Yup! The subscript is the counterfactual we’re working in, so you can think of it as a sort of conditional pricing.
The prices aren’t necessarily unique, we set them anew on each turn, and there may be multiple valid prices for each turn. Basically, the prices are just set so that the supertrader doesn’t earn money in any of the “possible” worlds that we might be in. Monotonicity is just “the price of a set of possibilities is greater than the price of a subset of possibilities”
Should PA(X) be thought of as P(X | A)? (Note this is conditional pricing, not conditional probability.)
Given a list of statements, their length, and whether they prove each other, can their prices all be determined?
Yup! The subscript is the counterfactual we’re working in, so you can think of it as a sort of conditional pricing.
The prices aren’t necessarily unique, we set them anew on each turn, and there may be multiple valid prices for each turn. Basically, the prices are just set so that the supertrader doesn’t earn money in any of the “possible” worlds that we might be in. Monotonicity is just “the price of a set of possibilities is greater than the price of a subset of possibilities”