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.
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.