Do Russian researchers of international relations collaborate too much?

ABSTRACT

This paper applies the model by Jackson and Wolinsky [1996] to analyze co-authorship connections among Russian international relations scholars. By using data on almost a thousand researchers, I check whether the co-author network is over-connected with respect to utilitarian efficiency, as the model claims. My findings clearly indicate that Russian experts reveal quite the contrary pattern as they tend to underinvest in co-authoring partnerships which might contribute to their failure of publishing in influential journals abroad. Finally, I conclude that the low density of research collaborations should be considered as evidence in favor of reforming institutional environment in Russian international relations science.

RESEARCH QUESTION

Co-authorships matter. Researchers benefit from publishing, and therefore seek collaborations to increase the output of their articles. However, pay-offs from co-authoring decrease when others do the same because any new collaboration of my partners is time-consuming and delays completion of current joint projects. That being said, what number of co-authorships is associated with optimal performance of scholars? Do collaborations between researchers have positive or negative spillover effects on others, if any? Or, bluntly put, may individual choices made by scholars hamper the development of the discipline they are active in?

These are some of the questions one has to deal with to be able to correct incentives and institutions that shape the state of the art in Russian international relations science. RIAC’s Global Science longs to do just that, and has taken effective steps towards identifying roots of poor performance of local scholars abroad. Ekaterina Chimiris [2013], for example, drew a social network mapping joint projects of a dozen of experts in international relations from all over the country and demonstrated applications of this method to visualize and analyze existing as well as potential collaborations. As useful as it is, there is still a long way to go as the questions raised above largely remain unanswered.

This paper expands and enriches research for the Global Science project by evaluating efficiency of the co-authorship web of international relations researchers in Russia. I begin by outlining the model of strategic link formation by Jackson and Wolinsky predicting that stable co-author networks are over-connected with respect to utilitarian welfare, so there is a conflict between individual and common good. Afterwards, I conduct an empirical test for this hypothesis by constructing a network of collaborations that includes all researchers who have published at least once the last years in any of four Russian largest international relations journals. The next section describes the empirical network and explains why it has so little to do with theoretical predictions. Finally, I conclude with the outline of institutional reform needed to create incentives to choose co-authorships leading to ‘socially’ optimal outcomes.

THEORY AND MODEL

It is intuitive to analyze co-authorships by referring to tools and ideas from social network analysis. SNA essentially consists in mapping empirical relationships between persons into a network where a set of links (= relations) is defined over nodes (= persons). We can either take networks as given and see how their structure influences behavior of individuals, or do just the opposite by examining how goals and interests of individuals shape these networks. Jackson and Wolinsky model behavior of scholars in the framework of the latter approach, that is, experts are viewed to have a particular type of utility functions that determine choices of forming and severing links to others. Before reconstructing the co-author model itself, I devote the following sub-section to presenting basic concepts used in SNA. If you are acquainted with the notions of utility functions, pairwise stability and utilitarian efficiency as well as under- and over-connectedness, feel free to skip it.

Basic notions

Like elsewhere in economics, agents are seen as utility maximizers acting under certain constraints. In the context of co-authorship analysis, utility may be interpreted as the index of citation, job promotion, expansion of funds allocated to one’s research etc. Furthermore, utility functions generally satisfy the property of additive separability, i.e. utility is calculated by subtracting costs of link maintenance from benefits these connections yield,

 (1.1) u_i = β_i – cl_i, ∀i ∈ N, where n is a set of nodes in network g (Individual utility (u_i) is the difference between benefits from collaboration (β_i) and cost parameter (c) times the number of links (l_i))

Utility functions determine which links are present in a given network. It is assumed that the addition of links is a bilateral process and thus takes consent from both players. So, any given pair {i,j} agree to form a link if and only if it strictly increases utility of i and does not decrease that of j. On the contrary, severance is essentially unilateral so a link is deleted if the deletion strictly increases utility of i independent of corresponding welfare consequences for j. Wrapping up, a network is called pairwise stable when no pair of players have an incentive to form a link, and no-one is willing to sever one (note that pairwise stability is not equivalent to Nash stability known from Game theory).

SNA theory also enables one to evaluate efficiency of a network by referring to its welfare. Of all welfare measures that satisfy the basic requirement of weak Pareto improvement, the one employed oftenest is utilitarian welfare which is a sum of all individual utilities,

 (1.2) w (g) = ∑u_i, ∀i ∈ n, where w(g) is welfare of network g

So, the network is efficient with respect to utilitarian welfare if there exists no set of links defined over the same set of agents that would promote a higher net sum of individual utilities. With a large enough number of agents, unfortunately, the chance of observing an efficient network is close to zero because some altering of the link structure is bound to improve utilitarian welfare. Therefore, what matters is how much a given network is inefficient rather than whether it is efficient. In order to make meaningful comparisons of welfare, SNA classifies inefficient networks into under-, over-connected, both, or none. If a network is under-connected, its welfare can be improved by adding a set of links; similarly, over-connected networks gain efficiency with some of their links severed.

Utility function

Jackson and Wolinsky assume the following utility function of researchers:

 (1.3) u_i (g) = ∑_{j: ij∈g} [1/l_i + 1/l_j + 1/l_i l_j], where l_i is the number of links of i and l_j is the number of links of i’s neighbor

The model implies that every agent has an equal unit of time they equally distribute among projects. “The output of each project depends on the total time invested in it by the two collaborators, 1/l_i + 1/l_j, and on some synergy in the production process captured by the interactive term 1/l_il_j” (Ibid, p. 56). It is straightforward to see some immediate implications of this function. Firstly, it is strictly decreasing in the number of links of i’s neighbors because the more joint projects my partners are involved in with others, the less time is available for me. Therefore, the model satisfies negative externalities, i.e. others forming links inflicts losses on one’s utility (spillover effects I was wondering about in the introduction). To see the impact of externalities, consider Figure 1 which illustrates the utility level decreasing with the number of i’s only partner’s connections l_j going up from 0 to 14.

Figure 1. u_i for 1 ≤ l_j ≤ 14 and l_i =1

Conversily, utility increases in own connections if the number of our partners’ links is fixed. This property seems to confirm our untuitions because I do benefit from others putting time and effort into my projects. Figure 2 demonstrates this positive relationship.

Figure 2. u_i for 0 ≤ l_i ≤ 10 and l_j = 1

To complete the overview of how utility responds to changes in the arguments, I attach an Excel-computed table that contains utility values for any combination of own and partners’ links (assumed that one value holds for all) within the diapason from 0 to 10. Examining the table from left to right helps to get a better understanding of negative consequences brought about by spillover effects whereas reading it top-down reveals benefits from expansion of coauthoring practices.

Table 1. Utility values for 0 ≤ l_i ≤ 10, 1 ≤ l_j ≤ 10

Efficient and Stable Co-Authorships

The model implies the following claims about efficiency and stability of networks:

1. if n is even, the strongly efficient network is that consisting of n/2 components of size 2
2. pairwise stable networks can be partitioned into fully intraconnected components with sizes m > k² where k is the next largest component after m

Graph 1. Efficient Co-Author Network, n = 16

Graph 2. Pairwise Stable Co-Author Network, n = 16: two intraconnected components of size 13 and 3

To see why efficient co-author networks are mere collections of isolated pairs, let us first reformulate utilitarian welfare by replacing u_i in (1.2) by its model specification from (1.3),

 (1.4) w (g) = ∑_i∈nu_i = ∑_{i: li>0}∑_{j: ij∈g} [1/l_i + 1/l_j + 1/l_i l_j]

The maximal sum of own and partners’ links inversed cannot be greater than twice the number of nodes, and this equality holds if a network does not have isolates, l_i > 0,

(1.5) ∑_i∈Nu_i ≤ 2n +∑_{i: li>0}∑_{j: ij∈g}1/l_i l_j

Similarly, the sum of inversed multiplication of the parameters may not exceed the number of nodes,

(1.6) ∑_{i: li>0}∑_{j: ij∈g}1/l_i l_j ≤ n

Here n can be obtained if l_i =  l_j = 1. Since the web of isolated pairs is the only feasible regular network of degree 1, proposition (i) is proven. However, the proof of proposition (ii) is not given here for two reasons: it takes too much time and space, and is so much more complex that I struggle to get a full understanding of it. Instead, I suggest simply accepting this claim and finish this subsection by summarizing basic properties of efficient and stable networks resulting under this model.

Table 2. Characteristics of Efficient and Stable Co-Author Networks

Table 2 helps to assess predicted empirical networks against the benchmark of efficiency. Firstly, due to intraconnectedness, scholars are expected to have as many links as there are agents in their component minus one whereas efficiency is associated with everyone having the degree of 1. This also implies different clustering coefficients because the latter is by definition minimal for nodes with one link and maximal for parts of connected components. Thirdly, empirical networks should include several components with very different sizes while efficient webs consist of isolated pairs. Finally, scholars are predicted to be very close to colleagues in their component and unreachable for the others while the average distance between nodes in efficient networks is almost infinitely large as only paired elements are connected.

Wrapping up

Scholars benefit from getting colleagues to work on joint projects because additional labor reduces time needed to finish work. However, co-authored articles come to take longer to complete when partners get involved in new collaborations. The unfortunate property of negative externalities poses the fundamental dilemma of co-authorship: one’s utility is highest when engaged in as many partnerships as is possible, but is lowest when the others do just that. Therefore, the link formation process is tricky and unpredicted, but bound to reach stability in over-connected networks as researchers tend to overlook utility losses inflicted on their ‘old’ co-authors when forming new links. The next section examines this nice and explicitly simplistic view on driving forces of collaboration on the sample of experts who publish in four major Russian journals of international relations.

EMPIRICAL ANALYSIS

Hypothesis: co-author networks consist of several fully intraconnected components with sizes m > k² where k is the next largest component after m

Data: the analysis examines authors that have published at least once in any of four leading Russian journals of international relations, International Affairs (‘Mezdunarodnaya Jizn’), International Trends (‘Mezdunarodnie Processi’), Russia in Global Affairs (‘Rossia v Global’noi Politike’), and International Organizations Research Journal (‘Vestnik Mezdunarodnih Organizacii’). Periods for which the respective websites provide information about their authors range widely, from 2002-2013 to just 2010-2013. This suffices to collect data on slightly more than 900 researchers, a far larger set of experts than that covered by RIAC’s own database including about 550 entries.

Mapping: each author is mapped into the network as a node, where nodes are homogeneous, i.e. they do not differ from each other according to age, sex, occupation, permanent job, and journals they publish. A link between two nodes is present only if these researchers co-authored an article published in the journals surveyed. A potentially crucial feature of the network is that it is unweighted, meaning that links are homogeneous, too. So, the network fails to discriminate between scholars that have collaborated at least once, or many times within the period in question. And it is also time-insensitive as no information about the year of collaboration is reflected in the network. This important simplification of representation is intentionally implemented in order to ease interpretation of findings, that is, they would be a less suitable source of the empirical test of the hypothesis otherwise as it is formulated in terms of unweighted and undirected networks.

Results:

Graph 3. Co-Authorships in Russian IR studies, n = 902

Quite a surprising design of the network emerges from these data. Most of 902 nodes have the degree of 0, which indicates that the overwhelming majority of articles have been written by one person (approximately 95%). More strikingly, International Organizations Research Journal has a disproportionately larger share of co-authored articles against to the number of researchers who published in this journal: 1/3 compared to 1/16, 1/11 and 1/7 in the others. Thus, if we control the statistics for this HSE-issued journal, a link becomes very rare which is dramatically inconsistent with the predictions. It does not resemble either efficient (set of pairs) or stable (see hypothesis) structures, but rather an empty one (though not in the strict sense). Despite having some set of non-isolates which are sometimes grouped into cliques (up to 20 agents), the network can definitely be improved in terms of utilitarian welfare where utility is defined by the Jackson-Wolinsky co-author function by adding links such as to increase the number of pairs. Consequently, contrary to the hypothesis, the network is under-connected, and scholars tend to underinvest in research collaborations.

Findings in other areas: to see if the inconsistency between the model and reality holds in other areas of research like physics, biology, economics etc., I couple Table 2 with the table from Jackson [2008] which summarizes properties of corresponding networks:

Table 3. Empirical findings vs. model predictions

The table clearly demonstrates that the network of collaborations in Russian international relations studies is unique in its low degree, small largest component, low clustering and short path lengths. Therefore, there should be a country- and discipline-specific explanation for the rare co-authoring as networks in other countries and other sciences reveal very different patterns. They share some properties with efficient networks when it comes to the degree or the size of largest components, but differ significantly in clustering and average path length. What is relevant for this study is the fact that the model is more successful in explaining other real-worlds co-author networks, so it cannot be simply dismissed as inadequate as tempting as it might be. In the next section I will give my account of the theory-model inconsistency.

INTERPRETATION

The model used to explain behavioral fundamentals of engaging in collaborations obviously fails to predict the structure of co-authoring for international relations studies in Russia. Not only do not experts prove to invest too much in joint projects, but reveal quite the opposite pattern because the overwhelming majority of articles are written by one person. In this section I attempt to provide comprehensive interpretation of the inconsistency between the findings and the predictions, and then reply to some of critical points that readers might raise against the solution to the inconsistency I am going to offer.

Science vs. Expertise

Generally, the theory-evidence controversy can be settled down in three ways. Firstly, facts may be judged as falsifying the theory, that is, if the latter says that events of type A bring about those of type B, but B-events are not observed when A-ones are present, then the universal law statement should be dismissed. Secondly, one may question the credibility of evidence by referring to the alleged inaccuracy of data collection or analysis, or the inappropriate choice of methods. Finally, the issue under consideration may fall beyond the intended range of application, i.e. the causal law does not cover the phenomenon analyzed which is why the findings cannot possibly falsify the theory in the first place.

The reason for the failure to predict the intensity of research collaborations appears to be well accounted for by the intended range of application explanation. Precisely, the case I will be making holds that while the model aims to capture pay-offs from collaborative scientific work, what is published in Russian journals of international relations is expert opinions rather than science. It is therefore illegitimate to treat my findings as evidence against the model or to make claims about methodological misconduct. I will say more about the grounds for rejecting the alternative hypotheses later, but it is important to dwell on the dichotomy between science and expertise at first and start with contrasting their basic properties.

Although what precisely science is and does is debated, it is nevertheless possible to outline key features of scientific research. Most importantly, hypothesis testing enables science to identify laws of nature that govern facts about the world around us as well as laws of mind that rule the human psyche and consequently relations between persons. In doing this, it heavily relies on objective methods of data collection and analysis, primarily through experiment and statistics. Also, scientific conclusions are up to (often anonymous) peer review and continuous critical revision of theories. Last but not least, science is ‘authority-blind’, that is, the perceived quality of research solely depends on how accurately conclusions are inferred from the data rather than on the status (e.g. fame, PhD degree, years of experience, office held) of who does it.

Expertise, as its name suggests, is a mode of knowledge obtainment that makes use of experience. It represents the body of opinion statements that may very well be compatible with rigorous scientific methods, but conclusions can be reached in many other ways, too (for example, intuition, insight, guess, foresight, and many others). Furthermore, since expertise is typically based on experience translated into judgments by reference to the best explanation and analogy, there are few other criteria for accepting or rejecting opinions than the formal (past or present) position of the author, and probabilistic logical consistency of their statements. All in all, expertise is an extremely diverse form of knowledge whose concrete form varies widely and depends on experts themselves. Perhaps, its vagueness and the absence of clear standards (except for the extensive use of exclusive knowledge and skills) is what best characterizes expertise.

Observe that these notions can enjoy a different interpretation as some define science by what is studied rather than how it is done. From this perspective, expertise is merely a form of science, the so-called ‘qualitative’, or ‘interpretative’ science, which allegedly makes up for the inability of quantitative techniques to map some elements of social reality into mathematical and statistical terms (think of constructivism as an example). As well as this argument works against ‘quanti’ research, this is nevertheless far from clear why expertise should fall into the broad category of scientific knowledge. It still fails to meet fundamental requirements of confirming and rejecting hypotheses and inferring theories which is why I insist these two notions be not mixed up and go strictly separately.

What implications do these differences have for co-authoring? To satisfy rising requirements for rigorous research, scholars feel pressure to acquire specialization in particular sub-disciplines, methods, and areas of interest. Consequently, opportunity costs of doing work one does not specialize at are growing and can be reduced by having someone better prepared to take on this part of study. For instance, this paper would have been completed quicker and be of higher quality if the “Theory and Model” part had been done by a math student while I would have concentrated on sections I feel more competent at. This idea seems to be what Jackson and Wolinsky implied by the interactive ‘synergy’ term of the utility function.

Experts also prefer to excel at a particular field of study (‘expert in the U.S.- Russia relations’, ‘expert in Chinese politics’ etc.). However, this reflects the division of knowledge rather than that of skills. Expertise relies on rough generalizations from (a) few facts, intertemporal or interregional analogy, reference to the best explanation and intuitive forecast. Methodology of studies that apply the techniques enumerated tends to be more homogeneous and is lacking the complex structure of empirical research that involves theory to produce hypotheses and data analysis to check them and creates the primary incentive for co-authorship. Moreover, if the value of work is associated with the formal position of the author, experts are harmed by collaborating with colleagues who do not enjoy a comparable status or fame.

A few objections against my explanation

• No descriptive evidence is given to confirm my thesis that articles on international politics are expertise, not science.

• Although this proposition is not inferred statistically, it follows the diagnosis by M. Feldman and {add_name }in their articles for RIAC. Also note that my thesis does not attempt to capture the essentials of every article, so some share of them could meet the standards of science.

• One is only eligible to make judgments about international relations studies in Russia from within ‘the system’; detached observers are inevitably missing something

• This is as absurd as to say that one can’t develop cure for AIDS without being HIV-positive or to analyze flows of sparrow migration without being a bird. Moreover, detachment from the object of research is a necessary condition for objectivity rather than an obstacle.

• That international relations are subject to expertise is a worldwide phenomenon and thus not peculiar to Russia.

• I do not state the opposite. On the contrary, if this objection is correct, my case enjoys cross-country support and might assume the universal form.

• SNA methodology is inaccurate. If i wrote an article with j in 2004 and with k in 2012, this is misleading to add both links as if i’s time is split between two projects at once.

• The objection is legitimate. However, dividing the whole network into several, 2- or 3-year ones would complicate the interpretation of results. Also, as the overwhelming majority of nodes have no connections even within the whole period, the network settings chosen do not tangibly distort reality.

• As the model does not apply to the case, expertise networks enjoy their own efficiency standards, which Russian international relations scholars may satisfy

• The statement is trivially right, but avoids the problem. The current structure of collaborations may maximize the total sum of individual welfare according to some ‘expert’ utility functions. However, it can be inefficient in a sense that it contributes to poor overall record of Russian experts in Western journals of international relations. Thus, it is always necessary to specify which kind of efficiency is meant.

CASE FOR REFORM?

In order to prepare the ground for tentative normative conclusions, I quickly summarize the argument that has been developed throughout the preceding pages. A reason for the failure of Russian experts to publish at influential international relations journals abroad was expected to be that the rationality of scientific co-authoring engenders excessively many joint projects that decrease the overall output of papers. However, the evidence suggests that researchers engage in dramatically fewer connections that predicted, which invites us to think that the model is not intended to cover the issue in question. Precisely, whereas the utility function introduces the synergy term to capture pay-offs from co-authoring, no such synergy is feasible for expertise work due to its methodological homogeneity and importance of the author’s credit. Consequently, links between experts are very unlikely which is just what we observed.

My findings can be embedded and found useful in the larger context of policy-making. Let us first take a look at two theoretical arguments that offer solutions to the problem that the Global Science project is concerned about:

• Globalization of science removes national barriers and enables one to publish in any country, thus exploiting arbitrage opportunities. That is, it is not easier or harder to get your paper published at home than abroad, so national standards for publications converge. When standards of quality are uniform, the chances of locals for success in top journals primarily depend on the national output. Therefore, Russians perform badly abroad because there are few PhDs in related disciplines, few well-paid professorships, few local journals, etc.
• Arbitrage between countries is unexploitable due to nationally specific demand for research. That the readership prefers its native language and is more interested in local issues creates demand for nationally specific content with comparative advantages for locals. It takes less to succeed at home than abroad, so standards for publications are largely determined by internal supply and thus diverge by regions. Consequently, the failure to publish in the U.S. and elsewhere is rooted in qualitative discontinuity, i.e. large increases in the output won’t compensate for the difference in standards between countries or regions.

What makes the choice so compelling is that the alternatives are mutually exclusive. The first argument requires pouring resources into creating jobs, expanding scholarships for prospective students, and stimulating co-authoring to increase produce. However, these measures are judged as wasteful under the second approach because the quality of research should be the primary object for investments. Despite the absence of central authority able to implement reform, the quality nevertheless can be improved indirectly, through mutually beneficial practices, most of which have to do with encouraging competition among scholars by removing entry barriers.

On the demand side, the government and state-sponsored organizations should no longer be the sole consumers of research on international relations. Bureaucracies are funded with taxes, not profits, so their welfare hinges on the ability to lobby a boost in their budgets. As science is hardly instrumental in this enterprise, there are serious doubts that government agencies are truly committed to invest in the quality of papers. Contrariwise, a bundle of other agents whose utility is very sensitive to the state of political and economic relations between countries, primarily transnational corporations and firms that import or export goods, value accurate predictions and are able to translate them into profits, thus monetarily rewarding their authors.

Diversification of demand is bound to bring about corresponding fluctuations in supply. Namely, private companies seek to expand it as much as possible because competition among scholars should slash the price for their services (wages and subscription fees). This can be achieved by, for instance, financially supporting journals in English, launching fellowship programs for researchers from Western countries, and bringing down excessive bureaucratic obstacles. In the final analysis, some locals succeed at catching up with new standards, the others perish. All in all, the logic behind the second argument is similar to the advocacy of free movement of labor in the migration debate, where the increase in the communal welfare is associated with some share of labor losing their jobs to migrants.

The bottom line is, can restructuring collaborative work increase chances of publishing in American journals? As long as this work resolves into expertise that is qualitatively inferior to what is in demand there, the answer is clearly ‘no’. In his interview for RIAC Andrey Korobkov [2012] is explicit on this point: “In Russia social sciences are often seen as political journalism rather than science. Propositions that are not justified by numbers and other relevant facts receive negative reviews”. Dmitriy Feldman [2013] has offered a similar line of argument in his article on the international relations science in Russia: «The heart of the matter seems to be in the customary use of backroom discussions or at best public debates, instead of empirical research of the facts, events and phenomena, as well as their comprehension and generalization through formalized conclusions, verification, refutation, and/or confirmation by other researchers. We tend to present scientific conclusions as commentaries on events or as a well-timed analytical memo, which is definitely helpful but far from sufficient to reflect the functions of the science of international relations as a rational basis for making and implementing expedient decisions». However, it is my belief that if the discipline goes through the changes outlined which will open it to global competition, the tuning of co-authorships should optimize the output of papers and thus enlarge the share of Russian names in the bibliographies of outstanding journals of international relations.

REFERENCES

Chimiris, Ekaterina (2013). Social Networks for 'Global Science'. – Russian International Affairs Council. Available at /blogs/methodology/?id_4=431

Feldman, Dmitriy (2013). The Russian Political Science on International Relations: Methods and Style of Cognition. – Russian International Affairs Council. Available at /en/inner/?id_4=1899#top

Jackson, Matthew (2008). Social and Economic Networks. – Princeton University Press.

Jackson, Matthew and Wolinsky, Asher (1996). A Strategic Model of Social and Economic Networks. – Journal of Economic Theory 71: 44–74.

Korobkov, Andrey (2012). Political Journalism, Not Science. – Russian International Affairs Council. Available at /inner/?id_4=919#top

If you have any questions concerning methodology, data, or any other issues related to the paper, do not hesitate to contact me at legkiyigor@yandex.ru or leave your comment below.