Gintropic scaling of scientometric indexes

Bı́ró, Tamás; Telcs, András; Józsa, Máté; Néda, Zoltán

doi:10.1016/j.physa.2023.128717

Cited by 7 publications

(2 citation statements)

References 28 publications

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“…Herein, we studied a significant number of socioeconomic systems through the framework of SOC architecture. This approach has been used to analyze a range of systems, including financial markets [40], citation evolution [39,41], cryptocurrencies [42], and political behavior [43], among others. Despite the diversity of these systems, our analysis reveals that the behavior of inequality indices, particularly the Gini (g) and Kolkata (k) indices, demonstrates near-universal characteristics across socioeconomic systems.…”

Section: Summary and Discussionmentioning

confidence: 99%

Sandpile Universality in Social Inequality: Gini and Kolkata Measures

Banerjee

Biswas

Chakrabarti

et al. 2023

Entropy

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Social inequalities are ubiquitous and evolve towards a universal limit. Herein, we extensively review the values of inequality measures, namely the Gini (g) index and the Kolkata (k) index, two standard measures of inequality used in the analysis of various social sectors through data analysis. The Kolkata index, denoted as k, indicates the proportion of the `wealth’ owned by (1−k) fraction of the `people’. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around g=k≈0.87, starting from the point of perfect equality, where g=0 and k=0.5) as competition increases in different social institutions, such as markets, movies, elections, universities, prize winning, battle fields, sports (Olympics), etc., under conditions of unrestricted competition (no social welfare or support mechanism). In this review, we present the concept of a generalized form of Pareto’s 80/20 law (k=0.80), where the coincidence of inequality indices is observed. The observation of this coincidence is consistent with the precursor values of the g and k indices for the self-organized critical (SOC) state in self-tuned physical systems such as sand piles. These results provide quantitative support for the view that interacting socioeconomic systems can be understood within the framework of SOC, which has been hypothesized for many years. These findings suggest that the SOC model can be extended to capture the dynamics of complex socioeconomic systems and help us better understand their behavior.

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Section: Summary and Discussionmentioning

confidence: 99%

Sandpile Universality in Social Inequality: Gini and Kolkata Measures

Banerjee

Biswas

Chakrabarti

et al. 2023

Entropy

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“…For example, x may denote the number of citations that an individual author receives and

the distribution of this number in the analyzed population. Then,

is the fraction of papers cited x times or more, and

is the fraction of citations received for these relative to all citations [ 30 ]. The above definitions and the following analysis of gintropy can be used for any PDF defined on non-negative variables

and having a finite expectation value.…”

Section: About Gintropymentioning

confidence: 99%

Analogies and Relations between Non-Additive Entropy Formulas and Gintropy

Biró,

Telcs,

Jakovác

2024

Entropy

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We explore formal similarities and mathematical transformation formulas between general trace-form entropies and the Gini index, originally used in quantifying income and wealth inequalities. We utilize the notion of gintropy introduced in our earlier works as a certain property of the Lorenz curve drawn in the map of the tail-integrated cumulative population and wealth fractions. In particular, we rediscover Tsallis’ q-entropy formula related to the Pareto distribution. As a novel result, we express the traditional entropy in terms of gintropy and reconstruct further non-additive formulas. A dynamical model calculation of the evolution of Gini index is also presented.

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