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@ -150,7 +150,9 @@ With that in mind, here are our results for the different assumptions:
| 1 | I(k) = 0.99^k | 97.92 | 0 | 97.92 | 195.85 | 97.92 | Yes | 49.15 | 50% |
| 1 | I(k) = 2/k^2 | 3.29 | 0 | 3.29 | 6.58 | 3.29 | Yes | 1.64 | 50% |
CI stands for (pure/naïve) counterfactual impact. Taking into account the above, my best guess is that OpenPhilantropy would be (Shapley-)responsible for something between a third and half of the impact of the projects it funds, because the real world seems to me to be closer to: projects are distributed according to a power law, there are many projects, and within EA OpenPhilantropy is close to a monopoly with respect to funding. OTOH, 2 seems to high an exponent for the power law, perhaps something like 1 - 1.5 would be more realistic. Similarly, if projects are distributed according to a power-law, then the impact of creating a new top charity (Re: Charity Entrepeneurship) actually seems quite high.
CI stands for (pure/naïve) counterfactual impact. Taking into account the above, my best guess is that OpenPhilantropy would be (Shapley-)responsible for something between a third and half of the impact of the projects it funds, because the real world seems to me to be closer to: projects are distributed according to a power law, there are many projects, and within EA OpenPhilantropy is close to a monopoly with respect to funding. Similarly, if projects are distributed according to a power-law, then the impact of creating a new top charity (Re: Charity Entrepeneurship) actually seems quite high.
Note: 2 seems to high an exponent for the power law, perhaps something like 1 - 1.5 would be more realistic. In any case, the conclusion that OpenPhil gets 50% of the (Shapley)-impact if it's a monopoly remains true.
## An original result pertaining the above:
The Shapley value is too computationally expensive to naïvely calculate; it would require us to consider 2^1011 coalitions. In general, for large values the Shapley value will not be computationally tractable. See, for example: