Max-explanation with multiple constraints: a new method for representing complex and multifaceted realities and its application in estimating the potential economic development of Brazilian states

Abstract Composite indicators are widely used to represent multidimensional phenomena; however, existing weighting methods typically optimize statistical properties without explicitly incorporating construct validity into the estimation process. This study proposes Max-explanation with multiple constraints, a theory-driven optimization framework that estimates aggregation weights by maximizing adherence to a conceptually significant variable while simultaneously enforcing construct-validity criteria, including information transfer and construct non-dominance. Variables whose empirical relationships are inconsistent with their theoretical polarity are identified as noise and excluded before optimization. The proposed method is applied to construct composite indicators of present and potential economic development for the 27 Brazilian states. Sensitivity and robustness analyses demonstrate that the method performs best when the input variables provide complementary rather than redundant information. As intercorrelation among the variables increases, the weighting degrees of freedom available for optimization progressively decrease, reducing the attainable adherence to the conceptually significant variable and eventually preventing feasible solutions under highly redundant correlation structures. Compared with conventional weighting methods, the proposed framework produces composite indicators with stronger conceptual representation while explicitly controlling construct dominance and information transfer. The proposed optimization framework is readily applicable to other multidimensional phenomena whenever a conceptually significant reference variable is available.