From Composite Indicators to Partial Orders: Evaluating Socio-Economic Phenomena Through Ordinal Data

Abstract

In this paper we present a new methodology for the statistical evaluation of ordinal socio-economic phenomena, with the aim of overcoming the issues of the classical aggregative approach based on composite indicators. The proposed methodology employs a benchmark approach to evaluation and relies on partially ordered set (poset) theory, a branch of discrete mathematics providing tools for dealing with multidimensional systems of ordinal data. Using poset theory and the related Hasse diagram technique, evaluation scores can be computed without performing any variable aggregation into composite indicators. This way, ordinal scores need not be turned into numerical values, as often done in evaluation studies, inconsistently with the real nature of the phenomena at hand. We also face the problem of “weighting” evaluation dimensions, to account for their different relevance, and show how this can be handled in pure ordinal terms. A specific focus is devoted to the binary variable case, where the methodology can be specialized in a very effective way. Although the paper is mainly methodological, all of the basic concepts are illustrated through real examples pertaining to material deprivation.