Mathematical reflections on modified fractional counting

TL;DR

This paper rigorously characterizes modified fractional counting (MFC) as a weighted geometric mean between full counting and normalized fractional counting, and explores its properties in measuring institutional contributions in multi-institutional research articles.

Contribution

It provides a formal mathematical framework for MFC, compares it with other counting methods, and introduces three formulas for assessing institutional production in multi-institutional publications.

Findings

MFC is a weighted geometric average of full and fractional counting.

Three formulas for measuring institutional production are proposed.

The Sivertsen, Rousseau, and Zhang method is intermediate between participation and contribution counts.

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.