The role of the power law distributions in describing social complex systems. Implications in the field of knowledge performance assessment

The present research aims at verifying the possibility to model one or more aspects of a complex organization in terms of a power law distribution, in order to propose new approaches for the personnel and/or the processes management. Nevertheless in the literature there is a large amount of research on the capability of the power functions to describe phenomena apparently very diverse in a large range of fields, an evident limit is the possibility to simply transfer complexity concepts to the social sciences. A social system, indeed, is generally composed by many agents, affected by emotions, moods, aptitudes that can generate unpredictable effects, such as in a metastable situation “on the edge of chaos”. For this reason, many authors transferred with metaphors some complexity concepts into their studies on social-economic systems, sometimes with very disputable parallelisms to natural and biological world. After the discussion about the characteristics of complex systems, we try to face the difficulty in modeling social-economic complex systems, respect to physical or chemical phenomena, reviewing in particular the literature regarding economic issues, which adopted a more rigorous statistical and mathematical approach. In particular, we focuses on the growth dynamics model applied to economic entities like firms, countries, universities (Stanley et al., 1996; Amaral et al., 1997; Axtell, 2001; Lee et al., 1998; Gabaix, 1999; Plerou, 1999). Exploiting the scale free property of the power laws, these authors described a common growth mechanism for these apparently so different subjects, for which the fluctuations of the annual growth rate distributions always scale as a power law of the initial size. As original contribution, we test the model also for Italian universities, even if limited to the published ISI papers. Our results confirm that also our national academies growth according the previous model (Giuffrida S., 2014). The identified formal model is applicable to complex social organizations; it takes advantage of the scale invariance of a determined feature of these systems but it is substantially only descriptive of the complex phenomenon, detecting only a transversal property for enterprises, countries, universities. On the other hand, an intrinsic potential for the normalization of data is inside the model, as self-similar probability distributions are made collapsing on a single curve by a simply scaling process. Indeed, we demonstrate that the scale-free property of power laws can be used in an innovative manner, as a scaling relationship to normalize data, in order to be independent of the size of the studied organization. We verify that a normalization process, based on the power law scale free property, can be applied by a case study, the most recent Italian Evaluation of Research Quality (ERQ), concerning 2004-2010 period of activity of the Italian university system (ANVUR Final Report, 2013). On the base of these available data, we built an indicator of university productivity of knowledge, whose frequency distribution show fluctuations correlated to university size in terms of a power law. This fact introduces a dimensional bias that can partially falsify the results of periodical university assessment exercises, favoring one university over another, sometimes with unfair consequences, particularly where a share of public funding is allocated on the basis of the research assessment. The proposed normalization process can be a solution of this dimensional bias conditioning the results of a performance assessment. The proposed framework is intended to be generic, to be applied in any knowledge productivity or quality assessment at any time that the size of the monitored organizations becomes relevant and must be appropriately weighed to validate the evaluation process.