked on a blog why betters were so confident, given the likelihood of an "October surprise." The best answer was from a guy who said he was "hedging his bets" buying Obama stock. If Obama wins, he said his taxes would go up, but at least he'd make money on Intrade.

I doubt there's a better way to get rich than buying up land (or other assets), and then paying politicians to make it more valuable. You can do it in towns all across America. It's almost entirely legal. I mean, why wouldn't you contribute to the guy who's in favor of the development you seek? Why wouldn't you throw a fundraiser for him, and why would anyone think less of you for doing so? Many towns wind up with a greedy combination of politicians and developers running the place.

Another interesting thing on Intrade was watching the guy who was trying to manipulate the market dump around $2M selling Obama stock. For several days before the election he repeatedly dumped many thousands of dollars all at once, tanking the market back down to about 60%, and then let it recover. The fact that he did it so consistently, every half hour to an hour, made it clear to anyone watching trades that there would be plenty of future opportunities to buy Obama stock at $6. So why did it rapidly recover every time? Two theories: first, it's possible and maybe even likely that most betters were not watching carefully, and were simply paying whatever the price happened to be when they logged on. Second, it's possible that a pro-Obama manipulator was constantly buying through small trades, regardless of the price. I'd love to know what actually happened.

Re:What?

[AK Marc]

Irrelevant without context. Were the choices "instantaneous, 5s, 15s, 30s and 60s"? And player "preferences" from a self-reported preference is not related to what I said. Players may "prefer" to have clocks visible so they can gauge time better, but the casinos know that lack of timekeepers leads to longer play times and more profits, by providing the opposite of the player's "preference."

And a cite that's not available for viewing is not much use. I searched on that article and could only find references to it, not the paper itself.

Re:What?

[AK Marc]

I can only speculate because the cited paper is not available for review. A single line taken out of context from a paper is not worth much, especially when it looks to be a catch-sentence cited many places. Until I read the paper, I can't even verify the quote is correct. Have you actually seen the paper, or did you re-quote from one of the hundreds of quotes of that sentence I found when trying to find the paper itself?

The fact that I ask what the parameters were for the test and you dodge the question just indicates that me speculation is well founded. That, and the sentence doesn't directly address my statement, either, though the paper might, which is why I went looking for it.