HCH is about deliberation, and logical inductors are about trial and error.
I think that’s true of the way I describe the relationship in the OP, but not quite true in reality. I think there’s also an aspect of deliberation that’s present in logical induction and not in HCH. If we think of HCH as a snapshot of a logical inductor, the logical inductor is “improving over time as a result of thinking longer”. This is partly due to trial-and-error, but there’s also a deliberative aspect to it.
I mean, partly what I’m saying is that it’s hard to draw a sharp line between deliberation and trial-and-error. If you try to draw that line such that logical induction lands to one side, you’re putting Bayes’ Law on multiple hypotheses on the “trial-and-error” side. But it’s obvious that one would want it to be on both sides. It’s definitely sort of about trial-and-error, but we also definitely want to apply Bayes’ Law in deliberation. Similarly, it might turn out that we want to apply the more general logical-induction updates within deliberation.
But part of what I’m saying is that LIC (logical induction criterion) is a theory of rational deliberation in the sense of revising beliefs over time. The LIA (logical induction algorithm) captures the trial-and-error aspect, running lots of programs without knowing which ones are actually needed to satisfy LIC. But the LIC is a normative theory of deliberation, saying that what it means for belief revisions over time to be rational is that they not be too exploitable.
The cost is that it doesn’t optimize what you want (unless what you want is the logical induction criterion) and that it will generally get taken over by consequentialists who can exercise malicious influence a constant number of times before the asymptotics assert themselves.
Yeah, if you take the LIA as a design proposal, it’s pretty unhelpful. But if you take the LIC as a model of rational deliberation, you get potentially useful ideas.
The benefit of deliberation is that its preferences are potentially specified indirectly by the original deliberator (rather than externally by the criterion for trial and error), and that if the original deliberator is strong enough they may suppress internal selection pressures.
For example, the LIC is a context in which we can formally establish a version of “if the deliberator is strong enough they can suppress internal selection pressures”.
I think that’s true of the way I describe the relationship in the OP, but not quite true in reality. I think there’s also an aspect of deliberation that’s present in logical induction and not in HCH. If we think of HCH as a snapshot of a logical inductor, the logical inductor is “improving over time as a result of thinking longer”. This is partly due to trial-and-error, but there’s also a deliberative aspect to it.
I mean, partly what I’m saying is that it’s hard to draw a sharp line between deliberation and trial-and-error. If you try to draw that line such that logical induction lands to one side, you’re putting Bayes’ Law on multiple hypotheses on the “trial-and-error” side. But it’s obvious that one would want it to be on both sides. It’s definitely sort of about trial-and-error, but we also definitely want to apply Bayes’ Law in deliberation. Similarly, it might turn out that we want to apply the more general logical-induction updates within deliberation.
But part of what I’m saying is that LIC (logical induction criterion) is a theory of rational deliberation in the sense of revising beliefs over time. The LIA (logical induction algorithm) captures the trial-and-error aspect, running lots of programs without knowing which ones are actually needed to satisfy LIC. But the LIC is a normative theory of deliberation, saying that what it means for belief revisions over time to be rational is that they not be too exploitable.
Yeah, if you take the LIA as a design proposal, it’s pretty unhelpful. But if you take the LIC as a model of rational deliberation, you get potentially useful ideas.
For example, the LIC is a context in which we can formally establish a version of “if the deliberator is strong enough they can suppress internal selection pressures”.