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

Abstract

The present debate on well-being measurement is clearly pointing out that a valuable evaluation process has to take into account many different and complementary aspects, in order to get a comprehensive picture of the problem and to effectively support decision-making. Assessing well-being requires sharing a conceptual framework about its determinants and about society and needs the identi fi cation of the most consistent and effective methodologies for building indicators and for communicating purposes. From a statistical perspective, one of the critical points concerns the preservation of the true nature of the socio-economic phenomena to be analysed. This calls for an adequate methodological approach. Several socio-economic phenomena have an intrinsic ordinal nature (e.g. material deprivation, democratic development, employment status), and correspondingly, there has been an increasing availability of ordinal datasets. Nevertheless, ordinal data have been often conceived as just a rough approximation of truly numerical and precise, yet non-observable, features, as if a numerical latent structure would exist under ordinal appearances. As a result, the search for alternative statistical procedures has been slowed down, and many epistemological, methodological and statistical problems regarding ordinal data treatment are still open and unsolved:

Partially Ordered Sets and the Measurement of Multidimensional Ordinal Deprivation

“…A final ''Appendix'' reports the formal proof of a technical result needed in the development of the procedure. The paper partly collects results from earlier works Fattore et al 2012;Fattore and Maggino 2014;Fattore 2014;Fattore and Maggino 2015), but extends and completes them adding new material and providing the first comprehensive exposition of the approach. The paper has a methodological aim; the theoretical concepts and the evaluation procedure are illustrated through simulated examples, to keep complexity at a moderate level, and to exploit visual representations, so common and useful in partial order theory.…”

A Poset-Generalizability Method for Human Development Indicators

“…Whenever x ≤ y or y ≤ x we can say that x and y are comparable; but when this is not the case they are said to be incomparable (written x||y). Following Fattore et al (2012) we define a chain or a linear order as a partial order P where any two elements are comparable and an antichain when they are not. When all attributes are comparable, we have the particular case of a complete order such that all objects x ∈ X can be arranged in a simple sequence, as it happens in CI, such that x 1 < x 2 < … < x n .…”

“…One alternative is to replace the popular use of complete orderings by the use of partial orderings (Bruggemann & Patil, 2011;Fattore and Bruggemann, 2017;Fattore et al, 2012). Somehow complete orderings represent an unnatural state of affairs because there are many elements in development and in life that are incommensurable and that produce ambiguities that scholars, as well as the general public, choose to ignore because they are difficult to handle.…”

Exploiting Ordinal Data for Subjective Well-Being Evaluation

“…Here we show how it can be used to evaluate well-being. Since the fundamentals of the evaluation procedure have been already introduced in other papers (Fattore, Brueggemann and Owsinski 2011;Fattore, Maggino and Colombo, 2012), in the following we limit ourselves to a brief outline.…”

“…Answering the needs of social scientists and policy-makers thus requires developing new statistical strategies, namely alternative procedures to exploit the information power of multidimensional ordinal data. Starting from this consideration, a new evaluation procedure has been recently proposed by the Authors (Fattore, Brueggemann and Owsinski, 2011;Fattore, Maggino and Colombo, 2012;Fattore and Maggino, 2015), capable to deal directly with ordinal data and to compute synthetic indicators without attribute aggregation. The procedure follows the classical steps of any evaluation process in the social field, namely identifying well-being attributes, choosing a well-being threshold and computing individual and overall statistics.…”