P.S. I just re-skimmed your article and see you dealt in Scenario 6 with ‘tragedy of the commons’ which i view as an n-person variant of the 2 -person prisoner’s dillema.
also your example 2 (Newton and Leibniz ) is an example which is sort of what i was thinking. The theorem i was thinking of would add to the picture and have something like a ‘god’ who would create either Newton, Leibniz, or both of them. Shapley value would be the same in all cases. (unless 2 calculus discoveries are better than 1----in sciences sometimes this is seen as true (‘replication’), or having ‘multiple witnesses’ in law as opposed to just an account by one (who is the victim and may not be believed )).
(its also the case for example that the 3 or 4 or even 5 early versions of quantum mechanics—schrodinger, heisenberg, dirac, feynman, bohm—though some say debroglie anticipated bohm , and feynman acknolwedged that he found his idea in a footnote in a book by Dirac—although redundant in many ways, each have unique perspectives . the golden rule also has many formulations i’ve heard)
(In my scenario, with ‘god’ , i think the counterfactual value of either newton or leibniz would be 1---because without either or both there would be no calculus with shapley value 1. god could have just created nothing---0 rather than 1).
In a way what you seem to be describing is how to avoid the ‘neglectedness’ problem of EA theory. This overlaps with questions in politics—some people vote for people in a major party who may win anyway, rather than vote for a ‘minor party’ they may actually agree with more. This might be called the ‘glow effect’—similarily some people will support some rock or sports star partly just to be in the ‘in crowd’. So they get ‘counterfactual value’ even if the world is no better off-voting for someone who will win any way is no better than voting for one who will lose—or rather they actually get additional Shapley value because they are ‘happier’ being in the ‘in crowd’ rather than being a less favored minority—but this involves a different calculation for the Shapley value, including ‘happiness’ and not just ‘who won’. But, some people are happier being in ‘minorities’, so thats another complication in the calculations.
(eg the song by Beck ‘i’m a loser’ comes to mind. pays to be a loser some times or support an unpopular cause because its actually a neglected one—people just didn’t know its actual or Shapley value. )
P.S. I just re-skimmed your article and see you dealt in Scenario 6 with ‘tragedy of the commons’ which i view as an n-person variant of the 2 -person prisoner’s dillema.
also your example 2 (Newton and Leibniz ) is an example which is sort of what i was thinking. The theorem i was thinking of would add to the picture and have something like a ‘god’ who would create either Newton, Leibniz, or both of them. Shapley value would be the same in all cases. (unless 2 calculus discoveries are better than 1----in sciences sometimes this is seen as true (‘replication’), or having ‘multiple witnesses’ in law as opposed to just an account by one (who is the victim and may not be believed )).
(its also the case for example that the 3 or 4 or even 5 early versions of quantum mechanics—schrodinger, heisenberg, dirac, feynman, bohm—though some say debroglie anticipated bohm , and feynman acknolwedged that he found his idea in a footnote in a book by Dirac—although redundant in many ways, each have unique perspectives . the golden rule also has many formulations i’ve heard)
(In my scenario, with ‘god’ , i think the counterfactual value of either newton or leibniz would be 1---because without either or both there would be no calculus with shapley value 1. god could have just created nothing---0 rather than 1).
In a way what you seem to be describing is how to avoid the ‘neglectedness’ problem of EA theory. This overlaps with questions in politics—some people vote for people in a major party who may win anyway, rather than vote for a ‘minor party’ they may actually agree with more. This might be called the ‘glow effect’—similarily some people will support some rock or sports star partly just to be in the ‘in crowd’. So they get ‘counterfactual value’ even if the world is no better off-voting for someone who will win any way is no better than voting for one who will lose—or rather they actually get additional Shapley value because they are ‘happier’ being in the ‘in crowd’ rather than being a less favored minority—but this involves a different calculation for the Shapley value, including ‘happiness’ and not just ‘who won’. But, some people are happier being in ‘minorities’, so thats another complication in the calculations.
(eg the song by Beck ‘i’m a loser’ comes to mind. pays to be a loser some times or support an unpopular cause because its actually a neglected one—people just didn’t know its actual or Shapley value. )