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Rank should be computed per qid but also per stance given in the Q0 column. My proposed fix would be:

run["rank"] = run.groupby(["qid", "Q0"])["rank"].cumsum().astype(int)

The added astype(int) fails when empty fields are encountered in the rank column, indicating a partial or faulty run. Omitting this will result in no failure but the the rank column will be converted to the float datatype, which supports NaN values. All normal ranks will then have floating point notation, e. g. 1.0, 2.0 etc.