The thing I usually do, when asked to elicit a probability, is report a probability (usually 2 sig figs) and then also a subjective sense of how easy it would be to shift that probability by giving me more evidence / allowing me more time to think.
What is the correct technical way to summarise the latter quantity (ease of shifting), in an idealised setting?
Uh, I dunno, something like, I currently have a belief about the probability distribution of kinds of evidence I expect to encounter in the future, and from there I can compute a probability distribution over what my posterior beliefs are after updating on that evidence, then compute some summary statistic of that distribution that measures how spread out it is. An easy setting in which this can be made completely formal is repeatedly flipping a coin of unknown bias.
What is the correct technical way to summarise the latter quantity (ease of shifting), in an idealised setting?
Uh, I dunno, something like, I currently have a belief about the probability distribution of kinds of evidence I expect to encounter in the future, and from there I can compute a probability distribution over what my posterior beliefs are after updating on that evidence, then compute some summary statistic of that distribution that measures how spread out it is. An easy setting in which this can be made completely formal is repeatedly flipping a coin of unknown bias.