, Volume 114, Issue 3, pp 839–857 | Cite as

Golden-ratio as a substitute to geometric and harmonic counting to determine multi-author publication credit

  • Yannick Berker


Countless bibliometric indexes have been proposed to assess researchers’ productivities, in particular, in fields where the author sequence is regarded helpful in determining authors’ individual credits. Unfortunately, the most popular h-index ignores author ranks and leads to bias with multi-author publications; and of the many bibliometric counting methods proposed for assigning credit to authors, such as harmonic or geometric counting, none seems to have been widely adopted yet. In this work, I challenge the assumption that the total credit for a publication be equal to 1. This total-credit normalization assumption diminishes first-author credit and may impede adoption of multi-author-aware credit assignment rules. Other than on relative contributions, author credit could be based on variables such as accountability, which remains unchanged for the first (and potentially, the last) author regardless of additional coauthors. Therefore, I study the adequacy of several counting methods for first-author-normalized credit, giving full credit to the first author while also crediting coauthors. Harmonic counting has been shown to agree well with empirical data; however, unlike geometric counting, harmonic counting results in unbounded total credit for a publication with first-author-credit normalization in the limit of many authors. I therefore propose adaptable geometric counting and evaluate how it combines the advantages of harmonic and geometric counting through an additional parameter. I show that the golden ratio is a parameter for geometric counting that agrees as well as harmonic counting with empirical data for total-credit normalization; and I discuss the impact of using adaptable geometric counting with first-author-normalized credit. In particular, the latter features bounded total credits even when full credit is given to first authors. In conclusion, geometric counting with the golden ratio can be used for credit assignment without having to choose a parameter value, yet offers customization potential and can be combined with either normalization assumption.


Bibliometric counting Coauthor problem Golden ratio Validation 



I thank Jessica Mueller and Dr. Benjamin Goldschmidt for critically reading an earlier version of the manuscript, and several anonymous reviewers for their suggestions to improve the focus of this manuscript. The work leading to this publication was supported by the German Academic Exchange Service (DAAD) (Grant No. 57178382) with funds from the German Federal Ministry of Education and Research (BMBF) and the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA Grant Agreement No. 605728 (P.R.I.M.E.—Postdoctoral Researchers International Mobility Experience).


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Department of RadiologyUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Department of Physics of Molecular Imaging SystemsRWTH Aachen UniversityAachenGermany
  3. 3.German Cancer Research Center (DKFZ)HeidelbergGermany

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