Statistical evaluation in multidimensional systems of ordinal variables through poset theory

The problem of ranking statistical units for evaluation purposes based on ordinal data is a hot topic in many fields of socio-economic sciences and is gaining importance day by day. Assessing the quality of public services, evaluating poverty and well-being, ranking nations in terms of development, freedom or democracy are just a few examples of the struggle towards ranking that socio-economic scientists keep on performing daily. Nevertheless, the mainstream approaches to ordinal evaluation suffer of deep epistemological and methodological inconsistencies, as we firstly show, discussing some paradigmatic real examples, pertaining to poverty and life satisfaction. Basically, such inconsistencies are due to the pretension of fitting ordinal data analysis into ‘’ordinary” data analysis, adopting coneptual models designed for quantitative data. Clearly, the way out to such issues is not looking for more sophisticated statistical evaluation models; it is shifting to more appropriate conceptual frameworks and languages, namely those of partial order theory. We address the topic at the fundamental level of data analysis: as linear algebra provides all the basic tools to classical metric data analysis, so partial order theory does to ordinal data analysis. To ‘’build a bridge” between poset theory and statistical evaluation procedures, we propose a new methodology for evaluation and ranking which draws uniquely upon partial order theory and proves effective in managing all the issues that are typical of descriptive evaluation studies. The methodology is designed to extract information directly out of the relational structure of the data, combining both objective and subjective variables, as typical in socio-economic evaluation problems. In order to make the presentation as clear as possible, the methodology will be introduced through real data examples, so as to highlight how it works and how it solves many of the inconsistencies of other approaches. A brief account of the limitations of the proposal and some suggestions for future research end the presentation.