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\title{Effective Peer Review}
\date{October 14, 2011}
\begin{document}
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Below are several examples of dialogue between a reviewer (Alice) and author (Bob). Consider what might be effective or ineffective about how they interact.
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\textbf{Example \#1}
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\noindent \textsc{Alice}: Well everything looked pretty good. It seems like you did all the math right and I can read it and stuff.
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\noindent \textsc{Bob}: Oh, thanks. So, were there any parts that needed some work?
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\noindent \textsc{Alice}: I don't know. There were a few parts where maybe you could have used some different words, but I understood all of it. There was guiding text and everything.
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\noindent \textsc{Bob}: Cool --- so I shouldn't change anything?
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\noindent \textsc{Alice}: Yeah. I think it's fine.
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\begin{center}
\textbf{Example \#2}
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\noindent \textsc{Alice}: Gosh, where to start? I guess there are some proofs, but just look at this! Your introduction: hardly makes sense. You state Theorem 1 without defining some of its terms. There's no indication of why you're introducing the sets $A$ and $B$ at the start of the proof. And you say you're proving by contrapositive but this is contradiction!
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\noindent \textsc{Bob}: Oh, um\ldots yeah, I guess I see what you're saying. So what about\ldots
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\noindent \textsc{Alice}: No, that paragraph is horrible.
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\noindent \textsc{Bob}: Hm. So, where do you think I should go from here?
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\noindent \textsc{Alice}: Well, starting over from scratch would be one idea\ldots
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\begin{center}
\textbf{Example \#3}
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\noindent \textsc{Alice}: This was pretty nice. There's strong motivation at the start and you state your claim in Theorem 1 very clearly. Now I did want to look at the start of your proof: you leap into a number of technical details without indicating why they're important. I thought you could ease into that with a short guiding paragraph.
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\noindent \textsc{Bob}: What do you mean? I mean, it's clear what I'm doing, you have to introduce all those concepts, and I put the pieces together in the fourth paragraph. It's perfectly clear!
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\noindent \textsc{Alice}: Right --- I figured it out eventually. I just think you'd place less of a burden on the reader by providing a roadmap of where things are headed.
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\noindent \textsc{Bob}: But then won't I say everything twice? I want this to be concise and clean, not boring.
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\noindent \textsc{Alice}: OK\ldots well, let's look at Theorem 2. In the proof, you argue for sequential compactness, but you never mention that Heine-Borel reduces the problem to that matter.
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\noindent \textsc{Bob}: Oh come on! Everyone knows Heine-Borel!
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\textbf{Example \#4}
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\noindent \textsc{Alice}: So I enjoyed this paper --- I think you have a nice perspective on the problem. Things are well-motivated in the first paragraph, the proofs seem complete, and you make some nice use of guiding text.
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\noindent \textsc{Bob}: OK, thanks.
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\noindent \textsc{Alice}: I did feel that some of the information could have been organized better. For instance, your proof of Theorem 1 is only two paragraphs, but there are at least four distinct steps to your argument.
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\noindent \textsc{Bob}: Uh-huh. So maybe it would be better if I split the ideas by paragraph?
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\noindent \textsc{Alice}: Exactly. I think that would help a lot. And then I also wanted to draw your attention to the third-to-last paragraph. It's a little hard to tell how you use $\Xi_{15}$ in the rest of the proof.
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\noindent \textsc{Bob}: Well, I guess I thought it was important because of the r\^{o}le it plays in a related problem\ldots
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\noindent \textsc{Alice}: Right --- I can sort of see that, but I wonder if you should cut that part since it's not really mentioned elsewhere in this paper.
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\noindent \textsc{Bob}: Hmm. OK, well, I'll consider that when I make my revisions.
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