It seems to me that some of LW’s attempts to avoid “a priori” reasoning have tripped up right at their initial premises, by assuming as premises propositions of the form “The probability of possible-fact X is y%.” (LW’s annual survey repeatedly insists that readers make this mistake, too.)
I may have a guess about whether X is true; I may even be willing to give or accept odds on one or both sides of the question; but that is not the same thing as being able to assign a probability. For that you need conditions (such as where X is the outcome of a die roll or coin toss) where there’s a basis for assigning the number. Otherwise the right answer to most questions of “How likely is X?” (where we don’t know for certain whether X is true) will be some vague expression (“It could be true, but I doubt it”) or simply “I don’t know.”
Refusing to assign numerical probabilities because you don’t have a rigorous way to derive them is like refusing to choose whether or not to buy things because you don’t have a rigorous way to decide how much they’re worth to you.
Explicitly assigning a probability isn’t always (perhaps isn’t usually) worth the trouble it takes, and rushing to assign numerical probabilities can certainly lead you astray—but that doesn’t mean it can’t be done or that it shouldn’t be done (carefully!) in cases where making a good decision matters most.
When you haven’t taken the trouble to decide a numerical probability, then indeed vague expressions are all you’ve got, but unless you have a big repertoire of carefully graded vague expressions (which would, in fact, not be so very different from assigning probabilities) you’ll find that sometimes there are two propositions for both of which you’d say “it could be true, but I doubt it”—but you definitely find one more credible than the other. If you can make that distinction mentally, why shouldn’t you make it verbally?
If it were a case like you describe (two competing products in a store), I would have to guess, and thus would have to try to think of some “upstream” questions and guess those, too. Not impossible, but unlikely to unearth worthwhile information. For questions as remote as P(aliens), I don’t see a reason to bother.
Have you seen David Friedman’s discussion of rational voter ignorance in The Machinery of Freedom?
It seems to me that some of LW’s attempts to avoid “a priori” reasoning have tripped up right at their initial premises, by assuming as premises propositions of the form “The probability of possible-fact X is y%.” (LW’s annual survey repeatedly insists that readers make this mistake, too.)
I may have a guess about whether X is true; I may even be willing to give or accept odds on one or both sides of the question; but that is not the same thing as being able to assign a probability. For that you need conditions (such as where X is the outcome of a die roll or coin toss) where there’s a basis for assigning the number. Otherwise the right answer to most questions of “How likely is X?” (where we don’t know for certain whether X is true) will be some vague expression (“It could be true, but I doubt it”) or simply “I don’t know.”
Refusing to assign numerical probabilities because you don’t have a rigorous way to derive them is like refusing to choose whether or not to buy things because you don’t have a rigorous way to decide how much they’re worth to you.
Explicitly assigning a probability isn’t always (perhaps isn’t usually) worth the trouble it takes, and rushing to assign numerical probabilities can certainly lead you astray—but that doesn’t mean it can’t be done or that it shouldn’t be done (carefully!) in cases where making a good decision matters most.
When you haven’t taken the trouble to decide a numerical probability, then indeed vague expressions are all you’ve got, but unless you have a big repertoire of carefully graded vague expressions (which would, in fact, not be so very different from assigning probabilities) you’ll find that sometimes there are two propositions for both of which you’d say “it could be true, but I doubt it”—but you definitely find one more credible than the other. If you can make that distinction mentally, why shouldn’t you make it verbally?
If it were a case like you describe (two competing products in a store), I would have to guess, and thus would have to try to think of some “upstream” questions and guess those, too. Not impossible, but unlikely to unearth worthwhile information. For questions as remote as P(aliens), I don’t see a reason to bother.
Have you seen David Friedman’s discussion of rational voter ignorance in The Machinery of Freedom?