To generalize Bayesianism, we want to instead talk about what the right “cooperative” strategy is when a) you don’t think any of them are exactly correct, and b) when each hypothesis has goals too, not just beliefs.
Unclear to me how (b) connects to the rest of this post. Is it about each hypothesis being cautious not to bet all of their wealth, because they care about other stuff than winning the market?
The most obvious/naive/hacky solution is something like sub-probability (adds up to ≤1, so the truth might lie beyond your hypothesis space) with Jeffrey updating or updating via virtual evidence (which handles the “none of them are exactly correct” part).
Someone somewhere connected sub-probability measures with intuitionistic logic, where a market, instead of resolving at exactly one of the options, may just fail to resolve, or not resolve in a relevant time frame.
Indeed in algorithmic information theory, the lower semicomputable semimeasures are an example of “subprobabilities.” Much has been written about updating in this context.
Unclear to me how (b) connects to the rest of this post. Is it about each hypothesis being cautious not to bet all of their wealth, because they care about other stuff than winning the market?
The most obvious/naive/hacky solution is something like sub-probability (adds up to ≤1, so the truth might lie beyond your hypothesis space) with Jeffrey updating or updating via virtual evidence (which handles the “none of them are exactly correct” part).
Someone somewhere connected sub-probability measures with intuitionistic logic, where a market, instead of resolving at exactly one of the options, may just fail to resolve, or not resolve in a relevant time frame.
Indeed in algorithmic information theory, the lower semicomputable semimeasures are an example of “subprobabilities.” Much has been written about updating in this context.