This discussion suggests, that the puzzles presented to the guesser should be associated with a “stake”—a numeric value which says how much you (the asker) care about this particular question to be answered correctly (i.e. how risk averse you are at this particular occassion). Can this be somehow be incorporated into the reward function itself or needs to be a separate input (Is “I want to know if this stock will go up or down, and I care 10 times as much about this question than about will it rain today”, the same thing as “Please estimate p for the following two questions where the reward function for the first one is f(x)=10(x-x^2) and the second is f(x)=x-x^2”? Does it somehow require some additional output channel from the guesser (“I am 90% confident that the p is 80%?” or maybe even “Here’s my distribution over the values of p \in (0,1)”) or does it somehow collapse into one dimension anyway (does “I am 90% confident that the p is 80% and 10% that it’s 70%” collaps to “I think p is 79%”? Does a distribution over p collapse to it’s expected value?).
This discussion suggests, that the puzzles presented to the guesser should be associated with a “stake”—a numeric value which says how much you (the asker) care about this particular question to be answered correctly (i.e. how risk averse you are at this particular occassion). Can this be somehow be incorporated into the reward function itself or needs to be a separate input (Is “I want to know if this stock will go up or down, and I care 10 times as much about this question than about will it rain today”, the same thing as “Please estimate p for the following two questions where the reward function for the first one is f(x)=10(x-x^2) and the second is f(x)=x-x^2”? Does it somehow require some additional output channel from the guesser (“I am 90% confident that the p is 80%?” or maybe even “Here’s my distribution over the values of p \in (0,1)”) or does it somehow collapse into one dimension anyway (does “I am 90% confident that the p is 80% and 10% that it’s 70%” collaps to “I think p is 79%”? Does a distribution over p collapse to it’s expected value?).