This is extremely well produced, I think it’s the best introduction to Shapley values I’ve ever seen. Kudos for the simple explanation and approachable designs!
(Not an indictment of this site, but with this as with other explainers, I still struggle to see how to apply Shapley values to any real world problems haha—unlike something like quadratic funding, which also sports fancy mechanism math but is much more obvious how to use)
(maybe the part that seems unrealistic is the difficulty of eliciting values for the power set of possible coalitions, as generating a value for any one coalition feels like an expensive process, and the size of a power set grows exponentially with the number of players)
Thanks Austin, yes—the weeks I’ve spent trying to really understand why Shapley uses such a complicated method to calculate the possible coalitions, has left me feeling that it is actually prohibitively cumbersome for most applications. It has been popular in machine learning algorithms, but faces the problem that it is computationally expensive.
I created a comparison calculator to show Shapley next to my own method that simply weights by dividing all the explicit marginal values by the total of all the explicit marginal values and multiplying that by the grand coalition value. I found that, for realistic values being entered, it yields very similar results to Shapley, and yet is easy to calculate on a spare napkin. It also satisfies Shapley’s 4 axioms, and seems more intuitive to me at least.
There might be an issue with mine that you need the total of all marginal values (which is involved in the weighting) to find any one weighted value, whereas Shapley can be used to calculate each weighted marginal value in isolation.
Regardless… who am I to argue with a Nobel Prize winning economist? But I can’t be accused of not trying to get on board :) I like the look of Quadratic Funding, perhaps for a future post.
This is extremely well produced, I think it’s the best introduction to Shapley values I’ve ever seen. Kudos for the simple explanation and approachable designs!
(Not an indictment of this site, but with this as with other explainers, I still struggle to see how to apply Shapley values to any real world problems haha—unlike something like quadratic funding, which also sports fancy mechanism math but is much more obvious how to use)
(maybe the part that seems unrealistic is the difficulty of eliciting values for the power set of possible coalitions, as generating a value for any one coalition feels like an expensive process, and the size of a power set grows exponentially with the number of players)
Thanks Austin, yes—the weeks I’ve spent trying to really understand why Shapley uses such a complicated method to calculate the possible coalitions, has left me feeling that it is actually prohibitively cumbersome for most applications. It has been popular in machine learning algorithms, but faces the problem that it is computationally expensive.
I created a comparison calculator to show Shapley next to my own method that simply weights by dividing all the explicit marginal values by the total of all the explicit marginal values and multiplying that by the grand coalition value. I found that, for realistic values being entered, it yields very similar results to Shapley, and yet is easy to calculate on a spare napkin. It also satisfies Shapley’s 4 axioms, and seems more intuitive to me at least.
There might be an issue with mine that you need the total of all marginal values (which is involved in the weighting) to find any one weighted value, whereas Shapley can be used to calculate each weighted marginal value in isolation.
Regardless… who am I to argue with a Nobel Prize winning economist? But I can’t be accused of not trying to get on board :) I like the look of Quadratic Funding, perhaps for a future post.