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Rereading the thread, the set theory comment helped me understand how folks that are asking for this are thinking about it.

If it helps, the current badge count is meant to tell you "Hey, you have X many reasons to pay attention to the stuff in your database right now". We feel that's more useful than a badge that says "You need to pay attention to X items in the database" without giving you any information as to why you should pay attention.

So, yeah, from an items perspective, we are "double-counting" but only because we think the additional information is useful/helpful.