For most topics, it’s probably not worth going very deep in the rabbit hole of “what does a probability mean in this context”. Yes, there are multiple kinds of uncertainty, and multiple kinds of ratio that can be expressed by a percentage. Yes, almost everything is a distribution, most not normal, and even when normal it’s not generally specified what the stddev is. Yes, probability is causally recursive (the probability that your model is appropriate causes uncertainty in the ground-level probability you hold). None of that matters, for most communication. When it does, then it’s probably best to acknowledge it and give the details that go into your beliefs, rather than the posterior belief itself.
For your example, the tradeoff between fast and careful, I doubt it can be formalized that way, even if you give yourself 10 dimensions of tradeoff based on context. “Slow is smooth, smooth is fast” is the classic physical training adage, and I can’t think of a numeric representation that helps.
For most topics, it’s probably not worth going very deep in the rabbit hole of “what does a probability mean in this context”. Yes, there are multiple kinds of uncertainty, and multiple kinds of ratio that can be expressed by a percentage. Yes, almost everything is a distribution, most not normal, and even when normal it’s not generally specified what the stddev is. Yes, probability is causally recursive (the probability that your model is appropriate causes uncertainty in the ground-level probability you hold). None of that matters, for most communication. When it does, then it’s probably best to acknowledge it and give the details that go into your beliefs, rather than the posterior belief itself.
For your example, the tradeoff between fast and careful, I doubt it can be formalized that way, even if you give yourself 10 dimensions of tradeoff based on context. “Slow is smooth, smooth is fast” is the classic physical training adage, and I can’t think of a numeric representation that helps.