Let’s say you had $5k to donate and you could donate it to:
An intervention that saves 3 lives, but is 99.9% going to be funded by another donor no matter what you do, and has only room for an extra $5k (if it gets $10k it still only saves 3 lives).
An intervention that saves 1 life, and would otherwise not be funded.
To maximize a naively calculated Shapley value you would choose the first one, even though the second one leads to better outcomes (more lives saved in expected value).
I’m a bit unsure about the general principle and the details, probably there’s a way to compute Shapley values that would maximize the expected value in this case as well, but I think it would also apply to the blood donor case.
Very low confidence in this, but I think Shapley values are useful for coordinating strategic agents that act in response to each other, and to avoid double counting, but not when the actions of other agents are not influenced by yours.
This comment on the Shapley values post explains it better
This post might be interesting for some details and proposes some solutions
Thanks. I think I need to dive deeper into the mathematical definition to understand this. It seems to me that counterfactual value is not as well defined.
the second one leads to better outcomes (more lives saved in expected value)
Short objection: it is not necessarily true that higher expected value = better. For example, in this scenario for low enough risk tolerance the first scenario would be better.
Let’s say you had $5k to donate and you could donate it to:
An intervention that saves 3 lives, but is 99.9% going to be funded by another donor no matter what you do, and has only room for an extra $5k (if it gets $10k it still only saves 3 lives).
An intervention that saves 1 life, and would otherwise not be funded.
To maximize a naively calculated Shapley value you would choose the first one, even though the second one leads to better outcomes (more lives saved in expected value).
I’m a bit unsure about the general principle and the details, probably there’s a way to compute Shapley values that would maximize the expected value in this case as well, but I think it would also apply to the blood donor case.
Very low confidence in this, but I think Shapley values are useful for coordinating strategic agents that act in response to each other, and to avoid double counting, but not when the actions of other agents are not influenced by yours.
This comment on the Shapley values post explains it better
This post might be interesting for some details and proposes some solutions
Thanks. I think I need to dive deeper into the mathematical definition to understand this. It seems to me that counterfactual value is not as well defined.
Short objection: it is not necessarily true that higher expected value = better. For example, in this scenario for low enough risk tolerance the first scenario would be better.