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2014 | OriginalPaper | Buchkapitel

9. Partial Orders in Socio-economics: A Practical Challenge for Poset Theorists or a Cultural Challenge for Social Scientists?

verfasst von : Marco Fattore, Filomena Maggino

Erschienen in: Multi-indicator Systems and Modelling in Partial Order

Verlag: Springer New York

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Abstract

In this “position paper” we discuss the potential role of partial order theory in socio-economic statistics and social indicators construction. We maintain that the use of concepts and tools from poset theory is needed and urgent to improve currently adopted methodologies, which often prove ineffective for exploiting ordinal data. We also point out that the difficulties in spreading partial order tools are cultural in nature, and that some open-mindedness is needed among social scientists. We address these issues introducing some examples of open questions in socio-economic data analysis: (i) the problem of multidimensional poverty evaluation, (ii) the problem of assessing inequality and societal polarization, and (iii) the problem of clustering in multidimensional ordinal datasets.

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Fußnoten
1
In this paper, we often use terms like “complex” or “complexity.” We use them informally, to mean problems or systems that cannot easily be solved, reduced or described, as they are made of many linked elements or facets. Perhaps the formal definition of complexity which is closest in spirit to the way we employ the term is that of “Kolmogorov complexity,” used in algorithmic information theory. However, we stress that this is only an analogy.
 
2
Measuring inflation should involve also measuring services and it is quite debatable how to precisely define the concept of quantity in this case.
 
4
These so-called scaling tools range from simply coding and using ordinal scores as integers, to running complex numerical algorithms, like in the Gifi homogeneity analysis (Michailides and de Leeuw 1998), or using various regression or model-based approaches.
 
5
Whenever cutoffs or thresholds are involved in the assessment, benchmarks are de facto introduced.
 
6
That is, the smallest set of profiles with the cited property.
 
7
Here, we assume that the lower the scores, the worse off the individual.
 
8
In Fattore et al. [2012], e.g., it is also suggested how the classical notion of “weighting” variables may be translated into purely poset terms.
 
9
This threshold has been chosen for exemplification purposes only.
 
10
The Abul Naga and Yalcin index is computed setting \( \alpha =\beta =1\), while the Generalized Entropy is computed setting a = 0.
 
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Metadaten
Titel
Partial Orders in Socio-economics: A Practical Challenge for Poset Theorists or a Cultural Challenge for Social Scientists?
verfasst von
Marco Fattore
Filomena Maggino
Copyright-Jahr
2014
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-8223-9_9