Posetic Tools in the Social Sciences:
A Tutorial Exposition
Marco Fattore and Alberto Arcagni
1 Why Partial Orders in the Social Sciences?
Why is partial order theory of interest in the social sciences? Simply because many
socio-economic problems are naturally conceptualized and formalized in terms of
order relations and must then be addressed in ordinal terms, i.e. by using concepts
and tools from the theory of partial orders (Davey and Priestley 2002). A typical
example is the evaluation of social traits, like deprivation or well-being, when
statistical units (e.g. individuals or households) are scored against multidimensional
systems of ordinal attributes (i.e. data systems with many variables or indicators
measured on a set of statistical units). If the observed achievement profiles of the
units have so-called conflicting scores (e.g. unit a scores better than unit b on a
dimension and scores worse on another), and this is quite often the case, data can
be ordered only partially, producing a partially ordered set (poset). What kind of
information can be extracted out of such a data structure and how? Here the theory
of order relations comes into play and provides the proper analytical toolbox.
Remark Interestingly, partial orders are useful also when numerical data systems
are to be addressed and one does not want to, or cannot, mix variables through
aggregated procedures, like those leading to composite indicators. In this respect,
one can argue whether using ordinal scales and partially ordered structures is
intrinsic to the phenomena under study or whether it depends upon the perspective
taken by the researcher. In any case, the data structure and the tools adopted in
M. Fattore ()
Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Milan, Italy
e-mail: marco.fattore@unimib.it
A. Arcagni
Department MEMOTEF, Sapienza University of Rome, Rome, Italy
e-mail: alberto.arcagni@uniroma1.it
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. Bruggemann et al. (eds.), Measuring and Understanding Complex Phenomena,
https://doi.org/10.1007/978-3-030-59683-5_15
219
A Tutorial Exposition
Marco Fattore and Alberto Arcagni
1 Why Partial Orders in the Social Sciences?
Why is partial order theory of interest in the social sciences? Simply because many
socio-economic problems are naturally conceptualized and formalized in terms of
order relations and must then be addressed in ordinal terms, i.e. by using concepts
and tools from the theory of partial orders (Davey and Priestley 2002). A typical
example is the evaluation of social traits, like deprivation or well-being, when
statistical units (e.g. individuals or households) are scored against multidimensional
systems of ordinal attributes (i.e. data systems with many variables or indicators
measured on a set of statistical units). If the observed achievement profiles of the
units have so-called conflicting scores (e.g. unit a scores better than unit b on a
dimension and scores worse on another), and this is quite often the case, data can
be ordered only partially, producing a partially ordered set (poset). What kind of
information can be extracted out of such a data structure and how? Here the theory
of order relations comes into play and provides the proper analytical toolbox.
Remark Interestingly, partial orders are useful also when numerical data systems
are to be addressed and one does not want to, or cannot, mix variables through
aggregated procedures, like those leading to composite indicators. In this respect,
one can argue whether using ordinal scales and partially ordered structures is
intrinsic to the phenomena under study or whether it depends upon the perspective
taken by the researcher. In any case, the data structure and the tools adopted in
M. Fattore ()
Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Milan, Italy
e-mail: marco.fattore@unimib.it
A. Arcagni
Department MEMOTEF, Sapienza University of Rome, Rome, Italy
e-mail: alberto.arcagni@uniroma1.it
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. Bruggemann et al. (eds.), Measuring and Understanding Complex Phenomena,
https://doi.org/10.1007/978-3-030-59683-5_15
219