Regarding your examples with banks and donations, when I imagine myself in such situations, I still don’t see how numbers derived from my own common-sense reasoning can be useful. I can see myself making a decision based a simple common-sense impression that one bank looks less shady, or that it’s bigger and thus more likely to be bailed out, etc. Similarly, I could act on a vague impression that one political candidacy I’d favor is far more hopeless than another, and so on. On the other hand, I could also judge from the results of calculations based on numbers from real expert input, like actuary tables for failures of banks of various types, or the poll numbers for elections, etc.
What I cannot imagine, however, is doing anything sensible and useful with probabilities dreamed up from vague common-sense impressions. For example, looking at a bank, getting the impression that it’s reputable and solid, and then saying, “What’s the probability it will fail before time T? Um.. seems really unlikely… let’s say 0.1%.”, and then using this number to calculate my expected returns.
Now, regarding your example with driving vs. fires, suppose I simply say: “Looking at the statistical tables, it is far more likely to be killed by a car accident than a fire. I don’t see any way in which I’m exceptional in my exposure to either, so if I want to make myself safer, it would be stupid to invest more effort in reducing the chance of fire than in more careful driving.” What precisely have you gained with your calculation relative to this plain and clear English statement?
In particular, what is the significance of these subjectively estimated probabilities like p=10^-1 in step 2? What more does this number tell us than a simple statement like “I don’t think it’s likely”? Also, notice that my earlier comment specifically questioned the meaningfulness and practical usefulness of the numerical claim that p~0.95 for this conclusion, and I don’t see how it comes out of your calculation. These seem to be exactly the sorts of dreamed-up probability numbers whose meaningfulness I’m denying.
Regarding your examples with banks and donations, when I imagine myself in such situations, I still don’t see how numbers derived from my own common-sense reasoning can be useful. I can see myself making a decision based a simple common-sense impression that one bank looks less shady, or that it’s bigger and thus more likely to be bailed out, etc. Similarly, I could act on a vague impression that one political candidacy I’d favor is far more hopeless than another, and so on. On the other hand, I could also judge from the results of calculations based on numbers from real expert input, like actuary tables for failures of banks of various types, or the poll numbers for elections, etc.
What I cannot imagine, however, is doing anything sensible and useful with probabilities dreamed up from vague common-sense impressions. For example, looking at a bank, getting the impression that it’s reputable and solid, and then saying, “What’s the probability it will fail before time T? Um.. seems really unlikely… let’s say 0.1%.”, and then using this number to calculate my expected returns.
Now, regarding your example with driving vs. fires, suppose I simply say: “Looking at the statistical tables, it is far more likely to be killed by a car accident than a fire. I don’t see any way in which I’m exceptional in my exposure to either, so if I want to make myself safer, it would be stupid to invest more effort in reducing the chance of fire than in more careful driving.” What precisely have you gained with your calculation relative to this plain and clear English statement?
In particular, what is the significance of these subjectively estimated probabilities like p=10^-1 in step 2? What more does this number tell us than a simple statement like “I don’t think it’s likely”? Also, notice that my earlier comment specifically questioned the meaningfulness and practical usefulness of the numerical claim that p~0.95 for this conclusion, and I don’t see how it comes out of your calculation. These seem to be exactly the sorts of dreamed-up probability numbers whose meaningfulness I’m denying.