# On the impossibility of a perfect counting method to allocate the credits of multi-authored publications

- 160 Downloads

## Abstract

The problem on how to distribute the publication credits among ordered coauthors has been extensively discussed in the literature. However, there is no consensus about what is the most adequate procedure. This paper studies the properties of the existing counting methods and shows an impossibility result regarding the existence of a general counting method able to satisfy no advantageous merging and no advantageous splitting simultaneously—two properties that we consider fundamental. Our results suggest that the generalized variations of the geometric and the harmonic counting methods are the most flexible and robust in theoretical terms.

## Keywords

Counting methods Properties Ordered coauthors Publication credits Bibliometrics## JEL Classification

C65 D04## Notes

### Acknowledgements

Author wish to thank to Juan Pablo Rincón-Zapatero and Ludo Waltman, as well as several seminar and congress participants for helpful comments and discussions. Financial support from the Spanish Ministerio of Ciencia y Innovación project ECO2016-75410-P, GRODE and the Barcelona GSE is gratefully acknowledged. The usual caveat applies.

## References

- Abbas, A. M. (2010). Generalized linear weights for sharing credits among multiple authors. arXiv preprint arXiv:1012.5477.
- Abbas, A. M. (2011). Polynomial weights or generalized geometric weights: Yet another scheme for assigning credits to multiple authors. arXiv preprint arXiv:1103.2848.
- Abramo, G., D'Angelo, C. A., & Rosati, F. (2013). The importance of accounting for the number of co-authors and their order when assessing research performance at the individual level in the life sciences.
*Journal of Informetrics*,*7*(1), 198–208.CrossRefGoogle Scholar - Assimakis, N., & Adam, M. (2010). A new authors productivity index: P-index.
*Scientometrics*,*85*(2), 415–427.CrossRefGoogle Scholar - Bornmann, L., Mutz, R., Hug, S. E., & Daniel, H.-D. (2011). A multilevel meta-analysis of studies reporting correlations between the h index and 37 different h index variants.
*Journal of Informetrics*,*5*(3), 346–359.CrossRefGoogle Scholar - Caruso, E. M., Epley, N., & Bazerman, M. H. (2006). The costs and benefits of undoing egocentric responsibility assessments in groups.
*Journal of Personality and Social Psychology*,*91*(5), 857–871.CrossRefGoogle Scholar - Cole, J. R., & Cole, S. (1974). Social stratification in science.
*American Journal of Physics*,*42*(10), 923–924.CrossRefGoogle Scholar - Cronin, B. (2001). Hyperauthorship: A postmodern perversion or evidence of a structural shift in scholarly communication practices?
*Journal of the Association for Information Science and Technology*,*52*(7), 558–569.Google Scholar - Egghe, L., Rousseau, R., & Van Hooydonk, G. (2000). Methods for accrediting publications to authors or countries: Consequences for evaluation studies.
*Journal of the Association for Information Science and Technology*,*51*(2), 145–157.Google Scholar - Gazni, A., Sugimoto, C. R., & Didegah, F. (2012). Mapping world scientific collaboration: Authors, institutions, and countries.
*Journal of the Association for Information Science and Technology*,*63*(2), 323–335.Google Scholar - Hagen, N. T. (2008). Harmonic allocation of authorship credit: Source-level correction of bibliometric bias assures accurate publication and citation analysis.
*PLoS ONE*,*3*(12), e4021.CrossRefGoogle Scholar - Hagen, N. T. (2010). Harmonic publication and citation counting: Sharing authorship credit equitably-not equally, geometrically or arithmetically.
*Scientometrics*,*84*(3), 785–793.CrossRefGoogle Scholar - Hagen, N. T. (2013). Harmonic coauthor credit: A parsimonious quantification of the byline hierarchy.
*Journal of Informetrics*,*7*(4), 784–791.CrossRefGoogle Scholar - Hu, X. (2009). Loads of special authorship functions: Linear growth in the percentage of equal first authors and corresponding authors.
*Journal of the Association for Information Science and Technology*,*60*(11), 2378–2381.Google Scholar - Katz, J. S., & Martin, B. R. (1997). What is research collaboration?
*Research Policy*,*26*(1), 1–18.CrossRefGoogle Scholar - Kim, J., & Diesner, J. (2014). A network-based approach to coauthorship credit allocation.
*Scientometrics*,*101*(1), 587–602.CrossRefGoogle Scholar - Kim, J., & Kim, J. (2015). Rethinking the comparison of coauthorship credit allocation schemes.
*Journal of Informetrics*,*9*(3), 667–673.CrossRefGoogle Scholar - Larivière, V., Gingras, Y., Sugimoto, C. R., & Tsou, A. (2015). Team size matters: Collaboration and scientific impact since 1900.
*Journal of the Association for Information Science and Technology*,*66*(7), 1323–1332.CrossRefGoogle Scholar - Lindsey, D. (1980). Production and citation measures in the sociology of science: The problem of multiple authorship.
*Social Studies of Science*,*10*(2), 145–162.CrossRefGoogle Scholar - Liu, X. Z., & Fang, H. (2012). Fairly sharing the credit of multi-authored papers and its application in the modification of h-index and g-index.
*Scientometrics*,*1*(91), 37–49.CrossRefGoogle Scholar - Lukovits, I., & Vinkler, P. (1995). Correct credit distribution: A model for sharing credit among coauthors.
*Social Indicators Research*,*36*(1), 91–98.CrossRefGoogle Scholar - Maciejovsky, B., Budescu, D. V., & Ariely, D. (2009). Research notethe researcher as a consumer of scientific publications: How do name-ordering conventions affect inferences about contribution credits?
*Marketing Science*,*28*(3), 589–598.CrossRefGoogle Scholar - O’Neill, B. (1982). A problem of rights arbitration from the talmud.
*Mathematical Social Sciences*,*2*(4), 345–371.MathSciNetCrossRefzbMATHGoogle Scholar - Persson, O., Glänzel, W., & Danell, R. (2004). Inflationary bibliometric values: The role of scientific collaboration and the need for relative indicators in evaluative studies.
*Scientometrics*,*60*(3), 421–432.CrossRefGoogle Scholar - Sekercioglu, C. H. (2008). Quantifying coauthor contributions.
*Science*,*322*(5900), 371.CrossRefGoogle Scholar - Stallings, J., Vance, E., Yang, J., Vannier, M. W., Liang, J., Pang, L., et al. (2013). Determining scientific impact using a collaboration index.
*Proceedings of the National Academy of Sciences*,*110*(24), 9680–9685.MathSciNetCrossRefzbMATHGoogle Scholar - Trenchard, P. M. (1992). Hierarchical bibliometry: A new objective measure of individual scientific performance to replace publication counts and to complement citation measures.
*Journal of Information Science*,*18*(1), 69–75.CrossRefGoogle Scholar - Trueba, F. J., & Guerrero, H. (2004). A robust formula to credit authors for their publications.
*Scientometrics*,*60*(2), 181–204.CrossRefGoogle Scholar - Tscharntke, T., Hochberg, M. E., Rand, T. A., Resh, V. H., & Krauss, J. (2007). Author sequence and credit for contributions in multiauthored publications.
*PLoS Biology*,*5*(1), e18.CrossRefGoogle Scholar - Van Hooydonk, G. (1997). Fractional counting of multiauthored publications: Consequences for the impact of authors.
*Journal of the American Society for Information Science*,*48*(10), 944–945.CrossRefGoogle Scholar - Vinkler, P. (2000). Evaluation of the publication activity of research teams by means of scientometric indicators.
*Current Science*,*79*, 602–612.Google Scholar - Waltman, L. (2016). A review of the literature on citation impact indicators.
*Journal of Informetrics*,*10*(2), 365–391.CrossRefGoogle Scholar - Wren, J. D., Kozak, K. Z., Johnson, K. R., Deakyne, S. J., Schilling, L. M., & Dellavalle, R. P. (2007). The write position: A survey of perceived contributions to papers based on byline position and number of authors.
*EMBO Reports*,*8*(11), 988–991.CrossRefGoogle Scholar - Wuchty, S., Jones, B. F., & Uzzi, B. (2007). The increasing dominance of teams in production of knowledge.
*Science*,*316*(5827), 1036–1039.CrossRefGoogle Scholar - Xu, J., Ding, Y., Song, M., & Chambers, T. (2016). Author credit-assignment schemas: A comparison and analysis.
*Journal of the Association for Information Science and Technology*,*67*(8), 1973–1989.CrossRefGoogle Scholar - Zhang, C.-T. (2009). A proposal for calculating weighted citations based on author rank.
*EMBO Reports*,*10*(5), 416–417.CrossRefGoogle Scholar