"I am no doubt not the only one who writes in order to have no face. Do not ask who I am and do not ask me to remain the same: leave it to our bureaucrats and our police to see that our papers are in order. At least spare us their morality when we write." (Michel Foucault)
"If Lester Bangs were alive today, he'd know exactly why Miles Davis used to call Wynton Marsalis 'the police'." (Ron Silliman)*
Andrew Gelman is not the plagiarism police because there is no such thing as the plagiarism police. But there is, at any self-respecting university and any self-respecting academic journal, a plagiarism policy, and there sure as hell is a "morality" of writing in the world of scholarship. The cardinal rule is: don't use other people's words or ideas without attributing those words or ideas to the people you got them from. Everyone makes mistakes, but if you make one you have to correct it. Don't explain why your mistake isn't very serious or "set things right" by pointing to the "obvious" signs of your good intentions. If you've used somebody else's words or ideas in a way that suggests to a reader that these are your words or ideas then you have committed plagiarism.
Don't say you've cleared it with the original author. The real victim of your crime is not the other writer; it's your reader. That's whose trust you've betrayed.
The case that Andrew posted has met with the usual range of reactions. One of the most common is to suggest that the critics, "the police", are overreacting, an echo, perhaps, of Foucault's "spare me their morality when I write". "There are many worse sins," says one. "I find it extraordinarily difficult to get agitated about this," says another, implying of course that anyone who uses the word "plagiarism" is in some kind of tizzy about it. One commenter also introduced the red herring of intention: "we cannot assume that the existence of plagiarism is prima facie proof of deliberate plagiarism". Ironically, the assuming here is being done by the defenders. They are assuming that those who worry about plagiarism in the work of others are outraged about misconduct. But nobody said anything about motive. All they did was to point out an error of scholarship that needs to be fixed.
I run into this regularly when I try to get my critical scholarship published. I am trying to bring an error to the attention of the community of scholars (so we will no longer believe something that isn't true, or at least no longer believe it on a false basis), but I am then told that I have to be careful because plagiarism is a "serious accusation". I think that's the problem in dealing with these cases. It's the reason many cases are passed over in silence, I suspect.
*This quote originally referred to Branford Marsalis, which is what I'm pretty sure Silliman wrote in a comment stream seven years ago. But see Andrew Shield's comments to this post, which makes a plausible case that Wynton makes better sense here. I have decided to modify the quote to capture what Silliman must have meant. The comments are no longer available at Silliman's blog.