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 you could link me to these similar derivations I'd be interested to read them, I mostly wrote and worked through this because I couldn't find any existing ones from first principles and was sure it would be possible.

1. price = probability is a general rule for prediction markets, it's more that CPMMs can be derived from the probability function we described (no/(no+yes)).
2. The generalization I'm using in my current implementation is https://manifoldmarkets.notion.site/Multi-CPMM-62fe5b99013c4d5a87dfa84e0b8fa642, although I believe Manifold currently uses some bizarre auto arbitrage system between linked binary predictions for exclusive categories. Similarly, you can also extend CPMM by adding a parameter to allow market initialization at different probabilities, and also to allow users to inject liquidity without pushing probability towards 50%.

3. Regarding other probability functions, there are of course a whole family of constant function market makers that CPMM is a member of. As a trivial example, (no^2/(no2+yes^2)) should also match our desiderata, I believe. 

   Additionally, starting from the angle of "We have a market maker with pools of shares, how do they calculate probability from these pools" is just one approach you can take. 

   There's also the LMSR (Logarithmic Market Scoring Rule) also developed by Robin Hanson, which approaches it from an entirely different angle, starting from asking how you can score predictors based on how well they performed, and then applying this to rewards and incentive alignment in a prediction market. This is actually more reflective of the Bayesian structure of the market than CPMM is, I was largely joking when I made that claim. 

   There's also DPM (Dynamic Parimutuel), which adapts existing parimutuel betting systems to prediction markets. It does have the disadvantage of not being able to know ahead of time how much money you'll receive from your bet, only how much money you'll receive in expectation from your bet, but it has some advantages of its own.

   I have this paper saved to read through and think about, I don't really understand it yet but it also proposes a unique solution to this problem. 

   Largely, CPMM is the one I understand most intuitively out of all of these, which is part of why I'm using it in my personal prediction market implementation. 

Thanks for the questions!

I was inspired by this post and hope an image version of it will be appreciated:

Well, I don't think bear fat with honey and salt specifically would do well, due largely to supply problems. Lard is fairly neutral, but you might get good results with tallow, schmaltz, or duck fat. Another factor is that I'd expect it'd be something that'd get unpalatable if you ate a lot of it, because it's so fatty and the flavors are so strong, but if you only ate a little with crackers it tastes really good.

Did you ever end up doing this? I think this is a good idea.

I find it rather strange to list "Audere Snyder" as his name on the wiki—"Audere" is an online username rather than something he was changing his name to, he still went by Max/Maximilian to his close friends (Source: i am his ex). It'd be kind of like listing my name as "ToasterLightning Nightingale", either "Audere" or "Maximilian Snyder" would work instead.

....I know someone named Chase Novinha? I don't think it's the same person, though.

Edit: Confirmed same person, slimepriestess has said they are "safe and accounted for," and are one of the cofounders of its alignment company.

Oh, I don't mean to derail it, I'm just saying that if I pull the lever and pull it back, I still pulled it, so Omega will make their choice based off of that.

Many of these are solveable via the strategy "pull the lever and then quickly pull it back"