I think your “boldness” is a subset of the actual value of low-confidence predictions. In the cases where a prediction is DIFFERENT between two agents, it’s pretty clear how one could structure a bet that rewards accuracy of such. Where it’s different from most, there are lots of bets available.
This generalizes—the value of a prediction is in it’s effect on a decision. If knowing something is 50% likely makes you do something different than if you thought it were 30% or 70% likely, then the prediction has improved your (expected average across worlds) outcome.
I think your “boldness” is a subset of the actual value of low-confidence predictions. In the cases where a prediction is DIFFERENT between two agents, it’s pretty clear how one could structure a bet that rewards accuracy of such. Where it’s different from most, there are lots of bets available.
This generalizes—the value of a prediction is in it’s effect on a decision. If knowing something is 50% likely makes you do something different than if you thought it were 30% or 70% likely, then the prediction has improved your (expected average across worlds) outcome.