Complexity of social phenomena: measurements, analysis, representations and synthesis

During the three years of my Ph.D., I have analyzed and studied phenomena often very different and apparently distant from one another: well-being; sustainable development; gender inequalities; the Brexit vote. The aim has always been to understand these facets of reality, to give them an explanation based on a quantitative point of view. My interest was to provide a measure of concepts often considered difficult to deal with and to understand. When I finished my Ph.D., I tried to put together the experience I had gained. As mentioned, the research interests were many and, therefore, it was necessary to conceptualize them within a framework that would highlight the elements in common. This thesis is the result of such an attempt at conceptualisation. The title itself highlights the concepts common to my research work over the years. The first concept I deal with is complexity. I have realized that all different socioeconomic phenomena have in common their complex structure, often mistakenly exchanged with complication and difficulty. Nowadays, complexity is a concept that characterizes allthe natural and social sciences and defines our relationship with knowledge. Chapter 1 examines precisely the theme of complexity, presenting different approaches and definitions to this issue. I have tried to reconstruct the way in which complexity became central in the relationship with knowledge, together with its qualifying concepts such as subjectivity, the concept of system and circular causality. The second guiding concept of this research work is measurement. Understanding the world requires a sort of translation, a shift from the plane of reality in which we observe phenomena to the plane of numbers in which we try to encode them. This translation must be meaningful, it must reproduce as faithfully as possible in the world of numbers the phenomenon observed in the plane of reality. Measurement is a need for the knowledge of reality, which speaks to us with the language of numbers. This issue is the subject of Chapter 2, in which I address the question of the definition of this process. Subsequently, the measurement is contextualised within sociology, presenting the essential contribution on this theme offered by Paul Felix Lazarsfeld with the operationalisation. Finally, the concept of indicator is explored, by analysing their crucial importance in the measurement of social phenomena. The Chapter presents all the main aspects through which it is possible to obtain a system of indicators, a tool for measuring complex social phenomena. The way in which we can measure complex socio-economic phenomena is dealt with in Chapter 3. Synthesis is presented by a methodological point of view, considering both aspects of a system, units (rows) and indicators (columns). I focus on the synthesis techniques that allow a dynamic analysis of phenomena in order to obtain comparable measures not only in space, but also in time. Only in this way, a synthesis is meaningful. In the chapter, I define the object of study, the three-way data array X {xijt : i = 1, . . . ,N; j = 1, . . . ,M; t = 1, . . . , T}, where xijt represents the determination of the jth indicator in the ith unit at the tth temporal occasion. The methods of clustering these objects and summarising the indicators are addressed, considering both the aggregative and the non-aggregative approach (in particular, I propose an approach to apply posets to systems of indicators over time). In the last two chapters, I propose two applications to real data. Both applications concern regional data. The choice was made because of the importance that the regional dimension has for a country like Italy, characterized by strong territorial disparities. The first one (Chapter 4) concerns the concept of well-being and, from a methodological point of view, the synthesis of statistical units. In particular, using the time series of regional composites produced by the Italian National Institute of Statistics for the Equitable and Sustainable Well-being project (BES), we classify the Italian regions according to different domains. We use a time series fuzzy clustering algorithm, particularly suitable for that type of data. Chapter 5 deals with sustainable development and the issue of synthesis of statistical indicators over time. In particular, an aggregative method, the Adjusted Mazziotta-Pareto Index (AMPI), and a non-aggregative procedure based on posets will be compared.