Mathematical reflections on modified fractional counting

Abstract

We make precise what is meant by stating that modified fractional counting (MFC) liesbetween full counting and complete-normalized fractional counting by proving that forindividuals, the MFC values are weighted geometric averages of these two extremes. There aretwo essentially different ways to consider the production of institutes in multi-institutionalarticles, namely participation and actual number of contributions. Starting from an ideapublished by Sivertsen, Rousseau and Zhang in 2019, we present three formulas for measuringthe production of institutes in multi-institutional articles. It is shown that the one proposed bySivertsen, Rousseau and Zhang is situated between the two other ways. Less obviousproperties of MFC are proven using the majorization order.