The Nonlinear Library LW - Prediction Markets aren't Magic by SimonM
Dec 21, 2023
06:01
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Prediction Markets aren't Magic, published by SimonM on December 21, 2023 on LessWrong.
One common theme which I come across quite a bit in the prediction market space is:
Prediction markets would solve [x][1]
And the proposal for "solving" [x] is:
Set up prediction market
???
Profit
These people need to consider the idea that "prediction markets aren't as popular as think think because they aren't as good as you think". (And I say this as a person who is a big fan of prediction markets!) If you think prediction markets are valuable it's likely because you think they price things well - probably due to some kind of market efficiency... well why hasn't that efficiency led to the creation of prediction markets...
Where are all the prediction markets?
Maybe if prediction markets aren't popular for your specific usecase, it's because prediction markets are less efficient.
The cost to markets of acquiring information is high
Prediction markets are very good at enabling a diverse group of participants to ensemble their forecasts in sensible ways. However, they are not very good at compensating participants[2].
Simple example - all information from same source
For example, consider a market on a coin-flip, with some unknown probability p of heads. The market will resolve based on the outcome of a single coin flip. However, the coin is available for anyone else to come over and test, but there's a catch. You have to pay to flip the coin. How many times would you flip the coin?
To make this simplified model even simpler, lets assume that participants will always take as much profit from the market as possible (eg they are risk neutral or the size of the market is small relative to their bank-roll). Under these assumptions, after each flip the partipants will move the market price to their new posterior.
Well, after n flips the market price is going to be μn=1nni=11ith flip is success (this will depend on the initial prior, we can do all these calculations explicitly with a beta distribution but it doesn't alter the result). How much should we expect this to move by paying for an additional sample?
So we should expect to move the mean by O(1n), therefore our pnl will be will be O(1n2)[3]. So people will keep collecting samples for the market while costn2>liquidity. Therefore we can see that roughly speaking we will obtain O(liquiditycost) samples. But this is strictly much worse than if rather than seeding the market the liquidity provider just went out and collected liquiditycost
samples.
One other thing to notice about this model of the prediction market is that early participants benefit much more than later participants. (This appears to be a general "problem" with markets where the subsidies accrue to the fastest players, rather than those adding the most information[4]).
Additional theoretical justification
In our first example, we have given all the advantages to the market. There is one source of information, it is passed immediately between all participants (if there was only one participant the market would work just as well), the cost of collecting data is known upfront. Any duplication of effort is inefficient from the point of view of the market subsidizer.
From the point of view of any participant, their participation must be EV positive (in effort terms), but their EV must be equal to the EV lost by the market subsider. Therefore any duplication of effort must be a direct cost born by the subsidiser.
Concrete Example - Manifold.Love
To come back to the example which convinced me this article needed writing: Manifold.Love. I am assuming you're familiar with the premise. "Dating app powered by prediction markets".
My (simplified) model for dating apps, is roughly speaking:
Collect data on users (pictures, profile text, age, gender, location etc)
Collect more data ...
One common theme which I come across quite a bit in the prediction market space is:
Prediction markets would solve [x][1]
And the proposal for "solving" [x] is:
Set up prediction market
???
Profit
These people need to consider the idea that "prediction markets aren't as popular as think think because they aren't as good as you think". (And I say this as a person who is a big fan of prediction markets!) If you think prediction markets are valuable it's likely because you think they price things well - probably due to some kind of market efficiency... well why hasn't that efficiency led to the creation of prediction markets...
Where are all the prediction markets?
Maybe if prediction markets aren't popular for your specific usecase, it's because prediction markets are less efficient.
The cost to markets of acquiring information is high
Prediction markets are very good at enabling a diverse group of participants to ensemble their forecasts in sensible ways. However, they are not very good at compensating participants[2].
Simple example - all information from same source
For example, consider a market on a coin-flip, with some unknown probability p of heads. The market will resolve based on the outcome of a single coin flip. However, the coin is available for anyone else to come over and test, but there's a catch. You have to pay to flip the coin. How many times would you flip the coin?
To make this simplified model even simpler, lets assume that participants will always take as much profit from the market as possible (eg they are risk neutral or the size of the market is small relative to their bank-roll). Under these assumptions, after each flip the partipants will move the market price to their new posterior.
Well, after n flips the market price is going to be μn=1nni=11ith flip is success (this will depend on the initial prior, we can do all these calculations explicitly with a beta distribution but it doesn't alter the result). How much should we expect this to move by paying for an additional sample?
So we should expect to move the mean by O(1n), therefore our pnl will be will be O(1n2)[3]. So people will keep collecting samples for the market while costn2>liquidity. Therefore we can see that roughly speaking we will obtain O(liquiditycost) samples. But this is strictly much worse than if rather than seeding the market the liquidity provider just went out and collected liquiditycost
samples.
One other thing to notice about this model of the prediction market is that early participants benefit much more than later participants. (This appears to be a general "problem" with markets where the subsidies accrue to the fastest players, rather than those adding the most information[4]).
Additional theoretical justification
In our first example, we have given all the advantages to the market. There is one source of information, it is passed immediately between all participants (if there was only one participant the market would work just as well), the cost of collecting data is known upfront. Any duplication of effort is inefficient from the point of view of the market subsidizer.
From the point of view of any participant, their participation must be EV positive (in effort terms), but their EV must be equal to the EV lost by the market subsider. Therefore any duplication of effort must be a direct cost born by the subsidiser.
Concrete Example - Manifold.Love
To come back to the example which convinced me this article needed writing: Manifold.Love. I am assuming you're familiar with the premise. "Dating app powered by prediction markets".
My (simplified) model for dating apps, is roughly speaking:
Collect data on users (pictures, profile text, age, gender, location etc)
Collect more data ...