Yes, definitely. There is something about the presence of other agents with differing beliefs that changes the structure of the mathematics in a deep way.
P(X) is somehow very different from P(X|another agent is willing to take the bet).
How about using a “bet” against the universe instead of other agents? This is easily concretized by talking about data compression. If I do something stupid and assign probabilities badly, then I suffer from increased codelengths as a result, and vice versa. But nobody else gains or loses because of my success or failure.
Yes, definitely. There is something about the presence of other agents with differing beliefs that changes the structure of the mathematics in a deep way.
P(X) is somehow very different from P(X|another agent is willing to take the bet).
How about using a “bet” against the universe instead of other agents? This is easily concretized by talking about data compression. If I do something stupid and assign probabilities badly, then I suffer from increased codelengths as a result, and vice versa. But nobody else gains or loses because of my success or failure.
I think the idea in the post works for all bets including those offered by smart agents, stupid agents, and nature.