Perhaps it goes without saying, but obviously, both frameworks are flexible enough to allow for most phenomena—the question here is what is more natural in one framework or another.
My main argument is that the procrastination paradox is not natural at all in a Savage framework, as it suggests an uncomputable utility function. I think this plausibly outweighs the issue you’re pointing at.
But with respect to the issue you are pointing at:
I try to think about what I expect to happen if I take that action (ie the outcome), and I think about how likely that outcome is to have various properties that I care about,
In the Savage framework, an outcome already encodes everything you care about. So the computation which seems to be suggested by Savage is to think of these maximally-specified outcomes, assigning them probability and utility, and then combining those to get expected utility. This seems to be very demanding: it requires imagining these very detailed scenarios.
Alternately, we might say (as as Savage said) that the Savage axioms apply to “small worlds”—small scenarios which the agent abstracts from its experience, such as the decision of whether to break an egg for an omelette. These can be easily considered by the agent, if it can assign values “from outside the problem” in an appropriate way.
But then, to account for the breadth of human reasoning, it seems to me we also want an account of things like extending a small world when we find that it isn’t sufficient, and coherence between different small-world frames for related decisions.
This gives a picture very much like the Jeffrey-Bolker picture, in that we don’t really work with outcomes which completely specify everything we care about, but rather, work with a variety of simplified outcomes with coherence requirements between simpler and more complex views.
So overall I think it is better to have some picture where you can break things up in a more tractable way, rather than having full outcomes which you need to pass through to get values.
In the Jeffrey-Bolker framework, you can re-estimate the value of an event by breaking it up into pieces, estimating the value and probability of each piece, and combining them back together. This process could be iterated in a manner similar to dynamic programming in RL, to improve value estimates for actions—although one needs to settle on a story about where the information originally comes from. I currently like the logical-induction-like picture where you get information coming in “somehow” (a broad variety of feedback is possible, including abstract judgements about utility which are hard to cash out in specific cases) and you try to make everything as coherent as possible in the meanwhile.
In the Savage framework, an outcome already encodes everything you care about.
Yes, but if you don’t know which outcome is the true one, so you’re considering a probability distribution over outcomes instead of a single outcome, then it still makes sense to speak of the probability that the true outcome has some feature. This is what I meant.
So the computation which seems to be suggested by Savage is to think of these maximally-specified outcomes, assigning them probability and utility, and then combining those to get expected utility. This seems to be very demanding: it requires imagining these very detailed scenarios.
You do not need to be able to imagine every possible outcome individually in order to think of functions on or probability distributions over the set of outcomes, any more than I need to be able to imagine each individual real number in order to understand the function x↦x2 or the standard normal distribution.
It seems that you’re going by an analogy like Jeffrey-Bolker : VNM :: events : outcomes, which is partially right, but leaves out an important sense in which the correct analogy is Jeffrey-Bolker : VNM :: events : probability distributions, since although utility is defined on outcomes, the function that is actually evaluated is expected utility, which is defined on probability distributions (this being a distinction that does not exist in Jeffrey-Bolker, but does exist in my conception of real-world human decision making).
Perhaps it goes without saying, but obviously, both frameworks are flexible enough to allow for most phenomena—the question here is what is more natural in one framework or another.
My main argument is that the procrastination paradox is not natural at all in a Savage framework, as it suggests an uncomputable utility function. I think this plausibly outweighs the issue you’re pointing at.
But with respect to the issue you are pointing at:
In the Savage framework, an outcome already encodes everything you care about. So the computation which seems to be suggested by Savage is to think of these maximally-specified outcomes, assigning them probability and utility, and then combining those to get expected utility. This seems to be very demanding: it requires imagining these very detailed scenarios.
Alternately, we might say (as as Savage said) that the Savage axioms apply to “small worlds”—small scenarios which the agent abstracts from its experience, such as the decision of whether to break an egg for an omelette. These can be easily considered by the agent, if it can assign values “from outside the problem” in an appropriate way.
But then, to account for the breadth of human reasoning, it seems to me we also want an account of things like extending a small world when we find that it isn’t sufficient, and coherence between different small-world frames for related decisions.
This gives a picture very much like the Jeffrey-Bolker picture, in that we don’t really work with outcomes which completely specify everything we care about, but rather, work with a variety of simplified outcomes with coherence requirements between simpler and more complex views.
So overall I think it is better to have some picture where you can break things up in a more tractable way, rather than having full outcomes which you need to pass through to get values.
In the Jeffrey-Bolker framework, you can re-estimate the value of an event by breaking it up into pieces, estimating the value and probability of each piece, and combining them back together. This process could be iterated in a manner similar to dynamic programming in RL, to improve value estimates for actions—although one needs to settle on a story about where the information originally comes from. I currently like the logical-induction-like picture where you get information coming in “somehow” (a broad variety of feedback is possible, including abstract judgements about utility which are hard to cash out in specific cases) and you try to make everything as coherent as possible in the meanwhile.
Yes, but if you don’t know which outcome is the true one, so you’re considering a probability distribution over outcomes instead of a single outcome, then it still makes sense to speak of the probability that the true outcome has some feature. This is what I meant.
You do not need to be able to imagine every possible outcome individually in order to think of functions on or probability distributions over the set of outcomes, any more than I need to be able to imagine each individual real number in order to understand the function x↦x2 or the standard normal distribution.
It seems that you’re going by an analogy like Jeffrey-Bolker : VNM :: events : outcomes, which is partially right, but leaves out an important sense in which the correct analogy is Jeffrey-Bolker : VNM :: events : probability distributions, since although utility is defined on outcomes, the function that is actually evaluated is expected utility, which is defined on probability distributions (this being a distinction that does not exist in Jeffrey-Bolker, but does exist in my conception of real-world human decision making).