Since the Shapley value of all players also has to sum to the value of the end result, I think the value of each A voter has to be just RB/n. I’m way out of my depth with the combinatorics here, but here’s a paper I found that gives a bit more information than the wikipedia page.
Good point, but I don’t think the value of the end result is necessarily equal to RB, for much the same reason that (I suspect) Shapley value would correspond to (something like) “market value” rather than “market value plus consumer surplus”. That is, no matter how badly you want you bathroom cleaned, the value of the labor to clean the bathroom is only equal to the market value of that labor, irrespective of how happy I am to have it done.
While voting doesn’t directly map onto a market like that, there is a similar sense in which being one of the voters for something that “had no chance of passing” (thus getting the high margin of victory) is worth less—even per voter—than voting for something whose fate was less certain.
Since the Shapley value of all players also has to sum to the value of the end result, I think the value of each A voter has to be just RB/n. I’m way out of my depth with the combinatorics here, but here’s a paper I found that gives a bit more information than the wikipedia page.
Good point, but I don’t think the value of the end result is necessarily equal to RB, for much the same reason that (I suspect) Shapley value would correspond to (something like) “market value” rather than “market value plus consumer surplus”. That is, no matter how badly you want you bathroom cleaned, the value of the labor to clean the bathroom is only equal to the market value of that labor, irrespective of how happy I am to have it done.
While voting doesn’t directly map onto a market like that, there is a similar sense in which being one of the voters for something that “had no chance of passing” (thus getting the high margin of victory) is worth less—even per voter—than voting for something whose fate was less certain.