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Shap­ley values

TagLast edit: 1 May 2024 0:25 UTC by Agustín Covarrubias

In the context of EA, Shapley values are a method for assigning credit for the impact of an intervention to each of a set of actors collaborating to make it happen. The concept of a Shapley value comes from cooperative game theory, where it is a general solution to the problem of distributing gains from cooperation. In impact assessment, it is often compared to the calculation of the raw counterfactual impact of an intervention.

Loosely, each Shapley value (each associated with a specific actor) corresponds to the average of the counterfactual impact produced by the actor, considering each possible way in which the agents could have assembled themselves to cooperate. Formally, we define a coalition, that is a potential set of actors cooperating with each other, and define each actor’s Shapley value as[1]:

This solution to the problem is known to fulfill some desirable properties, including that the sum of the values adds up to the total value provided, that agents that contribute the same amount get the same amount of credit, and that it doesn’t matter in which order actors choose to collaborate.

Furthermore, when used to assess the impact of projects, Shapley values can be helpful as adjustment factors to prevent coordination issues arising from multiple actors acting based on the estimated counterfactual impact of their contributions. Not using these adjustments can lead to, for example, the double counting of impact, because actors fail to consider what would happen if other actors didn’t cooperate.

Further reading

Sempere, Nuño (2019) Shapley values: Better than counterfactuals, Effective Altruism Forum, October 10.

Pinsent, Stan (2023) Shapley values: an introductory example, Effective Altruism Forum, November 2023.

Sempere, Nuño (2020) Shapley Values II: Philantropic Coordination Theory & other miscellanea, Effective Altruism Forum, March 10.

Related entries

altruistic coordination | impact assessment | counterfactual reasoning | philanthropic coordination | game theory | thinking at the margin

  1. ^

    Or using the notation of so-called coalitional games and permutations:

    Where denotes the worth of coalition , that is, the total expected value from all actors in collaborating with each other.

Shap­ley val­ues: Bet­ter than counterfactuals

NunoSempere10 Oct 2019 10:26 UTC
143 points
54 comments14 min readEA link

Shap­ley val­ues: an in­tro­duc­tory example

Stan Pinsent12 Nov 2023 13:35 UTC
15 points
0 comments4 min readEA link

Shap­ley value, im­por­tance, eas­i­ness and neglectedness

Vasco Grilo🔸5 May 2023 7:33 UTC
27 points
0 comments4 min readEA link

Co­op­er­a­tive or Com­pet­i­tive Altru­ism, and An­ti­so­cial Counterfactuals

Davidmanheim20 Mar 2023 17:54 UTC
53 points
25 comments5 min readEA link

Offset­ting is more ex­pen­sive than it’s assumed

emre kaplan28 Feb 2024 9:16 UTC
21 points
4 comments1 min readEA link
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