### Shapley Values: Unlocking Intuition with Venn Diagrams

I stumbled upon Shapley values through my interest in explainable AI. For reference, check out the Python package 'SHAP': https://shap.readthedocs.io/en/latest/ The package analyzes the importance of each feature in a model's decision. It works for black-box models (e.g. deep neural networks), which has made SHAP extremely popular. Interestingly, very few explainers on Shapley values discuss the concept of 'synergy,' and NO explainers use Venn diagrams. I was surprised, because the visual intuition for Shapley values is simple and powerful. The value of my article lies in the gap it fills. If you're willing, I encourage you to explore the existing explainers on Shapley values and see how mine compares. Above all, this piece is a work in progress—it is my first ever online explainer, and any feedback is invaluable! Thanks so much for reading, and I hope you enjoy.

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### Comments

Nice, well-motivated article. The Venn diagrams really do make the concept much clearer. Two small criticisms: first, when you introduced the characteristic and synergy functions, that begs the question of how to calculate the second from the first. It would have been nice to see this worked out. Second, the description of linearity in the concluding notes confused me for a minute: if you were to open a second lemonade stand, then presumably the profits wouldn't actually be additive, because each worker would have to multitask. This could be clarified a bit; for example, by imagining the two enterprises running one after the other.

5.8Very readable, accessible, and interesting. Would have been even better if it didn’t pre suppose some interest in Shapely values. But that’s okay, since that was made clear from the outset.

6.9The article does offer better data visualization using Venn diagrams, but does not offer much novelty with respect to some deep math explanation.

2.8great initial setup - I really wanted to know the solution to how to split the profits fairly, and it wasn't obvious to me - the idea of "synergy bonus" with the venn diagram was really an aha moment for me! - after seeing the wikipedia page I think your work is really well motivated cause the wikipedia page would've been much harder to understand

8.3Really cool article. I never knew about Shapley values before. I thought your overall structure of the article was great and your writing style was concise while also being informative. Keep it up!

6.5This was amazing. Quick, fun and clear. Thank you so much. I even sent this article to a friend!

8.8Simply explained !

8.6Motivation: Good. While the lemonade stand example excelled in speaking to a broad audience, a few words before the formalities about more realistic scenarios might be an improvement for the more practically-minded. Clarity: Exceptional in the intuition section, adequate beyond that. As a memorable example, it took me a bit to notice that in the "more compact notation" the sum is over S rather than i; introducing some notation for the Shapely value might have helped. Novelty: I can't speak to this. But with the breadth of audience that the article attempted to reach (successfully!), I suspect many folks will have my reaction and enjoy this introduction to a different way of thinking. Memorability: On the downside, once we got past the intuition section, there wasn't a lot for me to take away, even as someone fairly comfortable with interpreting formulas. The "concluding notes" were probably intended to be that takeaway, but they hadn't been signposted up to that point. On the upside, the Venn diagram with the three linear cuts is a very elegant image. That will definitely pop into my head when I hear "Shapely values" in the future.

7.1I think the explaination of the Shapley values with the venn diagram was quite illustrative and easy for people to get a hold of the basic concept on why Shapley values are a fair distribution system and the basic properties are described elegantly by it. I would have liked a bit detail on how Shapley values could be abstracted into a more complex example, where we start to use the math to be able to visualize more complex objects.

6.3Clear and concise. I'm taking off some points for novelty but love the focus.

5.3Good, short, simple, clear, useful. Thanks!

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