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I've already read this question in this arena, but I couldn't find an answer.

The question is: if someone obtains first co-authorship, does the "third" author gain "second authorship"?

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    What is the significance of "second authorship"? In my field (which is one where author order matters), the only meaningful positions are "first author, " "last author," and "middle author" (middle=not first and not last.) – ff524 Feb 16 '16 at 9:27
  • In the policy of our Institute, a Cancer Comprehensive Center in Italy, and in the Ministry of Health'policy as well, the meaningful positions are: first, second, last and corresponding author – Ivana Truccolo Feb 16 '16 at 9:35
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    If second author has a different weight in your institution, then you should be asking them for advice. Also, by no definition third does equal second. – Alexandros Feb 16 '16 at 11:39
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In this case, first authorship is being used for some sort of competitive ranking. As such, if there are two first authors, then in the typical custom of competitive ranking there is no second author: the next author is the third author.

If this is being defined and used for a specific purpose by a specific institution, however, it is possible that institution has its own interpretation of rankings, which can only be determined by consulting the appropriate people or documentation at that institution.

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