When soaking chickpeas (garbanzo beans), do I discard floaters?
Boy is THAT ever controversial. It seems that everybody has a theory as to why some beans float while most do not. The most common answer is that the "floaters" are older, and less hydrated to begin with. Some people insist that some beans float because worms have gotten into them. Hogwash, ignore those comments. The bottom line is that "floaters" are perfectly safe, and there is nothing "icky" about them, although they may take longer to fully cook. So, it becomes a matter of personal choice. If it's important to you that all of your chickpeas cook to exactly the same degree of tenderness, throw them out. If you don't mind a slightly (and I do mean slightly) chewier bean here and there, keep them. Personally, I keep them.

Welcome to Seasoned Advice by the way, great first question!