Yes, we can replace with E_i, and then argue that traders with accurate beliefs will accumulate more money over time, making market estimates more accurate in the limit
There’s a chicken-and-egg problem here. You’re assuming that markets are causal (meaning traders that are better at estimating causal probabilities) and then using that assumption to prove that markets are causal.
There’s a chicken-and-egg problem here[...] and then using that assumption to prove that markets are causal.
That argument was more about accomodating “different traders with different beliefs”, but here’s an independent argument for market being causal:
When I cause a particular effect/outcome, that means I mediate the influence between the cause of my action and the effect/outcome of my action, the cause of my action is conditionally independent of the effect of my action given me
Futarchy is a similar case: There may be many causes that influence market prices, which in turn determines the decision chosen, & market prices mediate the influence between the cause of market prices (e.g. different traders’ beliefs) and the decision chosen. Any information can only influence what decision will be chosen through influencing the market prices. This seems like what it means for market to be causal (In a bayesnet, the decision chosen will literally only have market prices as the parent, assuming we commit to using futarchy to choose decisions).
There’s a chicken-and-egg problem here. You’re assuming that markets are causal (meaning traders that are better at estimating causal probabilities) and then using that assumption to prove that markets are causal.
That argument was more about accomodating “different traders with different beliefs”, but here’s an independent argument for market being causal:
When I cause a particular effect/outcome, that means I mediate the influence between the cause of my action and the effect/outcome of my action, the cause of my action is conditionally independent of the effect of my action given me
Futarchy is a similar case: There may be many causes that influence market prices, which in turn determines the decision chosen, & market prices mediate the influence between the cause of market prices (e.g. different traders’ beliefs) and the decision chosen. Any information can only influence what decision will be chosen through influencing the market prices. This seems like what it means for market to be causal (In a bayesnet, the decision chosen will literally only have market prices as the parent, assuming we commit to using futarchy to choose decisions).