Greg Mankiw calculates the probability that McCain will raise taxes, using data from the Intrade prediction markets, which have contracts for who will be elected president and for what tax rates will be in the future. It seems pretty likely.
Of course, the error on these markets is pretty high, and the calculation requires subtraction, which just amplifies these errors. But it's an interesting thought. (And I have to admit I've played around with trying to extract conditional probabilities from prediction markets myself.)
Showing posts with label prediction markets. Show all posts
Showing posts with label prediction markets. Show all posts
09 September 2008
15 May 2008
Prediction markets aren't perfect
As of right now, intrade.com reports a 7.4 percent probability that Hillary Clinton will get the Democratic nomination for President -- and an 8.0 percent probability that she will be the next President.
That seems a bit unlikely to me.
Intrade isn't an efficient market; there are tons of arbitrage opportunities like this. (Some are more subtle.)
Although if you want to get technical, buying Clinton getting the Democratic nomination (at 74 cents for a contract that pays $10) and selling Clinton winning the '08 election (at 80 cents) isn't quite risk-free -- there's a nonzero chance that she might want so badly to be President that she'd run as an independent in order to do so. And it's my understanding that short selling (which would be necessary to pull this off) isn't possible on Intrade anyway.
That seems a bit unlikely to me.
Intrade isn't an efficient market; there are tons of arbitrage opportunities like this. (Some are more subtle.)
Although if you want to get technical, buying Clinton getting the Democratic nomination (at 74 cents for a contract that pays $10) and selling Clinton winning the '08 election (at 80 cents) isn't quite risk-free -- there's a nonzero chance that she might want so badly to be President that she'd run as an independent in order to do so. And it's my understanding that short selling (which would be necessary to pull this off) isn't possible on Intrade anyway.
01 February 2008
Sometimes crowds are stupid.
Chad Orzel of uncertain principles reminds us that "The 'point spread' for a football game is set at the level required to get equal numbers of bets on the two teams." Furthermore this is not the consensus of "experts". And since gambling serves as a form of entertainment for a lot of people, there are probably a lot of people that bet on the team they like, not the team they think will beat the spread. So you can't even say that the "wisdom of crowds" applies in situations like this. Sometimes crowds are stupid, especially when they have an emotional stake in the matter. (And not just in sports betting! Consider the current housing bubble, or the dot-com bubble.)
And it's not entirely clear that bookies even always act in the way Orzel says they do; they act to maximize their expected profits, which turns out to not be the same. (See Steve Levitt's paper for more detail.) Not surprisingly, this means there's a winning strategy for betting on football, or at least it looks like there is -- bet on home underdogs, or so Levitt says. (They tend to be undervalued.) I'd do it, but I'm pretty risk-averse when it comes to my own actual money, as opposed to other people's expected-value money.
And it's not entirely clear that bookies even always act in the way Orzel says they do; they act to maximize their expected profits, which turns out to not be the same. (See Steve Levitt's paper for more detail.) Not surprisingly, this means there's a winning strategy for betting on football, or at least it looks like there is -- bet on home underdogs, or so Levitt says. (They tend to be undervalued.) I'd do it, but I'm pretty risk-averse when it comes to my own actual money, as opposed to other people's expected-value money.
29 January 2008
Prediction markets do measure something!
So I've talked on and off before about prediction markets. One of the questions one wants to ask is -- are they actually measuring something? I asked this last week.
In a comment to that post, John Armstrong has informed me of this post from the Volokh Conspiracy that shows that yes, they are. At least in the case of certain prediction markets dealing with Major League Baseball, that is. The standard contract here pays $10 if a team wins a particular game. A plot is provided which aggregates all the trades for contracts on MLB games in each ten-cent interval.
Now, let's say the Phillies and the Qankees are playing each other. (Longtime readers may recall that the reason for the Qankees' existence is because their name starts with Q, which is the letter after P. I haven't talked about them for a while, because it's not baseball season.) And let's say that I think the Phillies have a probability of 62.5% of beating the Qankees. Then I will be willing to pay up to $6.25 for the aforementioned contract, since that's the expected payout.
Now, what does it mean that this probability is 62.5%? Well, it means that if lots and lots of games like that one were played, then the Phillies would win about 62.5% of them. (The meaning of "lots and lots" and "about" can be made precise via the law of large numbers.) But that particular game will never be played again, so we can't check if my intuition is right. But we can do the next best thing -- look at all the games where people paid $6.25 for a contract for some team to win $10, and ask if that team won 62.5% of the time.
It turns out that, basically, they do. That's the point of the chart over at Volokh, which is due to Michael Abramowicz, author of the book Predictocracy: Market Mechanisms for Public and Private Decision Making. It's nice to see some evidence that at least in the world of sports -- which seems to be a good test bed for a lot of statistical and economic work, because it's possible to collect basically all the relevant data -- these things appear to actually be measuring probabilities.
In a comment to that post, John Armstrong has informed me of this post from the Volokh Conspiracy that shows that yes, they are. At least in the case of certain prediction markets dealing with Major League Baseball, that is. The standard contract here pays $10 if a team wins a particular game. A plot is provided which aggregates all the trades for contracts on MLB games in each ten-cent interval.
Now, let's say the Phillies and the Qankees are playing each other. (Longtime readers may recall that the reason for the Qankees' existence is because their name starts with Q, which is the letter after P. I haven't talked about them for a while, because it's not baseball season.) And let's say that I think the Phillies have a probability of 62.5% of beating the Qankees. Then I will be willing to pay up to $6.25 for the aforementioned contract, since that's the expected payout.
Now, what does it mean that this probability is 62.5%? Well, it means that if lots and lots of games like that one were played, then the Phillies would win about 62.5% of them. (The meaning of "lots and lots" and "about" can be made precise via the law of large numbers.) But that particular game will never be played again, so we can't check if my intuition is right. But we can do the next best thing -- look at all the games where people paid $6.25 for a contract for some team to win $10, and ask if that team won 62.5% of the time.
It turns out that, basically, they do. That's the point of the chart over at Volokh, which is due to Michael Abramowicz, author of the book Predictocracy: Market Mechanisms for Public and Private Decision Making. It's nice to see some evidence that at least in the world of sports -- which seems to be a good test bed for a lot of statistical and economic work, because it's possible to collect basically all the relevant data -- these things appear to actually be measuring probabilities.
10 January 2008
What do prediction markets measure, anyway?
From "The Caucus", the New York Times' political blog:
Not so. Intrade users were willing to pay $3.90 for a contract that will pay them $10 if Obama wins the Democratic nomination, and $5.70 for the same contract with Clinton. Most (more than 57 percent) of these individuals probably feel that Clinton is more likely to win than Obama, and if they had to bet on a single candidate would pick Clinton. What the prediction market says is that people believe there is a 57% probability that Clinton will get the nomination. What this means is another issue; does it mean that if we reran the election 100 times, Clinton would get the nomination 57 times? No, because if we reran the election 100 times, people wouldn't show up to the polls. But it does seem to mean that if someone accepted 100 such contracts on different events, paying $5.70 for each of them, they'd expect 57 of them to pay, at $10 each. If they expected less than 57 contracts to pay, then they wouldn't take the bet. (I'm assuming here that expected value is a good way to measure these things. This is probably reasonable here, because neither Clinton winning nor Clinton losing is a rare event.)
In short, the prediction market says that Clinton has a 57% probability of getting the nomination, which is different than saying that 57% of people think Clinton is the most likely to be nominated.
On Intrade, the online political prediction market, 39 percent are predicting Mr. Obama will be the Democratic nominee, while 57 percent are betting on Mrs. Clinton.(This is as of intrade's weekly newsletter from yesterday.)
Not so. Intrade users were willing to pay $3.90 for a contract that will pay them $10 if Obama wins the Democratic nomination, and $5.70 for the same contract with Clinton. Most (more than 57 percent) of these individuals probably feel that Clinton is more likely to win than Obama, and if they had to bet on a single candidate would pick Clinton. What the prediction market says is that people believe there is a 57% probability that Clinton will get the nomination. What this means is another issue; does it mean that if we reran the election 100 times, Clinton would get the nomination 57 times? No, because if we reran the election 100 times, people wouldn't show up to the polls. But it does seem to mean that if someone accepted 100 such contracts on different events, paying $5.70 for each of them, they'd expect 57 of them to pay, at $10 each. If they expected less than 57 contracts to pay, then they wouldn't take the bet. (I'm assuming here that expected value is a good way to measure these things. This is probably reasonable here, because neither Clinton winning nor Clinton losing is a rare event.)
In short, the prediction market says that Clinton has a 57% probability of getting the nomination, which is different than saying that 57% of people think Clinton is the most likely to be nominated.
03 September 2007
Which million-dollar problem will fall first?
At Inkling Markets, you can bet on which of the seven Millennium Problems will be solved first.
The choices include the option "none", which is defined as "All problems will resist a solution indefinitely."; I'm not sure who would bet on that, because "indefinitely" means no one will ever be able to claim the prize.
I wonder about the efficiency of prediction markets when most of the people involved don't know what they're talking about. People talk about "the wisdom of crowds". But do the crowds need to be at least somewhat informed? And are the people who will take part in this particular prediction market informed enough as to not be totally worthless? (I suspect, for example, that people will vote for the problem they've heard of; the story of Perelman's proof of the Poincare conjecture was pretty widely distributed in the media about a year ago. It was overshadowed by the Pluto-isn't-a-planet story which broke around the same time, though.)
Incidentally, I'd bet on Poincare, for the obvious reason that Perelman came up with a proof! The CMI hasn't announced that they're giving him the prize yet, because there's a certain waiting period involved in order to make sure that the proof becomes widely accepted, but clearly that's the one furthest along the pipeline.
So in this particular case, the fact that people have heard of the Poincare conjecture is probably because of its connection to these prizes and the proposed proof.
A more interesting prediction market would be for the second Millennium Prize to be claimed.
The choices include the option "none", which is defined as "All problems will resist a solution indefinitely."; I'm not sure who would bet on that, because "indefinitely" means no one will ever be able to claim the prize.
I wonder about the efficiency of prediction markets when most of the people involved don't know what they're talking about. People talk about "the wisdom of crowds". But do the crowds need to be at least somewhat informed? And are the people who will take part in this particular prediction market informed enough as to not be totally worthless? (I suspect, for example, that people will vote for the problem they've heard of; the story of Perelman's proof of the Poincare conjecture was pretty widely distributed in the media about a year ago. It was overshadowed by the Pluto-isn't-a-planet story which broke around the same time, though.)
Incidentally, I'd bet on Poincare, for the obvious reason that Perelman came up with a proof! The CMI hasn't announced that they're giving him the prize yet, because there's a certain waiting period involved in order to make sure that the proof becomes widely accepted, but clearly that's the one furthest along the pipeline.
So in this particular case, the fact that people have heard of the Poincare conjecture is probably because of its connection to these prizes and the proposed proof.
A more interesting prediction market would be for the second Millennium Prize to be claimed.
03 August 2007
When is number 756?
You can put money at newsfutures.com on Barry Bonds hitting 21 or more home runs this season. (He came into the season with 734, and 734 + 21 = 755, so you're betting on him at least tying Hank Aaron's career record. He's currently at 20 for the season, 754 for the career.)
Not surprisingly, the contract (which pays $100 if he does, and nothing if he doesn't) currently trades for $98.
But I found the following interesting: the page claims "The likelihood of this prediction is computed in real time by a prediction market." Note the word computed. Is what a prediction market does really "computation"? ("Right now" is the middle of the fifth of tonight's Giants-Padres game.) I suppose you could make an argument that it is, but when I hear "computation" I expect to see something like Clay Davenport's prediction -- on May 11, he predicted that Bonds had an 89% chance of hitting #756 by now, basically by guessing how many plate appearances Bonds was likely to get and how likely he is to hit a home run in each plate apparance -- although that builds in an explicit and somewhat ad hoc allowance for injuries, so I'm not sure how accurate it is. But when I hear "compute" I expect the work to be going on in a single silicon-based entity, not a distributed mess of carbon-based ones.
Incidentally, it was this prediction by Davenport that inspired my predictions about the Phillies' ten thousandth loss, which came on July 15, a few days earlier than I expected it.
At the freakonomics blog, you can pick the pitcher you think will give up Bonds' 756th home run. If you guess right you get a signed copy of Freakonomics. Most of the plausible pitchers (i. e. anybody on the pitching staffs of the teams the Giants are playing in the near future) are already taken, though.
Not surprisingly, the contract (which pays $100 if he does, and nothing if he doesn't) currently trades for $98.
But I found the following interesting: the page claims "The likelihood of this prediction is computed in real time by a prediction market." Note the word computed. Is what a prediction market does really "computation"? ("Right now" is the middle of the fifth of tonight's Giants-Padres game.) I suppose you could make an argument that it is, but when I hear "computation" I expect to see something like Clay Davenport's prediction -- on May 11, he predicted that Bonds had an 89% chance of hitting #756 by now, basically by guessing how many plate appearances Bonds was likely to get and how likely he is to hit a home run in each plate apparance -- although that builds in an explicit and somewhat ad hoc allowance for injuries, so I'm not sure how accurate it is. But when I hear "compute" I expect the work to be going on in a single silicon-based entity, not a distributed mess of carbon-based ones.
Incidentally, it was this prediction by Davenport that inspired my predictions about the Phillies' ten thousandth loss, which came on July 15, a few days earlier than I expected it.
At the freakonomics blog, you can pick the pitcher you think will give up Bonds' 756th home run. If you guess right you get a signed copy of Freakonomics. Most of the plausible pitchers (i. e. anybody on the pitching staffs of the teams the Giants are playing in the near future) are already taken, though.
20 July 2007
Harry Potter and the pre-orders
As I wondered earlier: there are prediction markets in which you can bet on Harry Potter living. NewsFutures puts his probability of living at [redacted; click on the link if you want to know]. You can see a chart going back to March here. It's currently half past six in England; the answer will be publicly available in five and a half hours. Interestingly, the contract pays $100 (of virtual money) if Harry lives, $0 if Harry doesn't live, and $50 in "any other case".
Also, Amazon.com reveals that the Harry-est town in America is Falls Church, Virginia, as measured by the largest number of pre-orders per capita. (Only towns with more than 5,000 people were included.) The top twenty-two cities on this list are all within fifty-two miles of a major city. (Why 52? I was saying 50 at first, but Fredericksburg, VA was just outside the cutoff.) They are:
The Harry-est states in America is a different story; you'd expect from the first list that the states with lots of suburban population -- New Jersey or Virginia comes to mind, both states with no really large city within their borders but with one just outside -- would appear high up? Perhaps -- but the winner is actually the District of Columbia. (As a city, however, D.C. doesn't even make the top 100.) The six New England states are all high up -- Vermont is the highest at #2, Rhode Island the lowest at #16.
The moral of the story is that depending on how you sample you get very different results. Of course, the whole "Harry-est cities/states in America" thing is just a silly Amazon promotion.
Also, Amazon.com reveals that the Harry-est town in America is Falls Church, Virginia, as measured by the largest number of pre-orders per capita. (Only towns with more than 5,000 people were included.) The top twenty-two cities on this list are all within fifty-two miles of a major city. (Why 52? I was saying 50 at first, but Fredericksburg, VA was just outside the cutoff.) They are:
- Falls Church, VA (Washington, 10 miles)
- Gig Harbor, WA (Seattle 44)
- Fairfax, VA (Washington 21)
- Vienna, VA (Washington 16)
- Katy, TX (Houston 29)
- Media, PA (Philadelphia 22)
- Issaquah, WA (Seattle 17)
- Snohomish, WA (Seattle 31)
- Doylestown, PA (Philadelphia 40)
- Fairport, NY (Rochester 11)
- Woodinville, WA (Seattle 20)
- Princeton, NJ (Philadelphia 45; New York 51)
- Webster, NY (Rochester 15)
- West Chester, PA (Philadelphia 37)
- Williamsville, NY (Buffalo 11)
- Fredericksburg, VA (Washington 52)
- Port Orchard, WA (Seattle 22)
- Decatur, GA (Atlanta 6)
- Larchmont, NY (New York 27)
- Downingtown, PA (Philadelphia 39)
- Canton, GA (Atlanta 41)
- Woodstock, GA (Atlanta 31)
The Harry-est states in America is a different story; you'd expect from the first list that the states with lots of suburban population -- New Jersey or Virginia comes to mind, both states with no really large city within their borders but with one just outside -- would appear high up? Perhaps -- but the winner is actually the District of Columbia. (As a city, however, D.C. doesn't even make the top 100.) The six New England states are all high up -- Vermont is the highest at #2, Rhode Island the lowest at #16.
The moral of the story is that depending on how you sample you get very different results. Of course, the whole "Harry-est cities/states in America" thing is just a silly Amazon promotion.
18 July 2007
what happens to The Boy Who Lived? (no spoilers.)
At MSNBC's "iPredict" feature, you can vote on whether you think Harry Potter will live. (No spoilers.) There realy hasn't been any significant fluctuation since the voting started in early June.
This leads me to believe that people aren't taking the spoilers that are out there seriously (although I haven't read them, and I do not wish to), because if people knew whether Harry Potter was going to live or die you'd see a trend in one direction or the other. Then again, I suspect that prediction markets which involve actual money changing hands are better at predicting things, because people have a bit more incentive to make a correct prediction. I am not going to go seeking such prediction markets because I don't want to know the answer, and I have enough faith in prediction markets that I suspect they may know!
For what it's worth, I think he'll live -- I just don't see J. K. Rowling killing off a character loved by millions (although then again, she did kill off Dumbledore...) -- but I think that at some point it'll look like Harry will die. I don't think that he'll die and then be resurrected on the third day, but it would be kind of interesting if that happened.
What might be interesting to see is the probability, at any given moment in the book, that Harry will live. I'm inspired by the graphs at fangraphs.com, which show the probability of each team winning a baseball game after each plate appearance. (I swear this isn't a baseball blog!) It's not entirely clear what this means, though. The baseball probabilities are computed by looking at a sample of how things have gone in past games; there is only one Harry Potter. Could you compare it to other books? Could someone halfway through the book think "hmm, in most of the books I've read where it's been like this, the protagonist dies, so things don't going to look good for Harry?" But of course this couldn't be made into a prediction market, because the whole book is released at a single moment.
But what if you had some sort of medium where the story is released in pieces? Prediction markets for plot details of television shows -- even if you didn't let people trade during the episode's airing (because many TV shows air at different times in different places) -- could be interesting.
This leads me to believe that people aren't taking the spoilers that are out there seriously (although I haven't read them, and I do not wish to), because if people knew whether Harry Potter was going to live or die you'd see a trend in one direction or the other. Then again, I suspect that prediction markets which involve actual money changing hands are better at predicting things, because people have a bit more incentive to make a correct prediction. I am not going to go seeking such prediction markets because I don't want to know the answer, and I have enough faith in prediction markets that I suspect they may know!
For what it's worth, I think he'll live -- I just don't see J. K. Rowling killing off a character loved by millions (although then again, she did kill off Dumbledore...) -- but I think that at some point it'll look like Harry will die. I don't think that he'll die and then be resurrected on the third day, but it would be kind of interesting if that happened.
What might be interesting to see is the probability, at any given moment in the book, that Harry will live. I'm inspired by the graphs at fangraphs.com, which show the probability of each team winning a baseball game after each plate appearance. (I swear this isn't a baseball blog!) It's not entirely clear what this means, though. The baseball probabilities are computed by looking at a sample of how things have gone in past games; there is only one Harry Potter. Could you compare it to other books? Could someone halfway through the book think "hmm, in most of the books I've read where it's been like this, the protagonist dies, so things don't going to look good for Harry?" But of course this couldn't be made into a prediction market, because the whole book is released at a single moment.
But what if you had some sort of medium where the story is released in pieces? Prediction markets for plot details of television shows -- even if you didn't let people trade during the episode's airing (because many TV shows air at different times in different places) -- could be interesting.
26 June 2007
betting on the iPhone
You can bet on everything these days!
BetUS.com -- which appears to be mostly a sports betting site -- is giving odds on various iPhone-related events. (I came to this via Marginal Revolution.)
I can't get inside, but livescience.com (the first link above) claims that BetUS.com is offering the following odds:
Consumers are reported camping out waiting for an iPhone—3/1
At first glance, I'd take this bet. People camp out now for product launches, it's What They Do in this consumer culture. And the sort of people who do that are, to some extent, Apple's target market. However, the iPhone is being released at 6pm local time on Friday. And the iPhone is expensive -- $500 just for the physical device, and then depending on who you believe somewhere around $80 for the service -- so you've got to think that maybe the people buying them will have jobs. (I'm sure there's a Steve Jobs joke in here somewhere, but I can't find it.)
Apple’s stock jumps at least 10% in value in regards to the price on 6/30/07—1/2
Technically, this can't happen. Why? Because June 30 is a Saturday. Stocks don't trade on Saturdays. But assuming they mean the next trading day after the release -- that is, Monday, July 2nd -- this would be an interesting disproof of the efficient market hypothesis. This hypothesis claims that the price of a traded asset -- such as Apple stock -- reflects all the knowledge that's available about the company.
On the other hand, Apple has been trading around 125 lately; it was at 90 as recently as mid-April. Either a lot of information about Apple has suddenly come out, or investors are just crazy. Or both.
Consumers pay at least three times the original price ($1,500) on ebay - 2/1
Hard to call. Did consumers learn from when people tried to flip PS3s and Xboxes last winter? Sure, some people pulled it off, but a lot got stuck with them.
iPhone spontaneously combusts—150/1
I hope this is a joke.
Judging from the little information I have, though, and the fact that the odds are simple integer ratios, I'm guessing that these odds don't move, but are set by BetUS.com. I was expecting something like tradesports.com or intrade.com, in which people can buy and sell "contracts" on various events -- these are rapidly emerging as an interesting means of predicting the probability of various "complicated" events, where one can't come up with a simple model to make a decent guess at the probability of an event. We expect that, if people are willing to pay $25 for a "contract" that pays out $100 if people are reported camping out waiting for an iPhone, then if we could repeat this experiment over and over again, one time out of four there would be people camping out. (The question of what this even means is kind of tricky, though, because there aren't going to be three more iPhones. Tonight I prefer the interpretation of complicated probabilities like these in terms of wagers, but that could always change.)
edit, 5:08 pm: People are already camping out. Reuters reports that as of this morning, there were four people in line outside the Apple Store on 5th Avenue in Manhattan.
BetUS.com -- which appears to be mostly a sports betting site -- is giving odds on various iPhone-related events. (I came to this via Marginal Revolution.)
I can't get inside, but livescience.com (the first link above) claims that BetUS.com is offering the following odds:
Consumers are reported camping out waiting for an iPhone—3/1
At first glance, I'd take this bet. People camp out now for product launches, it's What They Do in this consumer culture. And the sort of people who do that are, to some extent, Apple's target market. However, the iPhone is being released at 6pm local time on Friday. And the iPhone is expensive -- $500 just for the physical device, and then depending on who you believe somewhere around $80 for the service -- so you've got to think that maybe the people buying them will have jobs. (I'm sure there's a Steve Jobs joke in here somewhere, but I can't find it.)
Apple’s stock jumps at least 10% in value in regards to the price on 6/30/07—1/2
Technically, this can't happen. Why? Because June 30 is a Saturday. Stocks don't trade on Saturdays. But assuming they mean the next trading day after the release -- that is, Monday, July 2nd -- this would be an interesting disproof of the efficient market hypothesis. This hypothesis claims that the price of a traded asset -- such as Apple stock -- reflects all the knowledge that's available about the company.
On the other hand, Apple has been trading around 125 lately; it was at 90 as recently as mid-April. Either a lot of information about Apple has suddenly come out, or investors are just crazy. Or both.
Consumers pay at least three times the original price ($1,500) on ebay - 2/1
Hard to call. Did consumers learn from when people tried to flip PS3s and Xboxes last winter? Sure, some people pulled it off, but a lot got stuck with them.
iPhone spontaneously combusts—150/1
I hope this is a joke.
Judging from the little information I have, though, and the fact that the odds are simple integer ratios, I'm guessing that these odds don't move, but are set by BetUS.com. I was expecting something like tradesports.com or intrade.com, in which people can buy and sell "contracts" on various events -- these are rapidly emerging as an interesting means of predicting the probability of various "complicated" events, where one can't come up with a simple model to make a decent guess at the probability of an event. We expect that, if people are willing to pay $25 for a "contract" that pays out $100 if people are reported camping out waiting for an iPhone, then if we could repeat this experiment over and over again, one time out of four there would be people camping out. (The question of what this even means is kind of tricky, though, because there aren't going to be three more iPhones. Tonight I prefer the interpretation of complicated probabilities like these in terms of wagers, but that could always change.)
edit, 5:08 pm: People are already camping out. Reuters reports that as of this morning, there were four people in line outside the Apple Store on 5th Avenue in Manhattan.
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