Evaluation of life satisfaction in Italy: proposal of a synthetic measure based on poset theory

Background: The measure of complex concepts in the social science, such as life satisfaction, job quality, or deprivation, is traditionally aimed to evaluate countries, universities, institutions, and other macro-units. In this case, the classical approach of composite indicators is often used. Today, the interest in measuring complex concepts is enlarging also to individuals, where many of the indicators are measured on an ordinal or dichotomous scale. In this case, the traditional approach to composite indicators is lacking, and ordinal data are often used in an improper way. Some recent proposals have been developed to compare and evaluate units observed on a qualitative or mixed scale in a socio-economic framework with the use of Partially Ordered Sets (poset) theory. This mathematical framework allows observed variables on individuals to be handled, without any need of aggregation while preserving the complexity of the data order. Objectives: The goal of this research is to define a synthetic measure starting from poset theory and to study the concept of life satisfaction using this measure. Starting from a method proposed by Fattore et al. (2011), a synthetic measure will be identified, with the main aim of studying life satisfaction in Italy. Methods: Inside the poset literature, one of the leading arguments is the computation of average rank of observations among all linear extensions, which is a measure that describes the average rank of an observation in a population that contains non-comparable elements. The method to measure multidimensional ordinal deprivation is a recent tool, in which the opinion of the decision-maker is requested for the definition of a threshold. The threshold is a border defined such that all elements below it are defined as deprived (or having an unsatisfactory level of the measured complex concept). In this work, we propose to interpret the threshold as a meaningful border between two opposite poles of a complex concept; for instance, it can represent the zero level between positive satisfaction and negative dissatisfaction. Some suggestions for the definition of the threshold are part of this work, together with observations on the meaning of the border in a synthetic measure framework. Given a threshold, a measure of severity of a condition is defined as the mean rank-distance between the observation and the threshold among the entire set of linear extensions of the observed poset. In this work we define a synthetic measure derived by the severity measures and investigate its features. Results: Proposals and observations on the meaning and characteristics of the threshold are presented to suggest a list of guidelines for recent users. In the results, the method is used to measure and analyze the life satisfaction of the Italian population, using the ISTAT yearly survey "Aspects of daily life". First, we obtain a reliable indicator of life satisfaction that is analyzed with respect to both the constituting variables of the poset and the external explanatory socio-economical variables. Secondly, this application permits a deeper evaluation of the informative power and the limits of the synthetic measure based on poset. Conclusions: A synthetic measure for qualitative data is possible without stretching the meaning of variables and without the use of a scaling procedure. Poset theory and its tools are great resources for social research, especially when dealing with the complexity of real data measured on individuals. The application on life satisfaction provided strong evidence of the relationships with socio-economical external variables. The application of quantile regression led to clear results about the positive effects of education, healthy habits, and northern geographical partitions on life satisfaction