It definitely should not move by anything like a Brownian motion process. At the very least it should be bursty and updates should be expected to be very non-uniform in magnitude.
In practice, you should not consciously update very often since almost all updates will be of insignificant magnitude on near-irrelevant information. I expect that much of the credence weight turns on unknown unknowns, which can’t really be updated on at all until something turns them into (at least) known unknowns.
But sure, if you were a superintelligence with practically unbounded rationality then you might in principle update very frequently.
The Brownian motion assumption is rather strong but not required for the conclusion. Consider the stock market, which famously has heavy-tailed, bursty returns. It happens all the time for the S&P 500 to move 1% in a week, but a 10% move in a week only happens a couple of times per decade. I would guess (and we can check) that most weeks have >0.6x of the average per-week variance of the market, which causes the median weekly absolute return to be well over half of what it would be if the market were Brownian motion with the same long-term variance.
Also, Lawrence tells me that in Tetlock’s studies, superforecasters tend to make updates of 1-2% every week, which actually improves their accuracy.
It definitely should not move by anything like a Brownian motion process. At the very least it should be bursty and updates should be expected to be very non-uniform in magnitude.
In practice, you should not consciously update very often since almost all updates will be of insignificant magnitude on near-irrelevant information. I expect that much of the credence weight turns on unknown unknowns, which can’t really be updated on at all until something turns them into (at least) known unknowns.
But sure, if you were a superintelligence with practically unbounded rationality then you might in principle update very frequently.
The Brownian motion assumption is rather strong but not required for the conclusion. Consider the stock market, which famously has heavy-tailed, bursty returns. It happens all the time for the S&P 500 to move 1% in a week, but a 10% move in a week only happens a couple of times per decade. I would guess (and we can check) that most weeks have >0.6x of the average per-week variance of the market, which causes the median weekly absolute return to be well over half of what it would be if the market were Brownian motion with the same long-term variance.
Also, Lawrence tells me that in Tetlock’s studies, superforecasters tend to make updates of 1-2% every week, which actually improves their accuracy.