No, the Polymarket price does not mean we can immediately conclude what the probability of a bird flu pandemic is. We also need to know the interest rate!
Consider the following argument made by Tim Babb:
So every (non-American) reader is forced to either bet against the market or concede that their credence is at least 16%.
However, there is an important 3rd possibility. Since the market cannot resolve before August, it could also imply that Polymarket has an extremely high interest rate!
Basically, betting against bird flu is a way to turn $0.84 now into $1 later. This is exactly what a loan is! So even if a reader does not want to take that bet, it could indicate their credence is less than 16%, but they do not want to give Polymarket that loan.
This interest rate isn’t unrealistic. Payday loans (which exist) have a similar interest rate. Keep in mind that Polymarket is a cryptocurrency company.
How to fix it: don’t force YES and NO to add to $1
But if the interest rate was so high, wouldn’t that imply that the YES shares should also be lower? No! Because anyone can, at any time, combine a YES and NO into $1. So the people holding the YES shares could just be predicting a sell-off of the NO shares, which would let them collect $1 immediately. In particular, this rule forces the YES and NO to always add to $1.
If we removed this rule, we could still estimate the odds as (Yes Price):(No Price). In addition, we could get insight on the interest based on (Yes Price) + (No Price) (since anyone holding a YES and a NO is just loaning $1 to Polymarket).
In particular, if the price was still $0.16 for YES shares after this change, we could honestly conclude the credence should be at least 16%, since the only way it payouts is if the event happens (not just if there is a sell-off of the NO shares). If the interest rate is quite high, we could even conclude the credence is higher!
There are also gas fees which dramatize this effect, but this is a very important point. A prediction market price gives rise to a function from interest rates to probability ranges for which a rational investor would not bet on the market if they had a probability in that range. The larger the interest rate or the farther out the market, the bigger the range.
Probably an easy widget to make: something that takes as input the polymarket price, gas fees, and interest rate and spits out this range or probabilities.
Polymarket pays for the gas fees themselves, users don’t have to pay any.
That’s incredible.
But how do they profit? They say they don’t profit on middle eastern war markets, so they must be profiting elsewhere somehow
VC money. That disclaimer was misleading, they don’t have fees on any markets.
Also, more generally, no prediction market price means you can immediately conclude what the probability of any outcome is, because most markets we have only subjective probability (maybe this is always true but I’m trying to ignore things like fair coin flips that have agreed upon “objective” probabilities), so there is no fact of the matter about what the real probability of something happening is, only the subjective probability based on the available information.
Instead a prediction market is simply, in the ideal case, the market clearing price at which people are willing to take bets on either side of the question at this moment in time. This price represents a marginal trading point—participants with higher subjective probabilities than the market price will buy, while those with lower will sell. This is importantly different from the true probability of an outcome, and it’s a general mistake people make to treat them as such.
Then there are other factors, like you mention with interest, but also issues with insufficient volume, large traders intentionally distorting the market, etc. that can make the market clearing price less useful for inferring what subjective probability an observer should treat a possible outcome as having.
Instead a prediction market provides aggregate information that can be used for a person to make their own assessment of the subjective probability of an outcome, and if they differ from the market in their assessment they can make a bet that will be subjectively positive value in expectation, but still in no way is the market price of any prediction market the probability of any outcome.
When you say “true probability”, what do you mean?
The current hypotheses I have about what you mean are (in part non-exclusive):
You think some notion of objective, non-observer dependent probability makes sense, and that’s the true probability.
You do not think “true probability” exists, you are referencing to it to say the market price is not anything like that.
You define “true probability” a probability that observers contextually agree on (like a coin flip observed by humans who don’t know the thrower).
This doesn’t seem right. To bet on No at 16%, you need to think there’s at least 84% chance it will turn into $1. To bet on Yes at 16%, you need to think there’s at least 16% chance it’ll turn into $1.
I.e., the interest rates, fees, etc. mean that in reality, you might only be willing to buy No at 84% if you think the best available probability should be significantly lower than 16%, and only willing to buy Yes if you think the probability it significantly higher than 16%.
For the market to be trading at 16%, there need to be market participants on both sides of the trade.
Transaction costs make the market less efficient, as you can collect as much money by correcting the price, but if there is trading, then there are real bets made at the market price, with one side betting on more than the market price, and another betting on less.
In your model, why would anyone buy Yes shares at the market price? Holding a Yes share means that your No share isn’t useful anymore to produce the interest; and there’s an equal number of Yes and No shares circulating.