Collective credit allocation in science

Consider a paper p₀ with m coauthors {a_i}(1 ≤ i ≤ m). To determine the credit share of each author, we first identify all papers that cite p₀, forming a set $\mathcal{D}$ ≡ {d₁, d₂,…,d_l}. Next we identify all cocited papers $\mathcal{P}$ ≡ {p₀, p₁,…,p_n}, representing the complete set of papers cited by papers in the set $\mathcal{D}$. The relevance of each cocited paper p_j (0 ≤ j ≤ n) to the target paper p₀ is characterized by its cocitation strength s_j between p₀ and p_j, defined as the number of times p₀ and p_j are cited together by the papers in $\mathcal{D}$ (29). For example, for p₁ in Fig. 2A, we have s₁ = 1 because only one paper (d₁) cites p₀ and p₁ together, whereas s₂ = 4 as four papers (d₁, d₂, d₃, and d₅) cite p₀ and p₂ together. Cocitation strength captures the intuition that papers by an author that are perceived to be very relevant to paper p₀ should increase the author’s perceived contribution to p₀. Note that the target paper p₀ is also viewed as a cocited paper of itself with cocitation strength equal to the citation count of p₀. Consequently, for papers with high citation count, the credit share of coauthors is less likely to be affected by other cocited papers.

Using the author list of the cocited papers, we next calculate a credit allocation matrix A, whose element A_ij denotes the amount of credit that author a_i gets from cocited paper p_j (SI Appendix, section S2.2). To develop a discipline-independent method for credit allocation, we use a fractional credit allocation matrix that does not depend on the order of authors in the author list. For example, paper p₁ assigns all credit to author a₁ who is the sole author of p₁, whereas p₀ assigns equal (half) credit to authors a₁ and a₂ (Fig. 1A). The total credit c_i of author a_i is the weighted sum of its local credit obtained from all cocited papersor in the matrix formThe vector c provides the credit of all authors of target paper p₀. By normalizing c, we obtain the fractional credit share among coauthors (Fig. 2E).

We apply the proposed procedure to the two extreme cases of Fig. 1. When author a₂ has only one paper on the topic of p₀, the fact that the community cites p₀ together with other papers of author a₁ indicates that they perceive p₀ a part of a larger body of work by author a₁ (Fig. 1A). Our method in this case obtains c = (0.75, 0.25)^T, hence allocating most credit to author a₁. When all subsequent work are joint, it gives c = (0.5, 0.5)^T, i.e., credit is equally shared between a₁ and a₂ (Fig. 1B).

To validate our method, we apply it to Nobel prize-winning publications, representing a case where the community (and the Nobel committee) has decided where the main credit goes. We therefore collected all Nobel prize-winning papers in Physics (1995–2013), Chemistry (1998–2013), Medicine (2006–2013), and Economics (1995–2013), since the Nobel committee started offering a detailed explanation with references for the prize. Table 1 shows the obtained credit share for five Nobel prize-winning physics papers in the year before the Nobel prizes were awarded, hence discounting the influence of the prize (see SI Appendix, Table S5–S8 for the complete set of results). We find that in four of the five cases, the laureates have the largest credit share, no matter whether they are the first (2010) or the last authors (2012) or occupy some intermediate position in the author list (2007). For example, as the third author of the prize-winning paper with nine coauthors (27), the 2007 Nobel laureate A. Fert gets nearly one fourth of all credit, and the remaining credit is almost evenly distributed among the other coauthors. A particularly interesting case is the 2010 prize-winning paper (30), where two of eight coauthors were awarded the Nobel prize, consistent with the predicted credit share. Indeed, the credit share of the laureates is almost equal, and it is 2.5 times higher than the credit share of the third-ranked coauthor. Another interesting example, out of the validation sample, is offered by the 1974 Nobel prize in Physics awarded to A. Hewish for the discovery of pulsars (31), with S. J. Bell as the second of five authors. Researchers in the community occasionally refer to the 1974 Nobel prize as the “No-Bell” prize because many feel that Bell should have shared it (http://en.wikipedia.org/wiki/Antony_Hewish). Applying our method to the prize-winning paper, we obtain c = [0.250, 0.189, 0.196, 0.185, 0.180]^T, assigning the largest credit to the laureate, indicating that the committee’s choice was consistent with the perceived credit within the scientific community. Fig. 3 shows the accuracy of our method at identifying the laureates from the author list of all of the 63 multiauthor prize-winning papers across three disciplines. We find that the authors with top credit share correspond to laureates in 51 papers (81%), despite the diversity of positions the laureates had in the author list. Note that we did not count single-author papers, for which credit is obvious. Counting those as well, accuracy increases to 86%.

Finally, it is useful to understand potential reasons for the method’s occasional failure. For example, for the two prize-winning papers of the 2011 Physics Nobel, our method fails to correctly identify the laureates, caused by the fact that one researcher (Filippenko) coauthors both prize-winning papers but is not the intellectual leader for either of them. Consequently, he gets the top credit on both papers. The laureates get the highest credit among the remaining coauthors; hence, if the anomaly is removed, our method correctly identifies them. This case could be corrected by incorporating contextual or exogenous information into the credit allocation matrix, like the order of the authors, as we discuss below. Another fascinating anomaly is the 1997 Nobel prize in Physics (32): S. Chu was awarded the prize, although A. Ashkin has the highest credit share according to our method. Considered by many scientists the father of the field of optical tweezers (33), Ashkin published several high-impact papers (34, 35) preceding the collaboration with Chu, developing the technology that made the Nobel prize-winning discovery possible. The prize-winning paper is repeatedly cocited with the preceding papers, explaining Ashkin’s higher score. As we show below, credit to Chu is restored if we restrict the cocited pool to papers published after the joint 1985 (Nobel-winning) paper, removing the influence of the preceding work.

The proposed methodology also allows us to determine the temporal evolution of credit share between coauthors. To illustrate this, we explore whether the Nobel prize affects the credit share of Nobel laureates relative to their coauthors. Fig. 4A shows the evolution of credit share for the 1997 Nobel prize-winning paper in Physics (32). We find that right after the publication, Ashkin gets virtually all of the credit for the discovery, and Chu’s credit share is tiny, given his lack of previous track record in this area (Fig. 4A). However, with time his credit share increases, whereas Ashkin’s credit share decreases, partly because Ashkin stopped publishing papers after 1986 and retired in 1992. The method also helps us explore how the papers preceding the publication (i.e., previous reputation) of a prize-winning paper influence the credit allocation. Indeed, when we consider all cocited papers, Ashkin’s credit share is higher than the credit share of the laureate Chu, given his work preceding the 1985 paper. However, Chu gets higher credit share than Ashkin if we only consider the cocited papers published after 1985 (Fig. 4A, Inset). This example indicates that, although established scientists receive more credit than their junior colleagues from their coauthored publications, this situation can change if the junior colleague makes important independent contribution to the field.

The effect of Nobel prize on credit share is also remarkable for the other 1997 Nobel prize-winning paper (36): the Nobel laureate W. D. Phillips’s credit share jumps after the prize year (Fig. 4B). Indeed, the prize, by canonizing credit, alters the subsequent citation patterns (37–39), reflecting a “rich get richer” phenomenon in science (40–46). To quantify how widespread this effect is, we systematically studied how the credit share of laureates relative to their coauthors changes when they are awarded the Nobel prize. Therefore, for each laureate, we calculate her average credit share c_b over 3 y before the award year and the average credit share c_a over 3 y after the award year. We quantify the increase of the credit share using the ratio c_a/c_b. For most Nobel laureates, the Nobel prize does improve their credit share relative to their coauthors (Fig. 4D), an effect that is strongest in Physics and weakest in Medicine. The two cases with the strongest effect in Physics (the outlier points in Fig. 4D) are shown in Fig. 4 A and B.

The developed method allows us to compare authors that are in the same research field but may not have published papers together. In this case, the cocitation strength is based on the citing papers that simultaneously cite at least one paper of each compared author, automatically identifying their common research topic (SI Appendix, Fig. S1). Therefore, the credit share of the compared authors reflects their relative contribution to their common research topic, just as the credit share quantifies the coauthors’ relative contribution to a joint paper. An excellent example is provided by the 2013 Nobel prize in Physics (see SI Appendix, Fig. S2 for more examples). The prize posed a widely publicized dilemma: six physicists and three key papers are credited for the 1964 discovery pertaining to the theory of Higgs boson, but the prize could be shared by a maximum of three individuals. F. Englert and R. Brout published the theory first (47) but failed to spell out the Higgs boson, whose existence was predicted in a subsequent paper by P. W. Higgs (48). G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, 1 mo later proposed the same theory (49), explaining how the building blocks of the universe get their mass. In 2010, the six physicists were given equal recognition by the American Physical Society (APS), sharing the Sakurai prize for theoretical particle physics. This symmetry was broken by the Nobel committee, awarding the prize to Higgs and Englert in 2013. To explore their credit share, we apply our method to compare these researchers (Fig. 4C) and find that Higgs gets the most credit, followed by Kibble, whereas Englert is third, getting only slightly higher credit than his coauthor Brout (deceased). Finally, Guralnik and Hagen equally share the remaining credit. Therefore, the scientific community assigns credit for the discovery recognized by the 2013 Nobel Physics prize to Higgs, Kibble, and Englert (and the deceased Brout), in this order. The committee, by bypassing Kibble, has clearly deviated from the community’s perception of where the credit lies (50).

We validate the robustness of our method by applying it to two disparate datasets, the publicly available APS dataset and the Web of Science (WOS) dataset (SI Appendix, section S1). The APS dataset consists of papers published by journals of APS between 1893 and 2009; hence, its coverage is biased toward the US-based physics community (51). The dataset does not contain papers published in interdisciplinary journals, like Science, where the 2010 Nobel winning paper was published. The WOS dataset, in contrast, contains all papers indexed by Thomson Reuters between 1955 and 2012 (52). By comparing the results obtained using these two datasets, we can evaluate the robustness of our method. In Table 1, we show the credit share of the papers obtained using each dataset individually. Overall, we find that the data incompleteness of the APS dataset never alters the relative ranking of the researchers. The same robustness is documented in Fig. 4C, where we calculated using both the APS dataset and the WOS dataset the dynamic credit share of the contenders for the 2013 Nobel prize, particularly important given that the European experimental particle physics community shuns the APS journals. Consequently, there are huge difference in coverage between the APS and WOS datasets. For example, for Higgs’ prize winning paper, we have $N_{\mathcal{D}}$ = 187, $N_{\mathcal{P}}$ = 1,847 in the APS dataset and $N_{\mathcal{D}}$ = 879, $N_{\mathcal{P}}$ = 24,596 in the WOS dataset. Despite the bias of the APS dataset and the huge difference in coverage, the relative credit of the six authors remains unchanged (Fig. 4C).

The proposed algorithm can incorporate exogenous information to improve its accuracy. To show this, we explored five priors for constructing the credit allocation matrix A, each reflecting a different hypothesis about the role of the authors. They are as follows: (i) count prior (12), each author is viewed as the sole author of the particular publication; (ii) fractional prior (14), authors equally share one credit independent of their position in the author list; (iii) harmonic prior (15), authors share one credit with their credit share proportional to the reciprocal of authors’ rank in the author list; (iv) axiomatic prior (17), authors share one credit but the credit share of each author is determined by the number of coauthors with lower rank in the author list; and (v) Zhang’s prior (16), the first and the corresponding authors get one credit, whereas other authors share one credit dependent on their rank in the author list (see SI Appendix, section S2.2 for details). The first two priors do not depend on the order of authors, whereas the last three do. We summarize the results of each prior separately for three Nobel-awarding disciplines (SI Appendix, Table S3). We find that when we incorporate corresponding author information (if not available, we take the last author as the corresponding author) for Medicine and Chemistry, the accuracy increases, but it decreases for Physics. Therefore, if contextual or exogenous information is available, our method can absorb that, improving its predictive power. However, these other priors should be only used in a disciplinary fashion.