Here’s a very late follow-up: the rationale behind linearity for Shapley values seems closely related to the rationale behind the independence axiom of VNM rationality, and under some decision theories we apparently can dispense with the latter.
This gives me the vocabulary for expressing why I find linearity constraining: if I’m about to play game A or game B with probabilities p and 1−p respectively, and my payout of A is lower, maybe I would prefer to get a lower payout in B in exchange for a higher payout in A. I’m not sure how much of that is just downstream from “what if my utility isn’t linear in the payout” or something like that, though.
Here’s a very late follow-up: the rationale behind linearity for Shapley values seems closely related to the rationale behind the independence axiom of VNM rationality, and under some decision theories we apparently can dispense with the latter.
This gives me the vocabulary for expressing why I find linearity constraining: if I’m about to play game A or game B with probabilities p and 1−p respectively, and my payout of A is lower, maybe I would prefer to get a lower payout in B in exchange for a higher payout in A. I’m not sure how much of that is just downstream from “what if my utility isn’t linear in the payout” or something like that, though.