Mathematical reflections on modified fractional counting

Abstract: We make precise what is meant by stating that modified fractional counting (MFC) lies between full counting and complete-normalized fractional counting by proving that for individuals, the MFC-values are weighted geometric averages of these two extremes. There are two essentially different ways to consider the production of institutes in multi-institutional articles, namely participation and actual number of contributions. Starting from an idea published by Sivertsen, Rousseau and Zhang in 2019 we present three formulae for measuring the production of institutes in multi-institutional articles. It is shown that the one proposed by Sivertsen, Rousseau and Zhang is situated between the two other ways. Less obvious properties of MFC are proven using the majorization order.