208
L. Carlsen
Both partial orders can be described by an adjacent matrix, say A_0 for PO_0
and A_j for PO_j.
Taken the Euclidian Distance (squared) quantifies the role of indicator qj in
PO_0. This is a sensitivity measure for the indicators of set Q, describing the
structural changes of the partial order leaving one indicator out. This is not
immediately a measure of the sensitivity of the indicators for a ranking, because
the ranking is per definition a linear order and here derived over many interim steps.
If a linear order is obtained by all orders in LE_0, the set of linear extensions
taken from PO_0, then any PO_j will also lead to a corresponding set LE_j. And
this set is the more differing from LE_0 the larger the sensitivity is. Therefore the
ranking due to averaged heights is as more affected by indicator r j as larger its
sensitivity is.
For detail information on the single tool the cited literature should be consulted
as a detailed description is outside the scope of the present paper.
2.4 Software
All partial order analyses were carried out using the PyHasse software (Bruggemann
et al. 2014). PyHasse is programmed using the interpreter language Python (version
2.6) (Ernesti and Kaiser 2008; Hetland 2005; Langtangen 2008; Weigend 2006;
Python 2015) Today, the software package contains more than 100 modules and is
available upon request from the developer, Dr. R.Bruggemann (brg_home@web.de).
2.5 Indicators
The seven indicators applied in the World Happiness Index (HI 2016, 2017, 2018)
has been stated above in the introduction.
As mentioned in the introduction, the Happy Planet Index (HPI), focussing
on sustainable wellbeing is based experienced wellbeing (EWB), life expectancy
(LEX), inequality of outcomes (IoO) and the ecological footprint (EFP), the latter
being expressed in global hectares per capital. One global hectare is the world’s
annual amount of biological production for human use and human waste assimilation, per hectare of biologically productive land and fisheries. An approximate
formula for calculating HPI is given by
H P I ≈
LEX ∗ EW B ∗ I oO
EF P
(2)
The eventual calculation of HPI uses a somewhat more elaborate formula
applying ‘some technical adjustments are made to ensure that no single component
L. Carlsen
Both partial orders can be described by an adjacent matrix, say A_0 for PO_0
and A_j for PO_j.
Taken the Euclidian Distance (squared) quantifies the role of indicator qj in
PO_0. This is a sensitivity measure for the indicators of set Q, describing the
structural changes of the partial order leaving one indicator out. This is not
immediately a measure of the sensitivity of the indicators for a ranking, because
the ranking is per definition a linear order and here derived over many interim steps.
If a linear order is obtained by all orders in LE_0, the set of linear extensions
taken from PO_0, then any PO_j will also lead to a corresponding set LE_j. And
this set is the more differing from LE_0 the larger the sensitivity is. Therefore the
ranking due to averaged heights is as more affected by indicator r j as larger its
sensitivity is.
For detail information on the single tool the cited literature should be consulted
as a detailed description is outside the scope of the present paper.
2.4 Software
All partial order analyses were carried out using the PyHasse software (Bruggemann
et al. 2014). PyHasse is programmed using the interpreter language Python (version
2.6) (Ernesti and Kaiser 2008; Hetland 2005; Langtangen 2008; Weigend 2006;
Python 2015) Today, the software package contains more than 100 modules and is
available upon request from the developer, Dr. R.Bruggemann (brg_home@web.de).
2.5 Indicators
The seven indicators applied in the World Happiness Index (HI 2016, 2017, 2018)
has been stated above in the introduction.
As mentioned in the introduction, the Happy Planet Index (HPI), focussing
on sustainable wellbeing is based experienced wellbeing (EWB), life expectancy
(LEX), inequality of outcomes (IoO) and the ecological footprint (EFP), the latter
being expressed in global hectares per capital. One global hectare is the world’s
annual amount of biological production for human use and human waste assimilation, per hectare of biologically productive land and fisheries. An approximate
formula for calculating HPI is given by
H P I ≈
LEX ∗ EW B ∗ I oO
EF P
(2)
The eventual calculation of HPI uses a somewhat more elaborate formula
applying ‘some technical adjustments are made to ensure that no single component