But if you already have this coalition value function, you’ve already solved the coordination problem and there’s no reason to actually calculate the Shapley value! If you know how much total value would be produced if everyone worked together, in realistic situations you must also know an optimal allocation of everyone’s effort. And so everyone can just do what that optimal allocation recommended.
This seems correct
A related claim is that the Shapley value is no better than any other solution to the bargaining problem. For example, instead of allocating credit according to the Shapley value, we could allocate credit according to the rule “we give everyone just barely enough credit that it’s worth it for them to participate in the globally optimal plan instead of doing something worse, and then all the leftover credit gets allocated to Buck”, and this would always produce the same real-life decisions as the Shapley value.
This misses some considerations around cost-efficiency/prioritization. If you look at your distorted “Buck values”, you come away that Buck is super cost-effective; responsible for a large fraction of the optimal plan using just one salary. If we didn’t have a mechanistic understanding of why that was, trying to get more Buck would become an EA cause area.
In contrast, if credit was allocated according to Shapley values, we could look at the groups whose Shapley value is the highest, and try to see if they can be scaled.
The section about “purely local” Shapley values might be pointing to something, but I don’t quite know what it is, because the example is just Shapley values but missing a term? I don’t know. You also say “by symmetry...”, and then break that symmetry by saying that one of the parts would have been able to create $6,000 in value and the other $0. Needs a crisper example.
Re: coordination between people who have different values using SVs, I have some stuff here, but looking back the writting seems too corny.
Lastly, to some extent, Shapley values are a reaction to people calculating their impact as their counterfactual impact. This leads to double/triple counting impact for some organizations/opportunities, but not others, which makes comparison between them more tricky. Shapley values solve that by allocating impact such that it sums to the total impact & other nice properties. Then someone like OpenPhilanthropy or some EA fund can come and see which groups have the highest Shapley value (perhaps highest Shapley value per unit of money/ressources) and then try to replicate them/scale them. People might also make better decisions if they compare Shapley instead of counterfactual values (because Shapley values mostly give a more accurate impression of the impact of a position.)
So I see the benefits of Shapley values as fixing some common mistakes arising from using counterfactual values. This would make impact accounting slightly better, and coordination slightly better to the extent it relies on impact accounting for prioritization (which tbh might not be much.)
I’m not sure to what extent I agree with the claim that people are overhyping/misunderstanding Shapley values. It seems plausible.
This seems correct
This misses some considerations around cost-efficiency/prioritization. If you look at your distorted “Buck values”, you come away that Buck is super cost-effective; responsible for a large fraction of the optimal plan using just one salary. If we didn’t have a mechanistic understanding of why that was, trying to get more Buck would become an EA cause area.
In contrast, if credit was allocated according to Shapley values, we could look at the groups whose Shapley value is the highest, and try to see if they can be scaled.
The section about “purely local” Shapley values might be pointing to something, but I don’t quite know what it is, because the example is just Shapley values but missing a term? I don’t know. You also say “by symmetry...”, and then break that symmetry by saying that one of the parts would have been able to create $6,000 in value and the other $0. Needs a crisper example.
Re: coordination between people who have different values using SVs, I have some stuff here, but looking back the writting seems too corny.
Lastly, to some extent, Shapley values are a reaction to people calculating their impact as their counterfactual impact. This leads to double/triple counting impact for some organizations/opportunities, but not others, which makes comparison between them more tricky. Shapley values solve that by allocating impact such that it sums to the total impact & other nice properties. Then someone like OpenPhilanthropy or some EA fund can come and see which groups have the highest Shapley value (perhaps highest Shapley value per unit of money/ressources) and then try to replicate them/scale them. People might also make better decisions if they compare Shapley instead of counterfactual values (because Shapley values mostly give a more accurate impression of the impact of a position.)
So I see the benefits of Shapley values as fixing some common mistakes arising from using counterfactual values. This would make impact accounting slightly better, and coordination slightly better to the extent it relies on impact accounting for prioritization (which tbh might not be much.)
I’m not sure to what extent I agree with the claim that people are overhyping/misunderstanding Shapley values. It seems plausible.