Measuring inequality through a non-compensatory approach

The aggregation of variables is one of the most critical procedures in the building of Composite Indicators. Most of the debate is about the issue of compensation between variables with poor and above-average performance. Researchers understand that non-compensatory aggregation is more appropriate than compensatory aggregation for measuring multidimensional phenomena for several reasons. Among them are the impossibility of substituting one element of the phenomenon for the other, the maintenance of weights as a measure of relative importance, and the emphasis on poorest performances. Despite its desirable properties, the literature review on Composite Indicators of inequality reveals a broad preference for compensatory aggregation of variables over non-compensatory aggregation. The absence of Composite Indicators of inequality built by non-compensatory aggregation leads to the following questions: to what extent does non-compensatory aggregation favor the representation of multidimensional social phenomena in geography? What are the shortcomings of non-compensatory aggregation, and how to resolve them? The results show that the Ordered Weighted Averaging (OWA) operator makes it possible to overcome problems associated with non-compensatory aggregation and obtain a statistically consistent Composite Indicator to represent inequality in a Brazilian city. The advantage of using non-compensatory aggregation is demonstrated by comparing the Composite Indicators constructed through OWA, Simple Additive Weighting, Principal Component Analysis, and Doubt Benefit. Another novelty of this research lies in demonstrating how the regulation of compensation levels between variables and the direction of bias can help in maximizing the Composite Indicator's capability to capture the most relevant variable of the multidimensional phenomenon.