Warren,
You're right, I erred. "Style" should be used to refer to more subjective
aspects of writing. Perhaps I should have described formal mathematical
writing as following a particular "structure."
All I can say in defense of how I wrote the manuscript is that I am
inexperienced at formal mathematical writing (physicists are to rigor what
jello is to structural integrity) so I took my cues from how Saari wrote in
"Basic Geometry of Voting."
The weaknesses of that approach are, as you point out, substantial. However,
Saari wrote for a wider audience than just formally-trained mathematicians,
including social scientists (some of whom are indeed schooled in formal
mathematical approaches, but not all) in his audience. There is some merit in
that, and I need to think things through as I consider restructuring the
paper. I appreciate your feedback on this.
Anyway, revising to a more formal structure will take some time. In the near
term, I'll try to include a table earlier in the paper to at least give the
reader a more organized summary and preview of what is to come.
Thanks for the feedback.
Alex
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