In case of the coin (I am assuming a coin that is making a fairly large number of bounces when it lands, so that it can’t be easily biased with trick tossing), you have high confidence in a process (coin bouncing around) which maps initial coin position and orientation into final orientation in such a way that the final distribution is almost independent on your prior for coin orientation and position. I.e. you have a highly objective probability of 0.5 , in the sense that it is not dependent on subjective, arbitrary quantification of unknown.
If you were to assign a probability of 0.7 instead, you’d have to entirely change the way physics works for the coin, or adopt a very ridiculous prior over coin’s initial orientation, which involves coin’s own motion as part of the prior.
Meanwhile, in the case of “We’re 50% sure that Strong AI will be invented by 2080.” , it’s a number entirely pulled out of your ass. You could of pulled 10%, or 90%, depending to what suits you best, without changing anything even about your knowledge of the world. Numbers pulled out of your ass have an interesting, empirically verifiable property that maximization of their products does not tend to actually result in win, irrespective of the labels that you give those numbers.
In case of the coin (I am assuming a coin that is making a fairly large number of bounces when it lands, so that it can’t be easily biased with trick tossing), you have high confidence in a process (coin bouncing around) which maps initial coin position and orientation into final orientation in such a way that the final distribution is almost independent on your prior for coin orientation and position. I.e. you have a highly objective probability of 0.5 , in the sense that it is not dependent on subjective, arbitrary quantification of unknown.
If you were to assign a probability of 0.7 instead, you’d have to entirely change the way physics works for the coin, or adopt a very ridiculous prior over coin’s initial orientation, which involves coin’s own motion as part of the prior.
Meanwhile, in the case of “We’re 50% sure that Strong AI will be invented by 2080.” , it’s a number entirely pulled out of your ass. You could of pulled 10%, or 90%, depending to what suits you best, without changing anything even about your knowledge of the world. Numbers pulled out of your ass have an interesting, empirically verifiable property that maximization of their products does not tend to actually result in win, irrespective of the labels that you give those numbers.