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Double counting is when someone in a pros-and-cons argument tries to count a single point more than once, by rephrasing it in various ways, counting things that are actually corellaries of it rather than distinct points, or just raising the same point again later in the conversation when you might not notice.
Let's practice identifying it with this article:
6 reasons you should use native web components
The first section has a bulleted list that claims 9 advantages of native web components, but there are at most 6 distinct ones. Let's point out all the cheating:
So the actual list of distinct points here is: composability, reusability, extensibility, scoping, interoperability, and accessibility. Even without any false statements, the case for native web components is made out to be 50% stronger than it is.
(I would actually argue every single one of the remaining 6 points is false, but that would involve a discussion more about software engineering than about double counting.)
The third section of the article, "Business Perspective", is another instance of double counting. It rehashes productivity from the first section, and to make it sound original, adds a discussion of the financial benefits of productivity.
The fourth section, "Developer Experience", rehashes productivity and reusability from the first section.