rossry
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However, if the node includes the entire meal, so that there are six nodes (chicken, pepsi), (chicken, coke), (pork, pepsi), (pork, coke), (steak, pepsi), (steak, coke), then the magnitude doesn’t matter.
I don’t think this is right; you still want to be able to decide between actions which might have probabilistic “outcomes” (given that your action is necessarily being taken under incomplete information about its exact results).
You could define a continuous DAG over probability distributions, but that structure is actually too general; you do want to be able to rely on linear additivity if you’re using utilitarianism (rather than some other consequentialism that cares about the whole distribution in some nonlinear way).
Of course, once you have your function from worlds to utilities, you can construct the ordering between nodes of {100% to be X | outcomes X}, but that transformation is lossy (and you don’t need the full generality of a DAG, since you’re just going to end up with a linear ordering.
(For modeling incomplete preferences, DAGs are great! Not so great for utility functions.)
In most of the situations where this is most salient to me, {B} is a social behavior, and {X} and {Y} are punishments that people mete out to people who do not conform to correct {B}-ness.
Notwithstanding this, I note that the model of affordance widths also seems apt for modeling binds in situations where the constraints are imposed by uncaring parts of the universe, rather than the social web.
Take as an example the task of riding a bike, where potential hazards include {X} riding too slowly and falling over and {Y} riding too quickly and losing control. Here, taking speed as {B}, it seems quite natural that different people might have different affordance widths for speed.
What does this buy us? Well, once again we see that the natural advice on “how to ride a bike better” for [A] might be actively misleading for [C], and the best advice for [D] and [E] might be in a different class entirely. So the concept seems like a useful tool for anyone considering how to give advice to other people on how to do things.
(A more complicated example that I’ve been thinking about recently is the task of forming predictions under uncertainty, where {B} is something like “trust your intuition”; generating various kinds of {X} and {Y} are left as an exercise.)
Eliezer, why on earth are you writing about this? [...] Can’t you just link to some econ-bloggers? There’s plenty of them out there, right? (I seem to recall you even mentioning one, in your previous post…)
It is worth noting that Scott Sumner called this post “probably the best single introduction to the market monetarist way of thinking in the entire blogosphere.”
I think I disagree; “tolerance”, to me, seems to point more towards the special case where {B} is some external events and {X} and {Y} are internal reactions. To talk about social affordances, as the OP does, you’d have to talk about the tolerances of others for {B} done by different people [A-E] -- and you’ve made less obvious the fact that the tolerance of [Q] for {B} done by [A] is different than the tolerance of [Q] for {B} done by [E] -- the entire content of the post.