From a9e8b51a0133cbe2afbafbfe8c842daa4620b584 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Nu=C3=B1o=20Sempere?= Date: Thu, 12 Sep 2019 13:14:30 +0200 Subject: [PATCH] Update Shapley.md --- ea/Shapley.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/ea/Shapley.md b/ea/Shapley.md index 6885c76..2b8e5ff 100644 --- a/ea/Shapley.md +++ b/ea/Shapley.md @@ -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: