Prediction markets
I haven’t posted for a while, but all that’s about to change. My longtime friend David Goodman recently managed to get an article in Sunday’s Times, so I should at least be able to churn out a few blog posts.
According to Dave (and his team of experts) the last 70 years may soon be viewed as an abnormality in the world of political prediction. Today we rely heavily on polling data, but back before 1930, betting on wall street was all the rage. During the 1916 election of Woodrow Wilson over $160 million (in today’s dollars) was wagered in Wall Street’s outdoor curb exchange (this later became the American Stock Exchange).
With money at stake, newspapers could predict elections simply by reporting how the masses were betting. This same idea is gaining prominence today. Dublin-based InTrade, for example, hosted close to $25 million dollars in bets for the US 2004 election (their founder, who also started TradeSports, recently engaged in q & a over at freakonomics.com).
InTrade (and TradeSports) is just one an example of a prediction market, a financial exchange in which the final value a position is tied to the occurrence of some real-world event. Another example is Predictify (also the focus of a recent freakonomics post), a new website where you don’t even need to wager to make money (although it’s too soon to tell if it actually works).
Since Dave didn’t have space, I thought I could supplement his article by briefly explaining how a prediction market works. For example, suppose you want to predict which candidate will win an election, Ms. X or Mr. Y.
A simple approach is to allow individuals to buy a share of the winnings if a particular candidate wins. In this case, you can choose to spend d dollars on Ms. X, and if Ms. X wins, you’ll get a share of the total amount bet on either candidate. If T dollars were bet in total, M of those dollars were bet on Ms. X, you’ll get d*T/M dollars.
The nice thing about this is that before the election, M/T can be interpreted as the probability Ms. X wins. Why is this? Well suppose M and T are both big numbers, and M/T is .15. If the election is about to occur, and you think Ms. X has a 20 percent chance of winning, the amount you expect to gain by betting 1 dollar on Ms. X is .2*[your payoff if Ms. X wins] = .2*T/(M + 1).
We assumed (M/T) = .15, and both M and T are large, so T/(M + 1) is very close to 1/(.15). This means that by betting a dollar on Ms. X, you expect to gain at least .2/.15 > 1 dollars. In other words, you expect to make money by betting on Ms. X. More generally, when M/T is less than Ms. X’s true probability of winning, an informed investor has the opportunity to make money by betting on Ms. X. Similarly if M/T is too large, an informed investor can bet on Mr. Y.
This all sounds great, but there’s a problem. Before the election, M and T change over time. If you notice one week before the election that M/T is way too small, when can invest a dollar in Ms. X, but your final payout is tied to the final values of M and T once the election takes. Unless the election is about to take place, you have no incentive to invest.
To fix this, prediction markets don’t simply act as betting pools, they create shares for a given event, and allow investors to buy the shares at a price depending on M/T. In our election example, a prediction market can initially sell each candidates shares for $0.50. After a while, when M and N dollars have been spent on Ms. X and Mr. Y, respectively, and T = M + N dollars have been spent in total, a Ms. X share is priced at M/T, and a Ms. Y share at N/T. Once the election takes place, if Ms. X wins, a given share of her stock originally bought for d dollars is worth d*T/M, and a share of Mr. Y stock is worthless.
Now let’s check that this works. As before, assume Ms. X has a .2 chance of winning. When the election is about to occur, the expected return on a Ms. Y share is .2*(M/T)*(T/M), so if M/T is less than .2, you should still buy her stock (and similarly if it is greater than .2, you should buy Mr. Y stock). Now observe that, unlike above, you should still buy even if the election is a week away.
If you expect M/T to eventually approach .2, but shares are selling for $0.15, you can still expect to profit. Even if you are wrong and M/T drops further, you’ll make even more money if Ms. X wins. Finally, if M/T starts to increase beyond .2, you can make money by selling your shares for a profit. In conclusion, the market works! Capitalists rejoice!
In the end, there’s actually much more flexibility regarding how a prediction market can operate (and other problems to worry about). If all you want to predict is the outcome of an event, as oppose to each outcome’s probability, money isn’t even required. All investors really need is a good incentive to choose correctly. Back in the days of the curb exchange, non-monetary bets were more than acceptable. Here in Providence the classic “roll a peanut up a steep hill with a wooden toothpick”-wager seems most appropriate.