Thinking out loud about credences and PDFs for credences (is there a name for these?):
I donât think âhighly confident people bare the burden of proofâ is a correct way of saying my thought necessarily, but Iâm trying to point at this idea that when two people disagree on X (e.g. 0.3% vs 30% credences), thereâs 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 âhigh confidence requires strong evidenceâ, but I think Iâm saying more than that.
Iâm observing that the high-confidence person needs an account of why the low-confidence person is wrong, whereas the opposite isnât 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 thereâs, 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/âforecasts from 0-100%.
E.g. âIâm 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 Iâm quite confident that the odds are not <30% or >70%. (We could draw a PDF).â
Or âIf I researched this for an hour I think Iâd probably conclude that itâs very likely false, or at least <1%, but on the surface it seems plausible that I might instead discover that itâs probably true, though itâd be hard to verify for sure, so my point-credence is ~15%, but after an hour of research Iâd expect (>80%) my credence to be either less than 3% or >50%.
Is there a name for the uncertainty (PDF) about oneâs credence?
Thinking out loud about credences and PDFs for credences (is there a name for these?):
I donât think âhighly confident people bare the burden of proofâ is a correct way of saying my thought necessarily, but Iâm trying to point at this idea that when two people disagree on X (e.g. 0.3% vs 30% credences), thereâs 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 âhigh confidence requires strong evidenceâ, but I think Iâm saying more than that.
Iâm observing that the high-confidence person needs an account of why the low-confidence person is wrong, whereas the opposite isnât 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 thereâs, 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/âforecasts from 0-100%.
E.g. âIâm 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 Iâm quite confident that the odds are not <30% or >70%. (We could draw a PDF).â
Or âIf I researched this for an hour I think Iâd probably conclude that itâs very likely false, or at least <1%, but on the surface it seems plausible that I might instead discover that itâs probably true, though itâd be hard to verify for sure, so my point-credence is ~15%, but after an hour of research Iâd expect (>80%) my credence to be either less than 3% or >50%.
Is there a name for the uncertainty (PDF) about oneâs credence?