The municipalities of Minas Gerais face significant challenges in managing public resources allocated to health, due to financial constraints and social disparities. These difficulties reinforce the need for an understanding of the effectiveness of resource allocation in the public health sector. By adopting Shannon Entropy for efficiency assessment, this methodology enhances the analysis to consider the variability and uncertainty inherent in the data, thus enabling an understanding of the nuances regarding the distribution of resources for health. This study conducts a comprehensive investigation into the efficiency of public health spending, employing Shannon Entropy as a weighting method in the calculation of Efficiency. The main objective is to provide an in-depth assessment of the effectiveness of resource allocation in the public health sector. The results obtained reveal a new perspective on the allocation of resources for health, highlighting specific areas for potential improvement and optimization, essential to increase the overall efficiency of public health spending. This robust framework serves as a valuable tool for public policymakers, facilitating decision-making processes and ensuring the effective use of public resources for health. The main contribution of this study focuses on the application of Shannon Entropy to efficiency analysis, which not only improves the understanding of public health spending but also provides a new perspective for optimizing resource allocation in the health sector.

Composite indicators are mathematical tools that assist sociologists, geographers, environmentalists, and urban planners in understanding and analyzing complex phenomena. Composite indicators also attract significant interest among researchers in operations research, who seek to improve and develop new methods for their construction. This study aligns with this latter line of research by proposing a new method for constructing composite indicators. The so-called Subjective Benefit-of-the-Doubt (S-BoD) was developed to address the uncertainty about the conceptual importance of sub-indicators in the data-driven definition of their respective weights. This logic ensures the weights adapt to the maturity of the theoretical-conceptual framework for the multidimensional phenomenon. On the one hand, absolute consensus among experts signals a mature theoretical-conceptual framework that prevents the BoD from modifying the weights. On the other hand, absolute disagreement among experts signals the presence of incipient theoretical-conceptual frameworks, which allow for full weight fluctuations, corresponding to the operationalization of the classic BoD algorithm. The results of applying the method show that the S-BoD outperforms BoD in multidimensional governance by better distinguishing units, extracting information, explaining GDP per capita, and generating scores without outliers, resulting in a composite governance indicator with greater discriminatory, informational, and explanatory power. Simulations confirm this superiority, except for the proportion of outliers, which is specific to governance data.

Interest in child health and well-being is growing, and both are multidimensional. Composite indicators (CIs) are useful tools for analyzing their relationships. This study examines the correlation between the CI of child well-being and that of public health system performance and proposes a weighting scheme for constructing CIs. Among schemes, entropy weighting yielded the strongest correlation. Uncertainty analysis revealed that country rankings with entropy weighting are the most stable, demonstrating robust CI. Strong explanatory power indicates that the CIs correlate with GDP, validating their compatibility with a key reference variable. High discriminant power confirms that CIs provide informational diversity, helping decision-makers distinguish between countries. The analysis shows that better health system performance is associated with higher child well-being, reinforcing the role of public health systems in promoting sustainable development and child well-being.

This paper introduces the Minimum Uncertainty Method (MinUn-M), a new approach for constructing composite indicators that integrate subjective expert opinions with objective, data-driven techniques to analyze multidimensional phenomena that are not measurable by a single indicator. The MinUn-M method provides a stable composite indicator in which variations in the model inputs do not lead to significant changes in the model outputs, ensuring greater reliability in representing multidimensional phenomena and facilitating informed decision-making by managers and policymakers. The methods also minimize incompatibilities between subjective and objective weights, thereby promoting alignment between theory and practice by treating the expert’s opinions as constraints on the objective function that minimizes the uncertainty of the composite indicator ranks. Through two case studies, the MinUn-M method is applied to address the challenges of measuring and correlating the child well-being and health systems in low- and middle-income countries, as well as child well-being in Brazilian states. The results demonstrate superior robustness and precision compared to traditional weighting methods (e.g., equal weights, factor analysis, entropy). The main methodological contribution is the balance between objectivity and subjectivity in allocating weights, providing practical tools for public management and future research on constructing multidimensional indicators.