I take it to mean that if Tim is acting optimally and has to take a bet on the outcome 1:4 would be the point where both sides of the bad are equally profitable to him while if the odds deviate from 1:4 one side of the bet would be preferable to him.
One thing this wouldn’t take into account is strength or weight of evidence. If Tim knew that all of the listeners had far more information than him, and thus probably could produce better estimates of X, then it seems strange for Tim to tell them that the chances are 20%.
I guess my claim that saying “There is a 20% probability that X will occur” is more similar to: “I’m quite confident that the chances are 20%, and you should generally be too” than it is to, “I personally believe that the chances are 20%, but have no idea o how much that should update the rest of you.”
I take it to mean that if Tim is acting optimally and has to take a bet on the outcome 1:4 would be the point where both sides of the bad are equally profitable to him while if the odds deviate from 1:4 one side of the bet would be preferable to him.
One thing this wouldn’t take into account is strength or weight of evidence. If Tim knew that all of the listeners had far more information than him, and thus probably could produce better estimates of X, then it seems strange for Tim to tell them that the chances are 20%.
I guess my claim that saying “There is a 20% probability that X will occur” is more similar to: “I’m quite confident that the chances are 20%, and you should generally be too” than it is to, “I personally believe that the chances are 20%, but have no idea o how much that should update the rest of you.”