Introduction

For many years, if not decades, various countries have been competing intensely for the leading positions in the world–class university (WCU) rankings. WCUs serve as a specific way of concentrating intellectual resources to ensure breakthrough scientific and technological developments. Experience has shown that a country must ‘earn’ the opportunity to have national WCUs through active economic development in the previous decades; otherwise, it is simply unrealistic to create such large–scale and expensive structures. However, their emergence in the national economy predetermines technological and cultural successes of the country in the long term. This is the main reason behind the battle for creating and maintaining WCUs.

At the same time, there is still a lack of understanding of what WCU is. The scientific community has not yet reached a consensus on strict criteria for defining this concept. After the start of the special military operation in Ukraine in 2022, when global aggregators of university–related information appeared to be involved in the sanction policy and failed to preserve scientific neutrality, the basis for such a consensus was completely lost.

The current article aims to examine the viability of the previously developed WCUs identification method and to revise the definition of the term “world–class university”.

World–class universities: The concept and identification criteria

The supposedly first and oversimplified interpretation of a WCU was offered by Charles William Eliot, president of Harvard University in 1869–1909, who believed that it would require 50 million dollars and two hundred years to create an equivalent of a world– class university. The falsehood of this statement was proved by the University of Chicago which managed to become a WCU in just two decades for slightly more than 50 million dollars [Altbach, 2004].

The scholarly discourse on WCUs was initiated by Philip G. Altbach in 2004. He stressed that “everyone wants a world–class university. The problem is that no one knows what a world–class university is, and no one has figured out how to get one” [Altbach, 2004, p. 21]. The researcher outlined the criteria that, in his opinion, should become the basis for WCU identification, these are excellence in research, academic freedom and an atmosphere of intellectual excitement, effective self–governance of the institution, innovative teaching, suitable facilities for academic work, and longterm adequate funding [Altbach, 2004].

The evidence from practice suggests that a breakthrough in creating WCUs is achieved with the super–generous funding exceeding 100 million dollars made available. For example, according to Project 985 implemented in China between 1999 and 2011 and aimed at promoting the development of the Chinese higher education system through the creation of WCUs, as early as at the first stage in 1999, Qinghua University and Peking University were provided with 285 million dollars in funding [Salmi, Frumin, 2013]. In turn, at the beginning of the 21^st century the annual costs per student at such WCUs as Harvard University and Stanford University were about 106 and 165 thousand dollars, respectively; at the University of Tokyo – 77 thousand dollars; at Utrecht University – 69 thousand dollars; at the Australian National University – 30 thousand dollars [Salmi, 2009].

Empirical studies mainly confirm the significance of the financial factor in the formation of WCUs. For instance, more than 50 % of the US wealthiest university endowments are in the top 100 of the QS World University Rankings and almost 70 % are in the Times Higher Education (THE) Rankings. Thus, a large university endowment is, if not a guarantee of success in the global market, then at least its very important component. Analysis of a sample of the US wealthiest universities allowed formulating a simple empirical threshold rule: universities with an endowment of less than 1.5 billion dollars actually cannot claim top positions in the global university rankings (GURs).

At the same time, the financial state of a university cannot be viewed as a sufficient criterion to categorise it as a WCU. Let us illustrate it with an example of Central European University (CEU) founded in 1991 by famous philanthropist George Soros, who also established the university’s endowment by making a one–time donation of 880 million dollars. This made CEU one of the wealthiest higher education institutions in continental Europe, but it never developed into a WCU [1]. The similar situation is typical of King Abdullah University of Science and Technology established in Saudi Arabia in 2009. It initially received a 20 billion dollars endowment from its founder [2]. Due to this, the Arabian university took a position on a par with the wealthiest American universities, but did not turn into a WCU.

In recent decades, the world scientific community have been concentrating on finding and developing WCUs’ central criteria and characteristics [Huisman, 2008; De los Rios–Carmenado et al., 2021]. For example, Kathryn Mohrman, Wanhua Ma and David Baker have identified eight key features of research universities claimed to be global leaders, these are global mission, research intensity, new roles for professors, diversified funding, worldwide recruitment, increasing complexity, new relationships with government and industry, and global collaboration with similar institutions [Mohrman, Ma, Baker, 2008].

Other researchers, such as [Altbach, 2004; Khoon et al., 2005; Salmi, 2009], argue that the fundamental characteristics of WCUs are high qualification of teaching staff, high–quality education, effective research activity, talented students, academic freedom, adequate facilities and advanced equipment for teaching and research, and autonomy of management structures. The list of key characteristics of WCUs was expanded with a number of criteria, which are rather difficult to formalise, such as contribution to the development of modern society and independence in mapping out one’s own development strategy [Alden, Lin, 2004].

In our opinion, the concept of WCUs by Jamil Salmi is of greatest interest. According to it, the excellent results of such universities are due to the skillful combination and interaction of three key success factors: a high concentration of talent among teachers, researchers, students and managers; an abundance of resources (financial, human and infrastructural); and effective management (strong management team, lack of bureaucratic barriers, academic freedom, and strategic thinking) [Salmi, 2009]. A higher degree of autonomy improves cost efficiency and leads to higher research productivity [Aghion et al., 2007]. In turn, the abundance of resources allows universities to attract leading scholars not only from their own country, but also from abroad [Salmi, Altbach, 2020].

In the following years, one more characteristic was added to the three features indicated above. It was associated with closer cooperation between universities and business corporations, which allowed WCUs not only to provide high–quality education through interaction effects [Geuna, Muscio, 2009; Perkmann, Walsh, 2009], but also to conduct research valuable for the economy [Muscio, Quaglione, Vallanti, 2013].

Thus, the scientific community has formulated four principal features of WCUs: advanced research, high–quality education, links with society through research projects, and flexible research and innovation management [Altbach, Salmi, 2011; Ca– zorla, Stratta, 2017]. The key role is attributed to scientific studies, which results in research universities being considered as the gold standard of the quality of higher education and the main contenders for the WCU title [Lavalle, de Nicolas, 2017].

Despite the clarity and indisputability of the WCU features, their main drawback is the impossibility of being measured quantitatively, and therefore they are unsuitable for analytical practice. This is the reason why top universities from various global rankings, of which there are several dozen today, are increasingly covered in the WCU list [Turner, 2013; Wang, Cheng, Liu, 2013]. Francisco Ramirez from Stanford University points to the significant role of GURs in shaping public opinion about the quality of university and its affiliation with WCUs (see, [Rigoglioso, 2014]). According to the new immigration policy in the Netherlands, skilled workers who have graduated from a university in the top 150 of either the ARWU or the THE–QS have a priority right for immigration to the country [Hazelkorn, 2011]. The Asian scientific community also believes that global rankings are a single option to quantitatively evaluate the success of universities [Wang, Cheng, Liu, 2013]: it was the intent to establish WCUs’ quantitative parameters that resulted in the creation of the ARWU, or the Shanghai Ranking [Liu, Cheng, 2005].

However, recognising GURs as a way to determine WCUs does not resolve the problem automatically. On the one hand, the ranking movement has caused a stream of criticism about the accuracy, objectivity and reliability of rankings [Van Raan, 2005; Kincharova, 2014; Olcay, Bulu, 2017]. On the other hand, a question arises about the size of the GURs top list that characterises WCUs. In other words, it is not clear how many universities in the world can have the status of a WCU. At an early stage of research, only the first 30 universities from GURs were recognised as WCUs, but soon it became apparent that this criterion was too strict, and the list was expanded to the top 100 positions [Balatsky, Ekimova, 2012]. Later, the depth of university subject (scientific) diversification was taken into account, which was based on subject rankings of universities (SURs) [Balatsky, Ekimova, 2018]. Another question is what GURs provide the most reliable identification of WCUs. According to Michelle Stack from the University of British Columbia, what makes a university world class is its inclusion in the ‘big three’ higher education rankings – the Quacquarelli Symonds (QS), the Times Higher Education (THE) and the Academic Ranking of World Universities (ARWU) [3].

Based on the ranking methodology, in 2018 an alternative definition of WCU was proposed that took into account the organisation’s achievements and the strength of its brand: a world–class university is a university that has won wide international recognition and demonstrates first–class scientific results in a wide range of research areas [Balatsky, Ekimova, 2018]. This interpretation of WCUs implicitly contains Salmi’s criteria, but at the same time allows proceeding to their identification. In this case, ‘wide international recognition’ corresponds to the fact that the university is in the top 100 of at least one of the reputable GURs; ‘first–class scientific results’ mean that the university is in the top 50 subject rankings of universities in a certain ranking system; and ‘a wide range of research areas’ is a heuristically determined number of SURs, in which the university is among their top 50 positions.

Hereinafter, the first part of the proposed definition (‘a university that has won wide international recognition’) is assumed as a criterion for the university’s global success, which will be referred to as G–criterion, whereas the second part (‘demonstrates first–class scientific results in a wide range of scientific areas’) acts as a local criterion, or L–criterion, that determines the number of subject areas of university researchers’ successful work. In addition to the number of research areas, in which the university is an international leader, the L–criterion also implies a minimum limit L*, which, if exceeded, indicates that the university’s scientific diversification is satisfactory. In the paper, we will build on this interpretation of WCUs.

WCUs identification algorithm: The basic and modified versions

In a number of publications, a certain basic WCU identification algorithm (BIA) was developed and repeatedly tested using G– and L–criteria [Balatsky, Ekimova, 2018, 2020]. This algorithm is a two–step procedure for successive digitisation of the two criteria. According to the BIA, the first step is to test the G–criterion, that is, whether the university is named in the top 100 of one of five reputable GURs: Quacquarelli Symonds (QS), the Times Higher Education (THE), the Academic Ranking of World Universities (ARWU), the Center for World University Rankings (CWUR), and the National Taiwan University Ranking (NTU).

The main indicator of the calculations is the number of WCUs in each country of the world [Balatsky, Ekimova, 2018]. If at least one of the indicated GURs ranks a university among its top 100, then it is a contender for the WCU title. In other words, for a university to meet the G–criterion, at least one global ranker should recognise its merits and include it in the top 100 of its GUR. Practice shows that meeting the G–criterion is a necessary but not sufficient condition. At the second step, the L–criterion is used as a sufficient condition, that is, whether the university is ranked among the top 50 by at least five SURs of any ranking system. In this case, the L value shows the actual number of scientific disciplines used as the basis for including the university in the top 50 SURs, and L* = 5 acts as the minimum threshold for ‘clipping’ universities. For better clarity, applied calculations were based on the data from the QS university subject ranking.

The above BIA made it possible not only to determine the pool of WCUs, but also to trace its change and trends. However, the study of dynamics based on the basic identification algorithm turned out to be extremely limited due to the lack of SUR data for the previous years. In this regard, an attempt was made to construct a simplified algorithm for WCU identification, which would allow analysing longer time series. The substance of this approach was to calculate the number of WCUs in different countries and regions of the planet using data from different GURs for different years, i.e. the F–criterion was ignored, but it was compensated by using the G–criterion for a larger number of GURs. To that end, the statistical data from nine leading GURs were applied: the Academic Ranking of World Universities (ARWU), the National Taiwan University Ranking (NTU), Quacquarelli Symonds (QS), the SCImago Institution Rankings (SIR), Round University Ranking (RUR), the Times Higher Education (THE), the Center for World University Rankings (CWUR), the CWTS Leiden Ranking (LR), and the Worldwide Professional University Ranking (RankPRO). In general, the applied method has produced similar, but less accurate results compared to the two–step algorithm [Balatsky, Ekimova, 2020].

Currently, there are numerous grounds for providing further improvements in the basic WCU identification algorithm. For example, the BIA revealed some unexpected methodological problems, which at the same time contained additional information about the properties of the very market for advanced universities. Let us look at this aspect in more detail.

The BIA–based WCU rankings for 2017, 2019 and 2021 show the permanent expansion of the market under consideration due to an increase in the number of its participants (Table 1). On average, one new participant a year was added to the list of WCUs at L* = 5. If this trend continues, by 2030 the WCU ranking will cover more than 120 universities. Firstly, a list of this size is too extensive for this kind of objects, and secondly, there is a notable increase in the inequality between market participants, when the universities at the top and bottom positions turn out to be qualitatively incomparable. Thus, there is empirical evidence that the operational (applied) definition of WCUs based on the ranking methodology cannot be static, but should be of the dynamic nature and be subjected to periodic adjustments. This is due to national universities gradually enhancing the number of scientific areas mastered.

Table 1. Change in WCU numbers with different ‘clipping’ criteria (L*)

The given trend is even more clearly manifested in WCU numbers if L* = 6 (Table 1). In this case, the annual growth of the top list is 1.75 units. Thus, a more stringent ‘clipping’ criterion L* does not stop the number of WCUs from growing, as one might hope, but, on the contrary, speeds up the rate of their ‘multiplication’ even more. This fact once again confirms that scientific personnel is actively concentrating in the world’s leading universities, which must be taken into account when defining and identifying WCUs.

The facts discussed are sufficient to clarify the BIA and develop a modified identification algorithm (MIA) of WCUs, which provides for the following methodological steps.

Firstly, it is expedient to proceed from the fact that in the world there is a limited number of WCUs that does not change over time. This principle of size invariance of the universities top list is compensated by the principle of WCU requirements variability in time. Considering that leading universities closely observed by the population are grouped in the top 100 list and stakeholders’ interest in universities outside this list is significantly lower, it is reasonable to limit the top list to 100 world leading universities that will qualify as WCUs, i.e., W = 100, where W is the size of the WCU list.

Secondly, to make the WCU identification procedure more flexible if W = const, it is expedient to make the clipping border L* floating in time. When the number of potential WCUs in the top list noticeably exceeds the limit of 100, universities should be assessed using a higher clipping limit. Formally, this rule is described as follows: if U (L*) > 100, then one proceeds to building the ranking U (L**) < 100, where L* and L** are the old and new (increased) clipping borders; L** = L* + 1. For convenience, it is reasonable to introduce a heuristic value of the permissible excess of the top list’s critical value, for example, A = 2. Then, the first condition is verified as follows: U (L*) > 102. If the initial top list includes 102 positions, then it is enough to discard the last two universities. Otherwise, it is advisable to increase the clipping border and rebuild the ranking.

Thirdly, if the condition U (L**) < 100 < U (L*) is met, then a simple top–list normalisation procedure is applied (i.e., keeping U = 100 constant): 100 – U** universities from the list U* by the ranking criterion H are added to the list of the size U** (for more details, see: [Balatsky, Ekimova, 2018]). For instance, the 2017 ranking with the border L** = 6 was U** = 94 positions, and the one with the border L* = 5 – U* = 107 positions (Table 1). To normalise the WCU list, the first list of U** = 94 universities is added with the first 6 universities from the second list U* = 107, which were not included in the first list. This procedure is fairer and more legitimate as it prevents contradictions emerging when universities with a broader disciplinary spectrum are discarded, while more specialised ones are kept in the WCU list.

To illustrate the proposed MIA, compare the 2017 WCU ranking (5) with the WCU ranking (6) compiled according to the proposed refinements of the university selection algorithm. In this case, there is a serious, i.e., qualitative, change in the results. For example, the American universities with the parameter F = 5, such as the University of Maryland, College Park and the University of Florida occupied the 90^th and the 91^st places in the initial WCU (5) ranking in 2017, respectively, and were confidently ahead of Texas A&M University and Korea University having the parameter F = 8 and ranked the 96^th and 97^th, respectively. When applying the MIA, Texas A&M University and Korea University were ranked the 89^th and 90^th, respectively, while the University of Maryland, College Park and the University of Florida occupied the 101^st and the 102^nd positions and, therefore, got left out of the normalised WCU (6) ranking. Here, we can see a fundamental distortion of the true state of affairs, which justifies the use of the modified algorithm for WCU identification, which makes it possible to correctly calibrate the initial calculations.

Two Latin American universities – the Brazilian University of Sao Paulo (USP) and the Mexican National Autonomous University of Mexico (UNAM) – can serve as a striking example of the L–criterion being underestimated. For example, in the 2021 QS World University Rankings, the University of Warwick (UK) with the parameter L = 9 was ranked the 62^nd and Tokyo Institute of Technology (Japan) with L = 7 was ranked the 56^th, while the USP with L = 13 was the 115^th (Table 2). At the same time, the UNAM having L = 12/13 in the period of 2017–2019 failed to enter the QS top 100 in these years. The two Latin American universities confront with the QS ranking system: while having more than worthy positions in the ranker’s SUR, they were not adequately assessed in its GUR. The proposed modified algorithm for WCU identification allows neutralising the shortcomings of the leading ranking products (I is the university’s number in the WCU ranking).

Table 2. WCU parameters in Latin America

As seen from Table 1, the MIA is of use for 2017 and 2019 and needs the local criteria L* = 5 and L* = 6 to be related, while for 2021 the basic identification algorithm with the criterion L* = 6 is sufficient and the last, the 101^st, university can simply be left out.

Refining the WCUs geopolitical map: The global disposition

The use of the MIA for WCUs allows shedding light on the power landscape in the global university market. Table 3 presents the results of two scenarios for WCUs identification, these are the BIA with the criterion L* = 5 and the MIA with two related criteria L* = 5 and L* = 6 for the enlarged regions of the world.

Table 3. Number of WCUs in world geopolitical centers according to the two algorithms

The results obtained allow us to draw the following conclusions.

Firstly, the number of WCUs for Asia requires only minimum adjustments, although there is a clear upward trend – during the 4–year period the number has increased from one to three. Thus, even for the countries of the Asian subcontinent, the basic and modified identification algorithms are not invariant. The revealed effect is easy to explain, given that many universities in South Korea and China have only recently begun to defend their global positions and have not yet been able to consolidate their initial phenomenal success.

Secondly, a strong violation of invariance between the BIA and the MIA is typical mainly of the American and European segments. The minimum discrepancy between the regional estimates of WCUs is 2, which no longer allows neglecting the identified discrepancies.

Thirdly, Europe appeared to be the most receptive to the refinements of the identification algorithm. If for the USA and Canada the discrepancy in the number of WCUs according to the basic and modified algorithms has remained unchanged over time and amounted to 2, then for Europe it has formed an alarming series: 4 in 2017, 6 in 2019, and 6 in 2021. It can be stated that in Europe there are plenty of universities that hardly fit into the WCUs criteria and fail to maintain their positions in the top list for a long time. Thus, we can assert that the European market for WCUs is more heterogeneous than the American one. Moreover, the reliability of European WCUs is not increasing, but decreasing over time, which makes it possible to take a fresh look at the power landscape in the world system.

Fourthly, adjustment calculations show that the trend towards establishing a balance between the American and European WCU segments is not confirmed. The basic identification algorithm indicates that in 2019 Europe even outstripped the US and Canada in the number of WCUs, and in 2021 full parity was established between them. However, according to the modified identification algorithm, the North American segment is steadily ahead of the European segment with a slight drift towards equilibrium: in 2017, the former had 7 more WCUs, 3 in 2019, and 4 in 2021. At the same time, one cannot deny that even according to the corrected data of the modified WCU identification algorithm, the number of world–class universities in Europe is growing, while in North America it is falling.

Thus, we can conclude that WCUs in North America are slowly but surely losing their positions, while European universities are stealing the initiative from them. At the same time, concentration of numerous scientific areas in leading universities in Europe is highly volatile, which makes their success unreliable. Asian WCUs have indicated their presence in the world market, but they are yet unable to build on the success of 2017. This situation is fully consistent with the overall geopolitical turbulence of recent years.

Refining the WCUs geopolitical map: Local shifts

It is impossible to fully realise the shifts in the disposition of WCUs geopolitical centres without analysing their internal heterogeneity. This applies primarily to Europe and Asia. To clarify this issue, consider the data in Table 4, which show that the three Asian leaders in the number of WCUs fail the reliability test. All the three nations – China, South Korea and Japan – have lost one WCU in four years. At the same time, China and South Korea are ‘young’ participants in the WCU market, which explains the fact that some of their universities are not ripe enough for the required parameters and can go up and down in international rankings. Japan, on the other hand, was a regional leader in the global university market as early as at the beginning of the 21^st century; therefore, its falling rank can be interpreted as a kind of decline of its national scientific and educational system. At that, it is quite obvious that it is primarily Chinese and Korean universities that are pushing the country out of the top list.

Certain rearrangements among European countries are also being outlined (Table 5). Among the obvious instances are British universities losing their positions, which, being a core element of the Anglo–Saxon scientific and educational system, still unconditionally dominate Europe: the number of their WCUs has decreased by a quarter over 4 years, but still remains unprecedented. Germany has found itself in a state of slight stagnation and is unsuccessfully trying to break into the lead, while the Netherlands confidently seizes the initiative and today has a more powerful university system compared to the most developed country in Europe. Sweden and Denmark are both demonstrating a considerable potential, but if the former is slightly increasing it, the latter is losing it.

Table 4. Number of Asian WCUs according to the two algorithms

Table 5. Number of European WCUs according to the two algorithms

Russia [4] occupies a special place among European countries with one WCU, namely Lomonosov Moscow State University (MSU), which also belongs to the category of unstable players in the world market. According to the modified identification algorithm, in 2017 the university held quite a confident position as a WCU; however, in 2019 it was left out of the top list and regained its ranking position in 2021 as a round–out member (Table 6).

Table 6. MSU position in the two versions of the WCUs ranking

Table 7. Position of Latin American universities in the two versions of the WCUs ranking

If MSU fails to make radical improvements in its management system in the nearest future, there is a risk of Russia being pushed out of the WCU market on a constant basis. In this sense, we can say that in the WCU ranking Russia is being replaced by Latin American universities, which are characterised by the opposite trend: with the tightening of the L–criterion, the Mexican UNAM manages to keep its position, and the Brazilian USP moves slightly up in the ranking (Table 7).

Based on the calculations made, we can conclude that Russia has not managed to integrate into the international scientific–educational community while the official targeted policy was underway. On the contrary, even in a loyal GUR, such as the Chinese ARWU, Lomonosov Moscow State University dropped from the 87^th place in 2017 to the 93^rd place in 2021. The rest of the Russian universities in the QS SURs struggled to reach the parameter L = 1/2, which does not allow them to apply for the WCU status in the foreseeable future. The mechanical ‘pumping up’ of the GURs and SURs parameters without the relevance and content of studies taken into account did not allow completing the task. However, the year of 2022 has crossed out even the insignificant successes achieved by Russia over the previous decade. Russia’s special military operation in Ukraine resulted in unprecedented international sanctions imposed on the country. One of the consequences was that Russian universities have been partially, or even completely in the future, separated from GURs and SURs: cooperation between the leading rating agencies and Russian universities is put on hold.

Verification of WCUs identification results

Currently, there are no generally accepted methods of rankings’ verification, including university rankings. Therefore, every case of verification turns into a unique analysis that cannot be replicated to other ranking products. In our case, the WCU rankings lead to an unambiguous conclusion that Russia is an outsider in the market for advanced universities. In this regard, it is reasonable to ask the following fundamental questions: how bad are things? how objective are the findings? are WCUs in their current understanding a relevant artefact of the country’s intellectual potential and technological power?

To answer the stated questions, we proceed from the following ideas. At present, in the world there is a kind of a pool of nuclear–weapon countries often referred to as the Nuclear Club. Typically, having nuclear weapons at its disposal implies that a country is in possession of advanced missile technologies, aircraft manufacturing and nuclear energy. In turn, the presence of these industries suggests that the country demonstrates a high level of technological development and has attained considerable success in the natural sciences and engineering. Based on the global experience, the creation of a modern military–industrial complex requires the involvement of highly qualified personnel who, first, received a good basic education, and, second, seriously enhanced their expert knowledge while working in specialised research centres.

The above allows us to put forward an important assumption: all nuclear–weapon countries must have at least one WCU in their economic arsenal. Hence, universities as representatives of the Nuclear Club states in the higher education market should be included in GURs and SURs. Moreover, their absence in the WCU rankings is a test to pointout omissions and shortcomings in the ranking methodology. Wewill proceed from this assumption when assessing the degree of validity (adequacy and efficiency) of the constructed WCU ranking.

The list of the Nuclear Club nations is presented in Table 8. It also covers Israel, which officially denies having nuclear weapons; South Africa, which possessed it in 1979–1989, but does not have it now; and Iran, which is a step away from its creation. The Nuclear Club countries present (+) or absent (–) in the list are shown according to three waves of the WCU ranking (L* = 6). The generated list can be used to construct an index (coefficient) of the WCU ranking validity (J):

(1)

where i is the index of the Nuclear Club country; N is the number of the nuclear– weapon countries (N = 9); M is the number of the Nuclear Club countries not having nuclear weapons (M = 2); t is the index of the WCU ranking’s year; T is the number of the rankings (waves) compiled (T = 3); 8_it is a Boolean variable of presence / absence of the i–th country in the WCU ranking in the year t.

To calculate 6_it, the following formula is used:

(2)

The numerator of the validity index J is the indicator of the Nuclear Club countries’ presence in the WCU ranking, and the denominator is its maximum number. Since the list of the Nuclear Club contains countries that do not yet or no longer have nuclear weapons (Iran and South Africa, respectively), the presence variable for them is equal to half of the standard variable in formula (2).

Calculations by formula (1) show that for the three waves of the WCU ranking, the value of the validity index J is 43.3 %. This is less than the critical level of 50 %, and therefore it can be considered an insignificant value indicating the extremely low accuracy of the WCU ranking.

Table 8. Universities of nuclear–weapon states in the WCU ranking

The result obtained is fairly significant, as it allows us to draw important and far– reaching conclusions.

All the most reputable university rankings appeared to be focused not so much on real economic and technological success due to the scientific and educational activities of universities, but on informational and theoretical aspects of research activities. This explains the fact why more than half of the Nuclear Club countries did not indicate their presence in the WCU list built on the basis of modern ranking products. And conversely, it includes the countries that can hardly be recognised as world technological leaders, for example, Australia, New Zealand, Belgium, and Denmark. Even five or six WCUs in Germany, which does not have nuclear weapons, the rocket and space industry, the aircraft and shipbuilding industry, raise big questions in terms of meeting modern high–tech needs. Against this background, MSU, as the only WCU in Russia and the last one in the WCU list, also seems somewhat illogical. Unlike the abovementioned countries, Russia has a space station, carrier rockets, the nuclear full cycle, advanced rocket technologies, all kinds of nuclear weapons, aircraft and shipbuilding, including the production of nuclear–powered icebreakers. In 2020–2021, Russia in a short time developed several COVID–19 vaccines, which are not inferior in quality to similar Western products. Thus, there is a certain discrepancy between the technological potential of many countries and their presence in the WCU ranking.

The data in Table 8 clearly demonstrate a kind of the Western–centricity of the WCU rankings: even if we leave out Iran and South Africa, the Western countries of the Nuclear Club are covered by 100 %, while the Eastern states – only by a third.

The reason for this discrepancy lies in the very GURs and SURs methodology. If in the first case, the main factor is the university’s reputation in the eyes of the experts being interviewed, then in the second case, universities’ scientific publications in specialised international databases are considered. However, it has to be noted that reputation is an elusive entity and cannot be accurately measured, while publishing activity can be evaluated precisely, but it seems to be only tangentially related to the real technological success of the country. Thus, GURs are aimed at assessing a virtual phenomenon, and SURs focus on digitising the scientific ‘semi–finished product’ in the form of articles.

The specificity of today’s advanced science can be expressed by the phrase “everything that is in the public domain is not valuable, and everything that is really valuable is not available.” Thus, when compiling university rankings, rankers are guided by outdated criteria for scientific productivity. It is widely known that the production of modern weapons implies the availability of domestic scientific (and educational!) schools in the field of mechanics, mathematics, physics, chemistry, materials science, etc., but this fact is not reflected in modern rankings. Summarising the above, we can state that the current methods of WCUs identification concentrate on the public component of researchers’ and organisations’ activities, which results in the undercounting of strategic scientific and technological results that are not subject to disclosure or not presented in the information field in the West.

To illustrate the poor validity of the WCU list, we use the following allegorical example. India, which does not have a single WCU in its territory, is capable of launching an absolutely critical nuclear strike on Australia, in response to which the green continent having six WCUs in 2021 can only bombard the potential adversary with a pile of highly–ranked articles and resolutions on the international recognition of its scientific achievements.

WCUs: A myth or reality?

The research conducted allows us to put forward a number of important theses.

First, the current ideas about such a phenomenon as world–class university no longer correspond to the new realities. Even if there is a link between world–renowned advanced universities in different countries and the real technological and economic successes of their parent state, it is extremely complex and obscure. Today, there is reason to believe that the very concept of WCU has largely lost its original meaning and needs to be radically revised. In the worst case, the absence of WCUs as such will have to be stated with the consequent transformation of this concept into a fashionable simulacrum.

Second, the information resources available to the world community today allow digitising the university competition with satisfactory accuracy only for two regions – Europe and North America. In fact, the entire Asian continent, which is a hotbed of increased economic activity, falls out of modern specialised rankings’ monitoring zone.

Third, the irrelevance of the WCU concept results in a wide range of practical issues. For example, is there a real need for the country to struggle to establish such structures in its territory? How expedient are the organisational and financial costs incurred in the creation of WCUs, which implicitly affect technological progress? To what extent are such ‘democratic’ norms justified for universities, such as a sizeable endowment, staff openness, a significant proportion of foreign employees, etc.?

Fourth, the low validity of the ranking data about the world’s leading universities raises the question of the WCU national model. There is every reason to believe that there exists no single and comprehensive model. To ensure their global competitiveness, it is more constructive for countries to find their own form of university organisation. This may involve a complex combination of voluntarism and democracy, openness and secrecy, freedom and responsibility, collectivism and individualism, etc.

Currently, many of these questions are left unanswered. In addition, a more serious issue is on the agenda of whether universities will keep their present role in the post–industrial world. Today’s large, red taped and inflexible universities cut off from direct participation in advanced technology programs will lose their positions, which they held for a millennium. Universities will possibly continue functioning, but their organisational model will change to such an extent that it will be more reasonable to speak of a qualitatively new phenomenon in the sphere of science and education.

Conclusion

Turning to the purpose of the study, we can state that the viability of the previously developed WCU identification method is extremely limited, as is the very concept of this object. If for the USA, Canada and the countries of Western Europe the specified concept and identification algorithms are rather efficient, then they are not suitable for other regions of the world. This means that even in the most general sense, world–class university is something indefinite and even mythical. The questions arising are left unanswered. It can only be argued that there is a need for a different definition of WCU and other selection criteria.

Nowadays, theoretical thought has already outlined its vector in explaining social evolution – from mono– to polycausal constructions [Polterovich, 2018a, 2018b]. Recently, Paata R. Leiashvily has gone a step further introducing the concept of causal openness: “... An economy is an organisationally closed, but causally open system of economic actions” [Leiashvily, 2022]. This means that the number of factors in the development of the economic system and its objects is virtually unlimited. And of course, the set of these factors for different countries may be different.

From this perspective, Russia more than ever needs structures like WCUs; however, their interpretation and identification should be based on other criteria. These questions are still open, and the way they are answered predetermines the policy on creating modern scientific–educational centres in Russia that can act as drivers of economic development and technological progress. We believe that the central property of WCUs should be their direct participation in real high–tech projects of the highest (world) level and, through this, their significant contribution to the development of the national economy. All virtual characteristics of universities, such as reputation and publication activity, should fade into the background and be treated as secondary details.

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