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.
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.