Hmm do you have a sense of what theoretical commitments you are making by allowing for a credible interval for probabilities?
A plausible candidate for a low-commitment solution is that idealized Bayesian agents don’t have logical uncertainty, but humans (or any agents implemented with bounded computation and memory) do.
An alternative framing I sometimes have is that I’ll have a “fair price” for my true probabilities, but for questions I’m more/less confused about, I’ll have higher/lower bands for my bid/asks in bets against general epistemic peers. I think this is justifiable against adversarial actors due to some analogy to the winner’s curse, tho I think my current intuitions are still not formal enough for me to be happy with.
My immediate response is that I’m making very few theoretical commitments (at least above the commitments I’m already making by using credences in the first place), though I haven’t thought about this a lot.
Note in particular that e.g. saying ’30-50%′ on my interpretation is perfectly consistent with having a sharp credence (say, 37.123123976%) at the same time.
It is also consistent with representing only garden-variety empirical uncertainty: essentially making a prediction of how much additional empirical evidence I would acquire within a certain amount of time, and how much that evidence would update my credence. So no commitment to logical uncertainty required.
Admittedly in practice I do think I’d often find the sharp credence hard to access and the credible interval would represent some mix of empirical and logical uncertainty (or similar). But at least in principle one could try to explain this in a similar way how one explains other human deviations from idealized models of rationality, i.e. in particular without making additional commitments about the theory of idealized rationality.
The discussion here might be related, and specifically this paper that was shared. However, you can use a credible interval without any theoretical commitments, only practical ones. From this post:
Give an expected error/CI relative to some better estimator—either a counterpart of yours (“I think there’s a 12% chance of a famine in South Sudan this year, but if I spent another 5 hours on this I’d expect to move by 6%”); or a hypothetical one (“12%, but my 95% CI for what a superforecaster median would be is [0%-45%]”). This works better when one does not expect to get access to the ‘true value’ (“What was the ‘right’ ex ante probability Trump wins the 2016 election?”)
This way, you can say that your probabilities are actually sharp at any moment, but more or less prone to change given new information.
That being said, I think people are doing something unjustified by having precise probabilities (“Why not 1% higher or lower?”), and I endorse something that looks like the maximality rule in Maximal Cluelessness for decision theory, although I think we need to aim for more structure somehow, since as discussed in the paper, it makes cluelessness really bad. I discuss this a little in this post (in the summary), and in this thread. This is related to ambiguity aversion and deep uncertainty.
Hmm do you have a sense of what theoretical commitments you are making by allowing for a credible interval for probabilities?
A plausible candidate for a low-commitment solution is that idealized Bayesian agents don’t have logical uncertainty, but humans (or any agents implemented with bounded computation and memory) do.
An alternative framing I sometimes have is that I’ll have a “fair price” for my true probabilities, but for questions I’m more/less confused about, I’ll have higher/lower bands for my bid/asks in bets against general epistemic peers. I think this is justifiable against adversarial actors due to some analogy to the winner’s curse, tho I think my current intuitions are still not formal enough for me to be happy with.
My immediate response is that I’m making very few theoretical commitments (at least above the commitments I’m already making by using credences in the first place), though I haven’t thought about this a lot.
Note in particular that e.g. saying ’30-50%′ on my interpretation is perfectly consistent with having a sharp credence (say, 37.123123976%) at the same time.
It is also consistent with representing only garden-variety empirical uncertainty: essentially making a prediction of how much additional empirical evidence I would acquire within a certain amount of time, and how much that evidence would update my credence. So no commitment to logical uncertainty required.
Admittedly in practice I do think I’d often find the sharp credence hard to access and the credible interval would represent some mix of empirical and logical uncertainty (or similar). But at least in principle one could try to explain this in a similar way how one explains other human deviations from idealized models of rationality, i.e. in particular without making additional commitments about the theory of idealized rationality.
The discussion here might be related, and specifically this paper that was shared. However, you can use a credible interval without any theoretical commitments, only practical ones. From this post:
This way, you can say that your probabilities are actually sharp at any moment, but more or less prone to change given new information.
That being said, I think people are doing something unjustified by having precise probabilities (“Why not 1% higher or lower?”), and I endorse something that looks like the maximality rule in Maximal Cluelessness for decision theory, although I think we need to aim for more structure somehow, since as discussed in the paper, it makes cluelessness really bad. I discuss this a little in this post (in the summary), and in this thread. This is related to ambiguity aversion and deep uncertainty.