Sadullah Çelik

Democracy is a multifaceted institutional phenomenon that cannot be comprehensively captured by a single index. This paper defines unique institutional configurations in various countries according to six V-Dem democracy dimensions, including the Liberal Democracy Index, Electoral Democracy Index, Liberal Component Index, Egalitarian Component Index, Participatory Component Index, and Deliberative Component Index. It uses data on 179 countries and conducts a primary K-means clustering method, supplemented with Hopkins statistics and gap statistics, bootstrap stability tests, and Gaussian Mixture Model (GMM) robustness tests. The paper also uses Shannon entropy with Miller–Madow correction to measure a regime’s institutional heterogeneity, and the Rule of Law Index of the World Justice Project for external validation. As a result, the paper uncovers seven empirically identifiable democracy regimes featuring different institutional configurations. Different regimes have varying levels of internal institutional heterogeneity, being higher in hybrid regimes, lower in consolidated regimes. WJP analysis reveals additional systematic differences in rule of law outcomes in different regimes. Overall, the results are in line with the multidimensional approach to democracy and show how unsupervised learning and information-theoretic analysis may complement democracy indices.

There are great differences between the sustainable development success stories in various nations; however, such differences are not justifiable on the grounds of the ability of governance institutions or ecological dangers. The purpose of this research is to understand whether there are different regimes of the interplay of governance and ecological danger and whether such regimes are somehow related to the heterogeneity of sustainable development success. In order to reveal the regimes of the nations that are defined in terms of the following variables: Governance Score, Water Risk, Food Insecurity, Impact of Natural Events, and Demographic Pressure, the PCA‐GMM framework will be used based on the data from 164 countries for 2024–2025. The following three different regimes of the interaction between governance and ecological risk were revealed, distinguished by the presence of different combinations of the variables of governance capacity, ecological risk, and socioeconomic pressure. Importantly, the regimes are not linear in terms of being organized from high to medium to low, since there may be situations where two countries demonstrate the same level of sustainable development but at the same time have very different combinations of governance and ecological variables, implying the presence of several distinct ways to achieve sustainable development. The outcomes of machine learning and SHAP analyses provide further evidence of nonlinear dependencies between the variables used, as three variables—Food Insecurity, Governance Score, and Demographic Pressure—are especially important.

The rule of law can be considered as a multidimensional institutional phenomenon, which emerges through interplay between legal, governance and administrative institutions. The paper offers an exploratory statistical modeling approach to find empirical patterns in national rule-of-law profiles according to the 2024 World Justice Project (WJP) Rule of Law Index. Eight dimensions of the index are considered to identify differences between countries and similarities of their multidimensional institutional performance. Principal Component Analysis reveals strong associations between eight dimensions, which are structured along the same performance institutional scale; the first principal component explains 85.7% of the overall variation and two principal components explain 92.5% of it. K-Means, hierarchical and DBSCAN clustering methods are then used to examine the empirical similarities between countries. While the six-cluster solution of K-Means offers distinct group descriptions, low bootstrap stability of this solution suggests that these groups cannot be regarded as fixed rule-of-law regimes. In addition, the Random Forest analysis reveals Regulatory Enforcement, Absence of Corruption, and Criminal Justice as the three dimensions, which contribute to the empirical differentiation of the described profiles the most. In general, the results imply that international variations in rule-of-law performance are viewed as heterogeneous locations in a multidimensional institution space, rather than as stable and distinct legal systems. The above-presented methodology allows for an exploratory approach to analyze international variations in rule-of-law performance that considers the limitations of cross-section data and instability of clusters.

Multidimensional poverty is a socioeconomic problem that results from nonlinear interdependencies of various socioeconomic indicators such as educational, health, and living standards indices. This paper considers an XAI-based approach for studying the structural topology and dependency structures of multidimensional poverty systems. It relies on a combination of machine learning approaches, network science, spectral graph theory, and entropy-based complexity measures for revealing the systemic interdependencies between different poverty indicators. The structure of interdependencies between socioeconomic indices associated with education is represented by the multilayer perceptron (MLP). The interpretability of the model is provided via the computation of SHAP values by means of the KernelSHAP method. Higher-order interactions between variables are revealed via the construction and analysis of SHAP-based interaction networks. The proposed methodology is then employed on the GEMPI 2025 dataset consisting of 109 countries. The results show significant consistency in the structural map (R² = 0.9890) in combination with stable internal consistency in cross-validation (R² = 0.9864, SD = 0.0074). The SHAP analysis shows that standards of living and health have a high influence on the structural mapping of education, while the contribution of income-related features is lower compared to other features. Entropy analysis points toward partially fragmented dependency networks with a moderate concentration of explanatory influences (H = 1.705). The proposed framework can be used to characterize structural dependencies, identify influencing system components, and map informational processes in multidimensional poverty systems by combining the methodology of explainable artificial intelligence with entropy–spectral network analysis.