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.
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.