“The alternative approach (which I argue is wrong) is to say that each of the n A voters is counterfactually responsible for 1/n of the $10bn benefit. Suppose there are 10m A voters. Then each A voter’s counterfactual social impact is 1/10m$10bn = $1000. But on this approach the common EA view that it is rational for individuals to vote as long as the probability of being decisive is not too small, is wrong. Suppose the ex ante chance of being decisive is 1/1m. Then the expected value of Emma voting is a mere 1/1m$1000 = $0.001. On the correct approach, the expected value of Emma voting is 1/10m*$10bn = $1000. If voting takes 5 minutes, this is obviously a worthwhile investment for the benevolent voter, as per common EA wisdom.”
I am not sure, whether anyone is arguing for discounting twice. The alternative approach using the shapley value would divide the potential impact amongst the contributors, but not additionally account for the probability. Therefore, in this example both approaches seem to assign the same counterfactual impact.
More generally, it seems like most disagreements in this thread could be resolved by a more charitable interpretation of the other side (from both sides, as the validity of your argument against rohinmshah’s counterexample seems to show)
Right now, a comment from someone more proficient with the shapley value arguing against
“Also consider the $1bn benefits case outlined above. Suppose that the situation is as described above but my action costs $2 and I take one billionth of the credit for the success of the project. In that case, the Shapely-adjusted benefits of my action would be $1 and the costs $2, so my action would not be worthwhile. I would therefore leave $1bn of value on the table.”
So, on the Shapely value approach, we would ignore the probability of different states of affairs when deciding what to do? This seems wrong. Also, the only time the discount would be the same is when the probability of counterfactual impact happens to equal the discount applied according to the shapely value. This would only happen coincidentally: e.g. the chance of being decisive could be 1⁄1,000 and the shapely discount 1/1m.
“The alternative approach (which I argue is wrong) is to say that each of the n A voters is counterfactually responsible for 1/n of the $10bn benefit. Suppose there are 10m A voters. Then each A voter’s counterfactual social impact is 1/10m$10bn = $1000. But on this approach the common EA view that it is rational for individuals to vote as long as the probability of being decisive is not too small, is wrong. Suppose the ex ante chance of being decisive is 1/1m. Then the expected value of Emma voting is a mere 1/1m$1000 = $0.001. On the correct approach, the expected value of Emma voting is 1/10m*$10bn = $1000. If voting takes 5 minutes, this is obviously a worthwhile investment for the benevolent voter, as per common EA wisdom.”
I am not sure, whether anyone is arguing for discounting twice. The alternative approach using the shapley value would divide the potential impact amongst the contributors, but not additionally account for the probability. Therefore, in this example both approaches seem to assign the same counterfactual impact.
More generally, it seems like most disagreements in this thread could be resolved by a more charitable interpretation of the other side (from both sides, as the validity of your argument against rohinmshah’s counterexample seems to show)
Right now, a comment from someone more proficient with the shapley value arguing against
“Also consider the $1bn benefits case outlined above. Suppose that the situation is as described above but my action costs $2 and I take one billionth of the credit for the success of the project. In that case, the Shapely-adjusted benefits of my action would be $1 and the costs $2, so my action would not be worthwhile. I would therefore leave $1bn of value on the table.”
might be helpful for a better understanding.
So, on the Shapely value approach, we would ignore the probability of different states of affairs when deciding what to do? This seems wrong. Also, the only time the discount would be the same is when the probability of counterfactual impact happens to equal the discount applied according to the shapely value. This would only happen coincidentally: e.g. the chance of being decisive could be 1⁄1,000 and the shapely discount 1/1m.