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M. Fattore and A. Arcagni
any statistical analysis must be as faithful and consistent as possible with the
phenomenon of interest and, in many situations, posets are the appropriate choice.
Although they have not attracted much statistical research yet, partial orders are
ubiquitous in socio-economics and make their appearance whenever multi-criteria
decision problems based on multi-indicator systems (MISes) are to be addressed (so,
for example, partial orders are also applied in environmental chemistry or ecology,
just to mention two further scientific research disciplines). To give the flavor of
possible applications of partial order theory to concrete problems in the socioeconomic field, we list a few cases that can be found in literature.
1. Refugees’ relocation in the EU (Carlsen 2017). The study builds a ranking
of European countries, for refugees’ relocation, based on a multidimensional
system of indicators reflecting territorial refugee absorption capacity.
2. Temporal analysis of the Fragile/Failed State Index (Carlsen and Bruggemann
2014, 2017). Here, poset theory is used to investigate the Fragile and the Failed
State Index, by considering explicitly the multidimensional configurations of
scores on the attributes/variables used in the assessment process, with the aim
to identify temporal trends and anomalous units.
3. European opinions on services (Annoni and Bruggemann 2009). This study
investigates Eurobarometer data, on social and political aspects of citizens’ daily
life, through purely “ordinal” computations, clustering European countries in
terms of satisfaction/dissatisfaction for the prices of different goods/services.p
4. Comparison of fiscal policies. These studies (Bachtrögler et al. 2016; Badinger
and Reuter 2015) analyze, from a multidimensional point of view, the properties
of the fiscal frameworks and the fiscal rules of 81 countries, building a ranking
of fiscal stringency.
5. Immigrants’ deprivation and vulnerability (Arcagni et al. 2019). Here, the
deprivation and the economic vulnerability of immigrants, in the Italian region
of Lombardy, are evaluated. The individual deprivation profiles of a sample of
units are multidimensionally compared to some reference profiles, getting overall
deprivation measures for the entire population of immigrants and for its main
subgroups.
6. Ranking Emergency Departments. In di Bella et al. (2018), partial order theory
is used to build a ranking of Emergency Departments in the Italian Liguria
region, assessed against a multi-dimensional system of attributes, addressing a
very relevant issue, given the increasing importance of emergency services in
regional healthcare systems.
7. Life satisfaction. In Caperna and Boccuzzo (2018), partial order theory is
applied to the study of life satisfaction in Italy, adapting posetic analytical tools
to a big data setting and revealing significant differences in satisfaction degrees
among regions, between genders and among levels of formal education.
M. Fattore and A. Arcagni
any statistical analysis must be as faithful and consistent as possible with the
phenomenon of interest and, in many situations, posets are the appropriate choice.
Although they have not attracted much statistical research yet, partial orders are
ubiquitous in socio-economics and make their appearance whenever multi-criteria
decision problems based on multi-indicator systems (MISes) are to be addressed (so,
for example, partial orders are also applied in environmental chemistry or ecology,
just to mention two further scientific research disciplines). To give the flavor of
possible applications of partial order theory to concrete problems in the socioeconomic field, we list a few cases that can be found in literature.
1. Refugees’ relocation in the EU (Carlsen 2017). The study builds a ranking
of European countries, for refugees’ relocation, based on a multidimensional
system of indicators reflecting territorial refugee absorption capacity.
2. Temporal analysis of the Fragile/Failed State Index (Carlsen and Bruggemann
2014, 2017). Here, poset theory is used to investigate the Fragile and the Failed
State Index, by considering explicitly the multidimensional configurations of
scores on the attributes/variables used in the assessment process, with the aim
to identify temporal trends and anomalous units.
3. European opinions on services (Annoni and Bruggemann 2009). This study
investigates Eurobarometer data, on social and political aspects of citizens’ daily
life, through purely “ordinal” computations, clustering European countries in
terms of satisfaction/dissatisfaction for the prices of different goods/services.p
4. Comparison of fiscal policies. These studies (Bachtrögler et al. 2016; Badinger
and Reuter 2015) analyze, from a multidimensional point of view, the properties
of the fiscal frameworks and the fiscal rules of 81 countries, building a ranking
of fiscal stringency.
5. Immigrants’ deprivation and vulnerability (Arcagni et al. 2019). Here, the
deprivation and the economic vulnerability of immigrants, in the Italian region
of Lombardy, are evaluated. The individual deprivation profiles of a sample of
units are multidimensionally compared to some reference profiles, getting overall
deprivation measures for the entire population of immigrants and for its main
subgroups.
6. Ranking Emergency Departments. In di Bella et al. (2018), partial order theory
is used to build a ranking of Emergency Departments in the Italian Liguria
region, assessed against a multi-dimensional system of attributes, addressing a
very relevant issue, given the increasing importance of emergency services in
regional healthcare systems.
7. Life satisfaction. In Caperna and Boccuzzo (2018), partial order theory is
applied to the study of life satisfaction in Italy, adapting posetic analytical tools
to a big data setting and revealing significant differences in satisfaction degrees
among regions, between genders and among levels of formal education.