Thinking out loud about credences and PDFs for credences (is there a name for these?):
I don’t think “highly confident people bare the burden of proof” is a correct way of saying my thought necessarily, but I’m trying to point at this idea that when two people disagree on X (e.g. 0.3% vs 30% credences), there’s an asymmetry in which the person who is more confident (i.e. 0.3% in this case) is necessarily highly confident that the person they disagree with is wrong, whereas the the person who is less confident (30% credence person) is not necessarily highly confident that the person they disagree with is wrong. So maybe this is another way of saying that “high confidence requires strong evidence”, but I think I’m saying more than that.
I’m observing that the high-confidence person needs an account of why the low-confidence person is wrong, whereas the opposite isn’t true.
Some math to help communicate my thoughts: The 0.3% credence person is necessarily at least 99% confident that a 30% credence is too high. Whereas a 30% credence is compatible with thinking there’s, say, a 50% chance that a 0.3% credence is the best credence one could have with the information available.
So a person who is 30% confident X is true may or may not think that a person with a 0.3% credence in X is likely reasonable in their belief. They may think that that person is likely correct, or they may think that they are very likely wrong. Both possibilities are coherent.
Whereas the person who credence in X is 0.3% necessarily believes the person whose credence is 30% is >99% likely wrong.
Maybe another good way to think about this:
If my point-estimate is X%, I can restate that by giving a PDF in which I give a weight for all possible estimates/forecasts from 0-100%.
E.g. “I’m not sure if the odds of winning this poker hand are 45% or 55% or somewhere in between; my point-credence is about 50% but I think the true odds may be a few percentage points different, though I’m quite confident that the odds are not <30% or >70%. (We could draw a PDF).”
Or “If I researched this for an hour I think I’d probably conclude that it’s very likely false, or at least <1%, but on the surface it seems plausible that I might instead discover that it’s probably true, though it’d be hard to verify for sure, so my point-credence is ~15%, but after an hour of research I’d expect (>80%) my credence to be either less than 3% or >50%.
Is there a name for the uncertainty (PDF) about one’s credence?
Thinking out loud about credences and PDFs for credences (is there a name for these?):
I don’t think “highly confident people bare the burden of proof” is a correct way of saying my thought necessarily, but I’m trying to point at this idea that when two people disagree on X (e.g. 0.3% vs 30% credences), there’s an asymmetry in which the person who is more confident (i.e. 0.3% in this case) is necessarily highly confident that the person they disagree with is wrong, whereas the the person who is less confident (30% credence person) is not necessarily highly confident that the person they disagree with is wrong. So maybe this is another way of saying that “high confidence requires strong evidence”, but I think I’m saying more than that.
I’m observing that the high-confidence person needs an account of why the low-confidence person is wrong, whereas the opposite isn’t true.
Some math to help communicate my thoughts: The 0.3% credence person is necessarily at least 99% confident that a 30% credence is too high. Whereas a 30% credence is compatible with thinking there’s, say, a 50% chance that a 0.3% credence is the best credence one could have with the information available.
So a person who is 30% confident X is true may or may not think that a person with a 0.3% credence in X is likely reasonable in their belief. They may think that that person is likely correct, or they may think that they are very likely wrong. Both possibilities are coherent.
Whereas the person who credence in X is 0.3% necessarily believes the person whose credence is 30% is >99% likely wrong.
Maybe another good way to think about this:
If my point-estimate is X%, I can restate that by giving a PDF in which I give a weight for all possible estimates/forecasts from 0-100%.
E.g. “I’m not sure if the odds of winning this poker hand are 45% or 55% or somewhere in between; my point-credence is about 50% but I think the true odds may be a few percentage points different, though I’m quite confident that the odds are not <30% or >70%. (We could draw a PDF).”
Or “If I researched this for an hour I think I’d probably conclude that it’s very likely false, or at least <1%, but on the surface it seems plausible that I might instead discover that it’s probably true, though it’d be hard to verify for sure, so my point-credence is ~15%, but after an hour of research I’d expect (>80%) my credence to be either less than 3% or >50%.
Is there a name for the uncertainty (PDF) about one’s credence?