I get conservation of expected evidence. But the distribution of belief changes is completely unconstrained.
Going from the class martingale to the subclass Brownian motion is arbitrary, and the choice of 1% update steps is another unjustified arbitrary choice.
I think asking about the likely possible evidence paths would improve our predictions.
You spelled it conversation of expected evidence. I was hoping there was another term by that name :)
To be honest, I would’ve preferred if Thomas’s post started from empirical evidence (e.g. it sure seems like superforecasters and markets change a lot week on week) and then explained it in terms of the random walk/Brownian motion setup. I think the specific math details (a lot of which don’t affect the qualitative result of “you do lots and lots of little updates, if there exists lots of evidence that might update you a little”) are a distraction from the qualitative takeaway.
A fancier way of putting it is: the math of “your belief should satisfy conservation of expected evidence” is a description of how the beliefs of an efficient and calibrated agent should look, and examples like his suggest it’s quite reasonable for these agents to do a lot of updating. But the example is not by itself necessarily a prescription for how your belief updating should feel like from the inside (as a human who is far from efficient or perfectly calibrated). I find the empirical questions of “does the math seem to apply in practice” and “therefore, should you try to update more often” (e.g., what do the best forecasters seem to do?) to be larger and more interesting than the “a priori, is this a 100% correct model” question.
I get conservation of expected evidence. But the distribution of belief changes is completely unconstrained.
Going from the class martingale to the subclass Brownian motion is arbitrary, and the choice of 1% update steps is another unjustified arbitrary choice.
I think asking about the likely possible evidence paths would improve our predictions.
You spelled it conversation of expected evidence. I was hoping there was another term by that name :)
To be honest, I would’ve preferred if Thomas’s post started from empirical evidence (e.g. it sure seems like superforecasters and markets change a lot week on week) and then explained it in terms of the random walk/Brownian motion setup. I think the specific math details (a lot of which don’t affect the qualitative result of “you do lots and lots of little updates, if there exists lots of evidence that might update you a little”) are a distraction from the qualitative takeaway.
A fancier way of putting it is: the math of “your belief should satisfy conservation of expected evidence” is a description of how the beliefs of an efficient and calibrated agent should look, and examples like his suggest it’s quite reasonable for these agents to do a lot of updating. But the example is not by itself necessarily a prescription for how your belief updating should feel like from the inside (as a human who is far from efficient or perfectly calibrated). I find the empirical questions of “does the math seem to apply in practice” and “therefore, should you try to update more often” (e.g., what do the best forecasters seem to do?) to be larger and more interesting than the “a priori, is this a 100% correct model” question.
Oops, you’re correct about the typo and also about how this doesn’t restrict belief change to Brownian motion. Fixing the typo.