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Consider a country's national output, measured by counting the number of authors from countryc that collaborate in every paper in a bibliography. Depending on whether countryc appears at least once in every paper, we are able to deduce the corresponding relationship betweenc's fractional score and its fraction of multinational papers to whichc belongs.  One of these models, a slowly decreasing concave function is similar to the relation observed byNederhof andMoed 1 between the fractionated score of a countryc and its fraction of multinational papers.    The proof of the models developed here uses a stochastic property of weighting schemes, namely that the average fractional score of a country equals its total score.

An explanation of the relation between the fraction of multinational publications and the fractional score of a country