While reading p vs. np for dummies recently, I was really intrigued by Scott’s probabilistic reasoning about math questions. It occurred to me that of all science areas, math seems like a really fruitful area for betting markets, because compared to areas like psychology where you have to argue with people what results of studies actually mean, it seems mathematicians are better at getting at a consensus (it could potentially also help to uncover areas where this is not the case?)
I also just remembered that There are a few math-related questions on Metaculus, but their aggregation method seemed badly suited for math questions (changed my mind after thinking of considerations below), because I’d expect thinking more about the question to have more payoff in this area, so it seems desirable for people to be able to stake more money.
So why are there no betting markets for math conjectures? Why would it be a bad idea?
Some ideas:
The cutting edge is hard to understand and probably also not the most useful stuff. Results that are actually uncertain take a long time for lay people to understand.
Results that haven’t been solved for a long time, on the other hand, probably will continue to do so for a long time.
This is an issue because it skews prices and incentives in ways that lead to “wrong” prices. I won’t bother correcting the price for p!=np if it is not significantly off, if I can make more money by just investing it.
In Math you can always ask more arbitrary questions and most of them would never be resolved, because no one bothers with them. (It would be hard to keep only relevant questions)
The intuition behind the math problems and the ideas behind the proofs are the things people are actually interested in. When someone makes a conjecture, the intuition that led her to it is actually the interesting bit. Pure probabilities are bad for transferring these intuitions.
While reading p vs. np for dummies recently, I was really intrigued by Scott’s probabilistic reasoning about math questions. It occurred to me that of all science areas, math seems like a really fruitful area for betting markets, because compared to areas like psychology where you have to argue with people what results of studies actually mean, it seems mathematicians are better at getting at a consensus (it could potentially also help to uncover areas where this is not the case?) I also just remembered that There are a few math-related questions on Metaculus, but their aggregation method seemed badly suited for math questions (changed my mind after thinking of considerations below), because I’d expect thinking more about the question to have more payoff in this area, so it seems desirable for people to be able to stake more money.
So why are there no betting markets for math conjectures? Why would it be a bad idea? Some ideas:
The cutting edge is hard to understand and probably also not the most useful stuff. Results that are actually uncertain take a long time for lay people to understand.
Results that haven’t been solved for a long time, on the other hand, probably will continue to do so for a long time. This is an issue because it skews prices and incentives in ways that lead to “wrong” prices. I won’t bother correcting the price for p!=np if it is not significantly off, if I can make more money by just investing it.
In Math you can always ask more arbitrary questions and most of them would never be resolved, because no one bothers with them. (It would be hard to keep only relevant questions)
The intuition behind the math problems and the ideas behind the proofs are the things people are actually interested in. When someone makes a conjecture, the intuition that led her to it is actually the interesting bit. Pure probabilities are bad for transferring these intuitions.