We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

In this innovative approach to the practice of social science, Charles Ragin explores the use of fuzzy sets to bridge the divide between quantitative and qualitative methods. Paradoxically, the fuzzy set is a powerful tool because it replaces an unwieldy, "fuzzy" instrument—the variable, which establishes only the positions of cases relative to each other, with a precise one—degree of membership in a well-defined set. Ragin argues that fuzzy sets allow a far richer dialogue between ideas and evidence in social research than previously possible. They let quantitative researchers abandon "homogenizing assumptions" about cases and causes, they extend diversity-oriented research strategies, and they provide a powerful connection between theory and data analysis. Most important, fuzzy sets can be carefully tailored to fit evolving theoretical concepts, sharpening quantitative tools with in-depth knowledge gained through qualitative, case-oriented inquiry. This book will revolutionize research methods not only in sociology, political science, and anthropology but in any field of inquiry dealing with complex patterns of causation.

Fuzzy-Set Social Science

The paper presents a general framework and an operative procedure for the evaluation of multidimensional deprivation with ordinal attributes. Evaluation is addressed in terms of multidimensional comparisons among achievement profiles, rather than through attribute score aggregations. This makes it unnecessary to scale ordinal attributes into numerical variables, overcoming the limitations of aggregative procedures and counting approaches. The evaluation procedure is fuzzy in nature, accounts for both vagueness and intensity of deprivation and produces a comprehensive set of synthetic indicators for policy-makers.

Partially Ordered Sets and the Measurement of Multidimensional Ordinal Deprivation

https://iris.unive.it/bitstream/10278/3725041/1/SSRN-id2973115.pdf

How does risk flow in the credit default swap market

Regional carbon imbalance within China: An application of the Kaya-Zenga index

In recent years, sustainable development has become one of the main issues of scientific and institutional debate. The literature on this concept is wide and often presents conflicting positions. This leads to considering sustainable development as a contested concept. The growing interest and importance of this topic has also led to an increasing focus on the aspect of its measurement. Dealing with the measurement of complex phenomena, like sustainable development, means dealing with synthesis. The traditional and dominant approach to the synthesis of multi-indicator systems of cardinal variables is the use of the aggregative-compensative approach. Despite its success, this approach presents a series of critical issues. In this paper, we propose a method of synthesizing multi-indicator systems over time based on the Partial Order Theory. Applying and comparing the method we proposed and an aggregative method, the Adjusted Mazziotta–Pareto Index, to one of the 15 sustainable development goals, we highlight the strengths of the new methodological proposal.

https://link.springer.com/content/pdf/10.1007/s11205-020-02398-5.pdf

Synthesis of Multi-indicator System Over Time: A Poset-based Approach

In this paper, we present a multidimensional fuzzy analysis of the levels and the patterns of poverty and social fragility of migrants’ families, in the Italian region of Lombardy, in year 2014 Migrants’ poverty emerges as a complex trait, better described as a stratification of nuanced patterns than in black and white terms; Lombard migrants are in fact affected, to different extents, by “a diffused sharing of deprivation facets” and cannot be trivially split into deprived and non-deprived The paper employs innovative data analysis tools from the Theory of Partially Ordered Sets; compared to mainstream monetary approaches, this leads to more realistic estimates of poverty diffusion and eliminates some well-known biases of standard evaluation procedures, providing strong support to the use of partial order concepts and tools in social evaluation studies

Multidimensional Analysis of Deprivation and Fragility Patterns of Migrants in Lombardy, Using Partially Ordered Sets and Self-Organizing Maps

The official Italian well-being measuring system (“Equitable and Sustainable Well-being—BES”) is probably the worldwide most advanced attempt to pursue the beyond GDP perspective effectively. In it, well-being is described in terms of 12 domains and a complex multi-indicator system of around 130 indicators, drawn mainly from Istat (official Italian statistical bureau) surveys and administrative archives. In order to get a more synthetic view of well-being, in the last four BES reports Istat employed aggregative procedures providing composite indicators for each well-being domain. The aggregative road to synthesis is however problematic, when complex and non-highly correlated indicator systems are to be summarized, mainly due to its compensative nature and interpretational difficulties. As a valuable alternative, in this paper we adopt a non-aggregative approach to synthesis, based on Partially Ordered Set Theory (Poset Theory) and show how it can be used to provide more “complexity-preserving”insights into well-being. In particular, we describe each well-being domain as a partially ordered set and compute synthetic indicators for well-being rankings at regional level for year 2017, getting more robust and interpretable results than with mainstream aggregative procedures.

Measuring Equitable and Sustainable Well-Being in Italian Regions: The Non-aggregative Approach

The paper introduces PARSEC, a new software package implementing basic partial order tools for multidimensional poverty evaluation with ordinal variables. The package has been developed in the R environment and is freely available from the authors. Its main goal is to provide socio-economic scholars with an integrated set of elementary functions for multidimensional poverty evaluation, based on ordinal information. The package is organized in four main parts. The first two comprise functions for data management and basic partial order analysis; the third and the fourth are devoted to evaluation and implement both the poset-based approach and a more classical counting procedure. The paper briefly sketches the two evaluation methodologies, illustrates the structure and the main functionalities of PARSEC, and provides some examples of its use.

PARSEC: An R Package for Poset-Based Evaluation of Multidimensional Poverty

In this paper, we discuss the existence of particular systems of generators for posets associated to multidimensional systems of ordinal indicators and derive a reduced posetic procedure for the measurement of multidimensional ordinal deprivation. The proposal is motivated by the need to lessen the computational complexity of the original posetic procedure described in Fattore (Soc Indic Res 128(2):835–858, 2015), so as to make it applicable to larger multi-indicator systems, particularly to those comprising many variables scored on “short” scales, as typical in deprivation studies. The reduced procedure computes identification and severity functions based only on so-called lexicographic linear extensions. These are a particular generating system for the basic achievement poset, naturally associated to rankings of deprivation attributes. After motivating this choice, both from an interpretative and a computational point of view, the paper provides some simulated examples, comparing the reduced and the non-reduced procedures.

Alberto Arcagni

Papers

Synthesis of Multi-indicator System Over Time: A Poset-based Approach

Multidimensional Analysis of Deprivation and Fragility Patterns of Migrants in Lombardy, Using Partially Ordered Sets and Self-Organizing Maps

Measuring Equitable and Sustainable Well-Being in Italian Regions: The Non-aggregative Approach

PARSEC: An R Package for Poset-Based Evaluation of Multidimensional Poverty

A Reduced Posetic Approach to the Measurement of Multidimensional Ordinal Deprivation