You can either have a local decision rule that doesnāt take into account future actions (and so excludes this sort of reasoning), or you can have a global decision rule that selects an entire policy at once. I was talking about the local kind.
Thanks, itās helpful to make this distinction explicit.
Arenāt such local decision rules generally vulnerable to Dutch book arguments, though? I suppose PAVs with local decision rules are vulnerable to Dutch books even when the future options are fixed (or otherwise donāt depend on past choices or outcomes), whereas EU maximization with a bounded utility function isnāt.
I donāt think anyone should aim towards a local decision rule as an ideal, though, so thereās 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. Weād underinvest in research, and individuals would underinvest in their own education. Many people wouldnāt work, since they only do it for their future purchases. Acquiring food and eating it are separate actions, too.
(Of course, this also cuts against the problems for unbounded utility functions I mentioned.)
You could have a global decision rule that compares worlds and ignores happy people who will only exist in some of the worlds. In that case Iād refer you to Chapter 4 of On the Overwhelming Importance of Shaping the Far Future.
Iām guessing you mean this is a bad decision rule, and Iād agree. I discuss some alternatives (or directions) I find more promising here.
(Nitpick: Under the view I laid out World 1 is not better than World 3? Youāre indifferent between the two.)
I donāt think anyone should aim towards a local decision rule as an ideal, though, so thereās 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 itās 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 Iāve 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) Iām often bracketing out (2) and (3), and similarly when I think about (2) or (3) I often ignore (1) by assuming thereās some utility function that evaluates outcomes for me. So Iām not saying āyou should make decisions using a local rule that ignores things like information valueā; Iām more saying āwhen thinking about (1) it is often a helpful simplifying assumption to consider local rules and see how they performā.
Itās plausible that an effective theory will actually need to think about these areas simultaneouslyāin 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 weāre 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/āSchulze. With an intransitive view, Iād say you havenāt 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 youāre changing which options are actually available over time, which, under one interpretation of an IIA-violating view, fails to respect the viewās 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 doesnāt make sense, because counterfactuals arenāt actual?
Against an intransitive view, itās 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 weāre unlucky about the order in which we consider the options.
Thanks, itās helpful to make this distinction explicit.
Arenāt such local decision rules generally vulnerable to Dutch book arguments, though? I suppose PAVs with local decision rules are vulnerable to Dutch books even when the future options are fixed (or otherwise donāt depend on past choices or outcomes), whereas EU maximization with a bounded utility function isnāt.
I donāt think anyone should aim towards a local decision rule as an ideal, though, so thereās 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. Weād underinvest in research, and individuals would underinvest in their own education. Many people wouldnāt work, since they only do it for their future purchases. Acquiring food and eating it are separate actions, too.
(Of course, this also cuts against the problems for unbounded utility functions I mentioned.)
Iām guessing you mean this is a bad decision rule, and Iād agree. I discuss some alternatives (or directions) I find more promising here.
Woops, fixed.
I think itās 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 Iāve 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) Iām often bracketing out (2) and (3), and similarly when I think about (2) or (3) I often ignore (1) by assuming thereās some utility function that evaluates outcomes for me. So Iām not saying āyou should make decisions using a local rule that ignores things like information valueā; Iām more saying āwhen thinking about (1) it is often a helpful simplifying assumption to consider local rules and see how they performā.
Itās plausible that an effective theory will actually need to think about these areas simultaneouslyāin 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 weāre 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/āSchulze. With an intransitive view, Iād say you havenāt 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 youāre changing which options are actually available over time, which, under one interpretation of an IIA-violating view, fails to respect the viewās 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 doesnāt make sense, because counterfactuals arenāt actual?
Against an intransitive view, itās 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 weāre unlucky about the order in which we consider the options.