I will try to dig up some references for you. Sorry it really was a small side project and has been several years.
Ah so I can’t imagine a probability function for that market that isn’t yy+n. y2y2+n2 is a fine pricing function that doesn’t appear to adhere to the rules of probability theory. If I try to compose two y2y2+n2markets, one conditional on the other, then can I multiply their prices to find the joint probability? Does this violate “price=probability”?
”price=probability is a general rule for prediction markets” is a very interesting claim. Seems obvious, but then you have to ask yourself whose probability?
I’m familiar with some of those operations (I’ve skimmed the Boyd paper). Unfortunately, there are a lot of different ways of expressing the same constraints, so I can’t immediately tell whether Manifold’s implementation is equivalent to what I had imagined.
Thanks for your answers, I’ll look into some of the other ideas you referenced.
What I mean is that the if the AMM estimates the probability at .75, it should charge .75 for a marginal YES share, by law of expected utility. I don’t think a different probability function should alter the probabulity theory, just change the pricing curve.
If “price=probability”, then changing the pricing curve is equivalent to changing how the AMM updates its probability estimates (on evidence of buy/sell orders).
Yes, but it just affects how liquidity is allocated, and it doesn’t just affect how the AMM updates, it affects how users trade as well since they respond to that, either way they’d want to bet to their true probability. So changing the pricing curve is largely a matter of market dynamics and incentives, rather than actually affecting the probabilistic structure.
I will try to dig up some references for you. Sorry it really was a small side project and has been several years.
Ah so I can’t imagine a probability function for that market that isn’t yy+n. y2y2+n2 is a fine pricing function that doesn’t appear to adhere to the rules of probability theory. If I try to compose two y2y2+n2markets, one conditional on the other, then can I multiply their prices to find the joint probability? Does this violate “price=probability”?
”price=probability is a general rule for prediction markets” is a very interesting claim. Seems obvious, but then you have to ask yourself whose probability?
I’m familiar with some of those operations (I’ve skimmed the Boyd paper). Unfortunately, there are a lot of different ways of expressing the same constraints, so I can’t immediately tell whether Manifold’s implementation is equivalent to what I had imagined.
Thanks for your answers, I’ll look into some of the other ideas you referenced.
What I mean is that the if the AMM estimates the probability at .75, it should charge .75 for a marginal YES share, by law of expected utility. I don’t think a different probability function should alter the probabulity theory, just change the pricing curve.
If “price=probability”, then changing the pricing curve is equivalent to changing how the AMM updates its probability estimates (on evidence of buy/sell orders).
Yes, but it just affects how liquidity is allocated, and it doesn’t just affect how the AMM updates, it affects how users trade as well since they respond to that, either way they’d want to bet to their true probability. So changing the pricing curve is largely a matter of market dynamics and incentives, rather than actually affecting the probabilistic structure.