SG

When you say "a simple set of conditional and unconditional markets", what do you have in mind?

Unconditional: "Will China invade Taiwan by 2030?"; Conditional: "If China experiences a recession any time before 2030, will China invade Taiwan by 2030?"

Your language makes me think you are referring to 1, and I agree that this will plausibly be of limited value.

Isn't estimating $P\left(Y\right)$ from $P\left(X_i\right)$ most of the value of LVPMs?! 

I think the $\log P\left(\overrightarrow{X}|\theta \right)-\log P\left(\overrightarrow{X}|\varphi \right)$ part of my scoring counts as an AMM liquidity provision?

Yes, that's correct; if the market creator is willing to issue these payouts, then they are playing the role of AMM. 

The question is how to add third-party liquidity provision to this system, i.e. where users can inject... (read more)

Thanks for writing such a thorough article! I’d be interested in seeing how LVPMs work in practice, but I must admit I’m coming from a position of extreme skepticism: Given how complicated real-world situations like the Russia/Ukraine war are, I’m skeptical a latent variable model can provide any marginal price efficiency over a simple set of conditional and unconditional markets. 

My suspicion is that if a LVPM were created for a question like “Will China invade Taiwan by 2030?” that most of the predictive power would come from people betting directly on the latent variable rather than from any model-provided updates as a result of people betting on indicator variables. The number, type,... (read more)