Thanks. Perhaps with the benefit of hindsight the blue envelopes probably should have been dropped from the graph, leaving the trace alone:
As you and Kwa note, having a ‘static’ envelope you are bumbling between looks like a violation of the martingale property—the envelope should be tracking the current value more (but I was too lazy to draw that).
I agree all else equal you should expect resilience to increase with more deliberation—as you say, you are moving towards the limit of perfect knowledge with more work. Perhaps graph 3 and 4 [I’ve added numbers to make referring easier] could signal that you’re moving from 10.1% to 10.2% in this hypothetical range from ignorance to omniscience.
Related to Kwa’s point, another benefit of tracking one’s beliefs is not only figuring out when to terminate deliberation, but also to ‘keep score’ about how rational one’s beliefs appear to be. Continued volatility (in G3, but also G4) could mean you are (rationally) in the situation where your weak prior is getting buffetted by a lot of strong evidence; but it could also mean you are under-damped and over-updating.
Thanks. Perhaps with the benefit of hindsight the blue envelopes probably should have been dropped from the graph, leaving the trace alone:
As you and Kwa note, having a ‘static’ envelope you are bumbling between looks like a violation of the martingale property—the envelope should be tracking the current value more (but I was too lazy to draw that).
I agree all else equal you should expect resilience to increase with more deliberation—as you say, you are moving towards the limit of perfect knowledge with more work. Perhaps graph 3 and 4 [I’ve added numbers to make referring easier] could signal that you’re moving from 10.1% to 10.2% in this hypothetical range from ignorance to omniscience.
Related to Kwa’s point, another benefit of tracking one’s beliefs is not only figuring out when to terminate deliberation, but also to ‘keep score’ about how rational one’s beliefs appear to be. Continued volatility (in G3, but also G4) could mean you are (rationally) in the situation where your weak prior is getting buffetted by a lot of strong evidence; but it could also mean you are under-damped and over-updating.