I don’t think anyone should aim towards a local decision rule as an ideal, though, so there’s an important question of whether your Dutch book argument undermines person-affecting views much at all relative to alternatives. Local decision rules will undweight option value, value of information, investments for the future, and basic things we need to do survive.
I think it’s worth separating:
How to evaluate outcomes
How to make decisions under uncertainty
How to make decisions over time
The argument in this post is just about (1). Admittedly I’ve illustrated it with a sequence of trades (which seems more like (3)) but the underlying principle is just that of transitivity which is squarely within (1). When thinking about (1) I’m often bracketing out (2) and (3), and similarly when I think about (2) or (3) I often ignore (1) by assuming there’s some utility function that evaluates outcomes for me. So I’m not saying “you should make decisions using a local rule that ignores things like information value”; I’m more saying “when thinking about (1) it is often a helpful simplifying assumption to consider local rules and see how they perform”.
It’s plausible that an effective theory will actually need to think about these areas simultaneously—in particular, I feel somewhat compelled by arguments from (2) that you need to have a bounded mechanism for (1), which is mixing those two areas together. But I think we’re still at the stage where it makes sense to think about these things separately, especially for basic arguments when getting up to speed (which is the sort of post I was trying to write).
Do you think the Dutch book still has similar normative force if the person-affecting view is transitive within option sets, but violates IIA? I think such views are more plausible than intransitive ones, and any intransitive view can be turned into a transitive one that violates IIA using voting methods like beatpath/Schulze. With an intransitive view, I’d say you haven’t finished evaluating the options if you only make the pairwise comparisons.
The options involved might look the same, but now you have to really assume you’re changing which options are actually available over time, which, under one interpretation of an IIA-violating view, fails to respect the view’s assumptions about how to evaluate options: the options or outcomes available will just be what they end up being, and their value will depend on which are available. Maybe this doesn’t make sense, because counterfactuals aren’t actual?
Against an intransitive view, it’s just not clear which option to choose, and we can imagine deliberating from World 1 to World 1 minus $0.98 following the Dutch book argument if we’re unlucky about the order in which we consider the options.
I think it’s worth separating:
How to evaluate outcomes
How to make decisions under uncertainty
How to make decisions over time
The argument in this post is just about (1). Admittedly I’ve illustrated it with a sequence of trades (which seems more like (3)) but the underlying principle is just that of transitivity which is squarely within (1). When thinking about (1) I’m often bracketing out (2) and (3), and similarly when I think about (2) or (3) I often ignore (1) by assuming there’s some utility function that evaluates outcomes for me. So I’m not saying “you should make decisions using a local rule that ignores things like information value”; I’m more saying “when thinking about (1) it is often a helpful simplifying assumption to consider local rules and see how they perform”.
It’s plausible that an effective theory will actually need to think about these areas simultaneously—in particular, I feel somewhat compelled by arguments from (2) that you need to have a bounded mechanism for (1), which is mixing those two areas together. But I think we’re still at the stage where it makes sense to think about these things separately, especially for basic arguments when getting up to speed (which is the sort of post I was trying to write).
Do you think the Dutch book still has similar normative force if the person-affecting view is transitive within option sets, but violates IIA? I think such views are more plausible than intransitive ones, and any intransitive view can be turned into a transitive one that violates IIA using voting methods like beatpath/Schulze. With an intransitive view, I’d say you haven’t finished evaluating the options if you only make the pairwise comparisons.
The options involved might look the same, but now you have to really assume you’re changing which options are actually available over time, which, under one interpretation of an IIA-violating view, fails to respect the view’s assumptions about how to evaluate options: the options or outcomes available will just be what they end up being, and their value will depend on which are available. Maybe this doesn’t make sense, because counterfactuals aren’t actual?
Against an intransitive view, it’s just not clear which option to choose, and we can imagine deliberating from World 1 to World 1 minus $0.98 following the Dutch book argument if we’re unlucky about the order in which we consider the options.