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Drawing upon Roman public law and the classical Western ius commune generally, I sketch a law-governed constitution of hierarchy, including its institutional form and its basic justification. Grounded in a popular delegation of sovereign authority and power (imperium and potestas) to the Roman emperors and subordinate officials, the constitution of hierarchy is pervasively shaped and constrained by law and legal norms, written and unwritten, that orient the lawful exercise of power to the public good; it includes subsidiary democratic mechanisms of petitioning, consultation, and local and provincial democracy. The alternative to the constitution of hierarchy is not political egalitarianism, but an alternative hierarchy of arbitrary and exploitative rule, dominated by an economic and social class of optimates.

Factor analysis is widely utilized to identify latent factors underlying the observed variables. This paper presents a comprehensive comparative study of two widely used methods for determining the optimal number of factors in factor analysis, the K1 rule, and parallel analysis, along with a more recently developed method, the bass-ackward method. We provide an in-depth exploration of these techniques, discussing their historical development, advantages, and limitations. Using a series of Monte Carlo simulations, we assess the efficacy of these methods in accurately determining the appropriate number of factors. Specifically, we examine two cessation criteria within the bass-ackward framework: BA-maxLoading and BA-cutoff. Our findings offer nuanced insights into the performance of these methods under various conditions, illuminating their respective advantages and potential pitfalls. To enhance accessibility, we create an online visualization tool tailored to the factor structures generated by the bass-ackward method. This research enriches the understanding of factor analysis methodology, assists researchers in method selection, and facilitates comprehensive interpretation of latent factor structures.

In recent years, the development of machine learning has introduced new analytical methods to theoretical research, one of which is Bayesian network—a probabilistic graphical model well-suited for modelling complex non-deterministic systems. A recent study has revealed that the order in which variables are read from data can impact the structure of a Bayesian network (Kitson and Constantinou in The impact of variable ordering on Bayesian Network Structure Learning, 2022. arXiv preprint arXiv:2206.08952). However, in empirical studies, the variable order in a dataset is often arbitrary, leading to unreliable results. To address this issue, this study proposed a hybrid method that combined theory-driven and data-driven approaches to mitigate the impact of variable ordering on the learning of Bayesian network structures. The proposed method was illustrated using an empirical study predicting depression and aggressive behavior in high school students. The results demonstrated that the obtained Bayesian network structure is robust to variable orders and theoretically interpretable. The commonalities and specificities in the network structure of depression and aggressive behavior are both in line with theorical expectations, providing empirical evidence for the validity of the hybrid method.

A simple approach is proposed to study the main factors related to the mining activity’s impact on society, through a corporate social responsibility (CSR) qualitative analysis based on the type of raw materials extracted, either by mine site or firm. A CSR index is defined by 30 environmental and socioeconomic elements and, subsequently, it is weighted by three primary factors; the recycling rate, the transition to green energy, and geographical conditions. The proposed method is adaptable to any change in raw material needs over time and, depending on the analyzed country or region, is applicable to any type of mineral resource. The system can be used to drive engagement with the different stakeholders, add value to a project, and establish a CSR continuous improvement system.

This study empirically examines the nexus between natural resource rent and financial development in the context of the developing economy of Nigeria, between 1990 and 2021, by considering the important role of corruption control under an asymmetric approach. The study further looked at the influence of information technology, and renewable energy, on financial development. The bound test result confirms the existence of a long-term relationship among the variables. This study first uses the nonlinear autoregressive distributive lag (NARDL) model to capture the asymmetry that arises from positive or negative components of natural resource rent. The empirical evidence of the NARDL estimation shows that natural resource rent negatively influences financial development; meanwhile, corruption control boosts financial development and positively moderates this relationship in the Nigerian context. This confirms the existence of a natural resource curse. The results further explained that both information technology, renewable energy, and corruption control enhance financial development. Furthermore, the causality test discovers that there exists a bidirectional causal relationship between financial development and the scrutinized variables. These findings offer valuable policy recommendations for policymakers.