Then if each person was optimizing for the counterfactual impact, they would all choose the first option, for a lower total impact.
I think that if this is true, they aren’t modelling the counterfactual correctly. If it were the case that all the others were definitely going for the 100 joint utility project no matter what you do, then yes, you should also do that, since the difference in utility is 100 > 20. That’s the correct solution in this particular case. If none of the others were pursuing the 100 utility project, then you should pursue the 20 utility one, since 20 > 0. Reality is in-between, since you should treat the counterfactual as a (subjective) probability distribution.
EDIT: “Reality is in-between” was inaccurate. Rather, the situation I presented had all decisions independent. In reality, they are not independent, and you should consider your impact on the decisions of others. See my reply below.
What you say seems similar to a Stag hunt. Consider, though, that if the group is optimizing for their individual counterfactual impact, they’ll want to coordinate to all do the 100 utility project. If they were optimizing their Shapley value, they’d instead want to coordinate to do 10 different projects, each worth 20 utility. 20*10 = 200 >100.
Consider this case: you choose the 20 utility project and single-handedly convince the others to each choose the 20 utility project, or else you convince everyone to do the joint 100 utility project. Now, your own individual counterfactual impact would be 20*10 = 200 > 100.
If you all coordinate and all agree to the 20 utility projects, with the alternative being everyone choosing the joint 100 utility project, then each actor has an impact of 20*10 = 200 > 100. Each of them can claim they convinced all the others.
So, when you’re coordinating, you should consider your impact on others’ decisions; some of the impact they attribute to themselves is also your own, and this is why you would end up double-counting if you just add up individual impacts to get the group’s impact. Shapley values may be useful, but maximizing expected utility still, by definition, leads to the maximum expected utility (ex ante).
In my mind, that gets a complexity penalty. Imagine that instead of ten people, there were 10^10 people. Then for that hack to work, and for everyone to be able to say that they convinced all the others, there has to be some overhead, which I think that the Shapley value doesn’t require.
FWIW, it’s a complex as you want it to be since you can use subjective probability distributions, but there are tradeoffs. With a very large number of people, you probably wouldn’t rely much on individual information anymore, and would instead lean on aggregate statistics. You might assume the individuals are sampled from some (joint) distribution which is identical under permutations.
If you were calculating Shapley values in practice, I think you would likely do something similar, too. However, if you do have a lot of individual data, then Shapley values might be more useful there (this is not an informed opinion on my part, though).
Perhaps Shapley values could also be useful to guide more accurate estimation, if directly using counterfactuals is error-prone. But it’s also a more complex concept for people to understand, which may cause difficulties in their use and verification.
I think that if this is true, they aren’t modelling the counterfactual correctly. If it were the case that all the others were definitely going for the 100 joint utility project no matter what you do, then yes, you should also do that, since the difference in utility is 100 > 20. That’s the correct solution in this particular case. If none of the others were pursuing the 100 utility project, then you should pursue the 20 utility one, since 20 > 0. Reality is in-between, since you should treat the counterfactual as a (subjective) probability distribution.
EDIT: “Reality is in-between” was inaccurate. Rather, the situation I presented had all decisions independent. In reality, they are not independent, and you should consider your impact on the decisions of others. See my reply below.
What you say seems similar to a Stag hunt. Consider, though, that if the group is optimizing for their individual counterfactual impact, they’ll want to coordinate to all do the 100 utility project. If they were optimizing their Shapley value, they’d instead want to coordinate to do 10 different projects, each worth 20 utility. 20*10 = 200 >100.
Consider this case: you choose the 20 utility project and single-handedly convince the others to each choose the 20 utility project, or else you convince everyone to do the joint 100 utility project. Now, your own individual counterfactual impact would be 20*10 = 200 > 100.
If you all coordinate and all agree to the 20 utility projects, with the alternative being everyone choosing the joint 100 utility project, then each actor has an impact of 20*10 = 200 > 100. Each of them can claim they convinced all the others.
So, when you’re coordinating, you should consider your impact on others’ decisions; some of the impact they attribute to themselves is also your own, and this is why you would end up double-counting if you just add up individual impacts to get the group’s impact. Shapley values may be useful, but maximizing expected utility still, by definition, leads to the maximum expected utility (ex ante).
Good point!
In my mind, that gets a complexity penalty. Imagine that instead of ten people, there were 10^10 people. Then for that hack to work, and for everyone to be able to say that they convinced all the others, there has to be some overhead, which I think that the Shapley value doesn’t require.
FWIW, it’s a complex as you want it to be since you can use subjective probability distributions, but there are tradeoffs. With a very large number of people, you probably wouldn’t rely much on individual information anymore, and would instead lean on aggregate statistics. You might assume the individuals are sampled from some (joint) distribution which is identical under permutations.
If you were calculating Shapley values in practice, I think you would likely do something similar, too. However, if you do have a lot of individual data, then Shapley values might be more useful there (this is not an informed opinion on my part, though).
Perhaps Shapley values could also be useful to guide more accurate estimation, if directly using counterfactuals is error-prone. But it’s also a more complex concept for people to understand, which may cause difficulties in their use and verification.