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

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Abstract

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.

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Notes

  1. This introduces a very interesting assumption, i.e. that the concept of sustainable development changes over time. However, this assumption is not explored by this paper: we compare the conditions over time taking into account the same indicators. Thus, the conceptual model is the same.

  2. The SDGs analysed by Alaimo and Maggino are: Goal 1—End Poverty; Goal 2—Zero Hunger; Goal 3—Good Health and Well-being.

  3. As explained by Alaimo and Maggino (2020), “the Brundtland Commission’s definition of SD has been the guide for the selection of the basic indicators. As mentioned above, in order to be sustainable, development must ensure the well-being of current generations and, at the same time, not compromise the ability of future generations to achieve it. Therefore, we selected all the indicators useful for the analysis of regional realities and appropriate for either monitoring the present condition, or for providing information on a future one (risk). We believe that by distinguishing these two aspects it is possible to analyse the phenomena considered. This distinction is partly inspired by the composition of the Human Development Report 2014 and in the Equitable and Sustainable Well-being (Bes) Report 2015, which described the framework of the sustainability of wellbeing by using the concept of risk and resilience factors”. (Alaimo and Maggino 2020, 392)

  4. A three-way data array is a specification of a multiway array (Coppi and Bolasco 1989) in which there are three indices.

  5. AMPI is a partially non-compensatory composite indicator, based on a Min-Max standardization and a re-scaling of the basic indicators in a range [70; 130] according to two goalposts, representing a minimum and a maximum value of each variable for all units and time periods. This method allows assessing absolute changes over time. For more information, see Mazziotta and Pareto (2016).

  6. In other words, the two elements are comparable, if the order can be inferred through the indicators without the introduction of any assumption. It is possible to note that such binary relation satisfies the three properties required by a partial order relation. If two or more elements share the same scores for all the indicators, they have the same profile, and they must be grouped into a unique element called equivalence class. Note that in our application, there are no equivalence classes.

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Authors and Affiliations

  1. Department of Social Sciences and Economics, Sapienza University of Rome, Rome, Italy

    Leonardo Salvatore Alaimo

  2. Italian National Institute of Statistics, Istat, Rome, Italy

    Leonardo Salvatore Alaimo

  3. MEMOTEF Department, Sapienza University of Rome, Rome, Italy

    Alberto Arcagni

  4. Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Milan, Italy

    Marco Fattore

  5. Department of Statistics, Sapienza University of Rome, Rome, Italy

    Filomena Maggino

Authors
  1. Leonardo Salvatore Alaimo
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  2. Alberto Arcagni
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  3. Marco Fattore
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  4. Filomena Maggino
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Correspondence to Leonardo Salvatore Alaimo.

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Appendix

Appendix

See Figs. 10, and 11.

Fig. 10
figure 10

Basic indicators of Goal 1—present condition: Italy and Italian Regions; time series 2009–2017

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Fig. 11
figure 11

Synthetic index of Goal 1 present condition: regional and national data; time series 2010–2017; AMPI: Italy 2010 = 100

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Alaimo, L.S., Arcagni, A., Fattore, M. et al. Synthesis of Multi-indicator System Over Time: A Poset-based Approach. Soc Indic Res 157, 77–99 (2021). https://doi.org/10.1007/s11205-020-02398-5

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