I would be convinced if you had a theory of rationality that is a Pareto improvement on IB (i.e. has all the good properties of IB + a more general class of utility functions). However, LI doesn’t provide this AFAICT. That said, I would be interested to see some rigorous theorem about LIDT solving procrastination-like problems.
As to philosophical deliberation, I feel some appeal in this point of view, but I can also easily entertain a different point of view: namely, that human values are more or less fixed and well-defined whereas philosophical deliberation is just a “show” for game theory reasons. Overall, I place much less weight on arguments that revolve around the presumed nature of human values compared to arguments grounded in abstract reasoning about rational agents.
I don’t believe that LI provides such a Pareto improvement, but I suspect that there’s a broader theory which contains the two.
Overall, I place much less weight on arguments that revolve around the presumed nature of human values compared to arguments grounded in abstract reasoning about rational agents.
Ah. I was going for the human-values argument because I thought you might not appreciate the rational-agent argument. After all, who cares what general rational agents can value, if human values happen to be well-represented by infrabayes?
But for general rational agents, rather than make the abstract deliberation argument, I would again mention the case of LIDT in the procrastination paradox, which we’ve already discussed.
Or, I would make the radical probabilist argument against rigid updating, and the ‘orthodox’ argument against fixed utility functions. Combined, we get a picture of “values” which is basically a market for expected values, where prices can change over time (in a “radical” way that doesn’t necessarily spring from an update on a proposition), but which follow some coherence rules like an expectation of an expectation equals an expectation. One formalization of this is Skyrms’. Another is your generalization of LI (iirc).
So to sum it up, my argument for general rational agents is:
In general, we need not update in a rigid way; we can develop a meaningful theory of ‘fluid’ updates, so long as we respect some coherence constraints. In light of this generalization, restriction to ‘rigid’ updates seems somewhat arbitrary (ie there does not seem to be a strong motivation to make the restriction from rationality alone).
Separately, there is no need to actually have a utility function if we have a coherent expectation.
Putting the two together, we can study coherent expectations where the notion of ‘coherence’ doesn’t assume rigid updates.
However, this argument of course does not account for InfraBayes. I suspect your real crux is the plausibility of coming up with a unifying theory which gets both radical-probabilism stuff and InfraBayes stuff. This does seem challenging, but I strongly suspect it to be possible. Indeed, it seems like it might have to do with the idea of a market which maintains a buy/sell spread rather than giving one price for a good.
I would be convinced if you had a theory of rationality that is a Pareto improvement on IB (i.e. has all the good properties of IB + a more general class of utility functions). However, LI doesn’t provide this AFAICT. That said, I would be interested to see some rigorous theorem about LIDT solving procrastination-like problems.
As to philosophical deliberation, I feel some appeal in this point of view, but I can also easily entertain a different point of view: namely, that human values are more or less fixed and well-defined whereas philosophical deliberation is just a “show” for game theory reasons. Overall, I place much less weight on arguments that revolve around the presumed nature of human values compared to arguments grounded in abstract reasoning about rational agents.
I don’t believe that LI provides such a Pareto improvement, but I suspect that there’s a broader theory which contains the two.
Ah. I was going for the human-values argument because I thought you might not appreciate the rational-agent argument. After all, who cares what general rational agents can value, if human values happen to be well-represented by infrabayes?
But for general rational agents, rather than make the abstract deliberation argument, I would again mention the case of LIDT in the procrastination paradox, which we’ve already discussed.
Or, I would make the radical probabilist argument against rigid updating, and the ‘orthodox’ argument against fixed utility functions. Combined, we get a picture of “values” which is basically a market for expected values, where prices can change over time (in a “radical” way that doesn’t necessarily spring from an update on a proposition), but which follow some coherence rules like an expectation of an expectation equals an expectation. One formalization of this is Skyrms’. Another is your generalization of LI (iirc).
So to sum it up, my argument for general rational agents is:
In general, we need not update in a rigid way; we can develop a meaningful theory of ‘fluid’ updates, so long as we respect some coherence constraints. In light of this generalization, restriction to ‘rigid’ updates seems somewhat arbitrary (ie there does not seem to be a strong motivation to make the restriction from rationality alone).
Separately, there is no need to actually have a utility function if we have a coherent expectation.
Putting the two together, we can study coherent expectations where the notion of ‘coherence’ doesn’t assume rigid updates.
However, this argument of course does not account for InfraBayes. I suspect your real crux is the plausibility of coming up with a unifying theory which gets both radical-probabilism stuff and InfraBayes stuff. This does seem challenging, but I strongly suspect it to be possible. Indeed, it seems like it might have to do with the idea of a market which maintains a buy/sell spread rather than giving one price for a good.