What is a prediction market?

“PredictIt is a unique and exciting real money site that tests your knowledge of political events by letting you trade shares on everything from the outcome of an election to a Supreme Court decision to major world events.” But how does it work?

Let’s take an example: “Will Donald Trump be president at year-end 2019?” Visiting that page, you see two options: “Buy Yes” (91¢) and “Buy No” (10¢). But what are you actually buying? If you “Buy Yes”, you’re buying a share that reads:

Equivalently, if you “Buy No”, you’re buying a share that reads:

Actually, you don’t immediately buy such shares: you submit buy offers and sell offers at any price you like. PredictIt then matches buy offers with sell offers. Imagine that PredictIt have the following offers:

Alice offers to buy a “Yes” share for 91¢.
Bob offers to buy a “No” share for 8¢.

PredictIt can’t match these offers: they don’t add to $1. But imagine now that I submit a new offer:

Jim offers to buy a “No” share for 9¢.

Jim’s offer can be matched with Alice’s! Together, Alice and Jim pay 91¢ + 9¢ = $1 to PredictIt. PredictIt then forges two new shares, a “Yes” share for Alice and a “No” share for Jim. At the end of 2019, either Alice or Jim will be able to redeem their token for $1. So PredictIt breaks even.

Why would I buy a “No” share for 9¢? It depends on my belief in how likely it is that Trump will be president at the end of 2019. Imagine I believe the chances are 90%. In that case, a “No” share has an expected value of 10% × $1 = 10¢. So I would be happy to buy a “No” share for 9¢. Therefore, the traded value of these shares has an obvious correspondence to the probability of the event that backs them. Since “Yes” shares are trading at 90¢ and “No” shares are trading at 10¢, we can say that the market’s estimate for the probability that Trump will be president at the end of 2019 is 90-91%.

There are other sites that operate like PredictIt. They’re called betting exchanges. One example is BetFair, which is predominantly for sports betting. But, nested under their “Sports” categories is an obscure sport called “Politics”! One of the markets here is in fact the same one on PredictIt: “Trump Exit Date”. It reads:

Selection	Back	Lay
Exit in 2019	16	19
Exit in 2020 or later	1.05	1.06

This table is the same market in disguise! First, we can convert these “decimal odds” to probabilities by taking the inverse:

Selection	Back	Lay
Exit in 2019	6%	5%
Exit in 2020 or later	95%	94%

Notice that “Exit in 2019” and “Exit in 2020 or later” are opposites, just as “back” and “lay” are opposites. For example, backing “Exit in 2019” is the same as laying “Exit in 2020 or later”. The same market is represented on BetFair twice! The numbers for this work out: 6% + 94% = 100%, and 5% + 95% = 100%. PredictIt’s interface for binary (yes/no) markets removes this duplication, and makes the probabilities and prices clearer.

What’s very odd, though, is that PredictIt’s market and BetFair’s market don’t agree on the probability. The PredictIt market puts the probability at 90-91%, while the BetFair market puts the probability at 94-95%! This is a significant difference, and there is perhaps a profit to be made here ...

Tagged #betting.

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What is a prediction market?

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