206
L. Carlsen
partial ordering techniques, disclosing, among other features that on an average
basis the following 10 countries were found as the happiest countries: Iceland, Australia, Switzerland, Norway, New Zealand, Denmark, the Netherlands, Finland and
Austria, whereas the bottom of the list displays Madagascar, Congo (Brazzaville),
Egypt, Benin, Chad, Gabon, Burundi, Angola, Armenia and Yemen as the least
happy countries, results that is somewhat different from the original study where
the index is generated by a simple arithmetic aggregation of the 7 indicator values
(HI 2016, 2017, 2018).
In today’s world nothing is free, so the obvious question that arises is now: who
is paying for our happiness? To some extent a study of the Happy Planet Index,
which is focused on sustainable wellbeing for all and is based on 4 indicators, i.e.,
experienced wellbeing (EWB), life expectancy (LEX), inequality of outcomes (IoO)
and the ecological footprint (EFP) (Jeffrey et al. 2016) may give some answers.
The present study focus on answering the above question by partial order
analyses of the World Happiness Index and the Happy Planet index in parallel.
2 Methodology
The present paper describes how selected partial order tools may be applied in
the evaluation of a series of countries taking several indicators simultaneously into
account as an alternative to conventional methods to study MIS (Bruggemann and
Carlsen 2012).
2.1 The Basic Equation of Partial Ordering
In its basis partial ordering appears pretty simple as the only mathematical relation
among the objects is “≤” (Bruggemann and Carlsen 2006a, b Bruggemann and
Patil 2011). The basis for a comparison of objects, here countries, characterized
by the subset of indicators describing their performance in relation a) to happiness
as well as b) to the planetary ‘happiness’ (vide infra). This series of indicators, r j ,
characterizes the single countries. Thus, characterizing one country (x) by a set of
indicators r j (x), j = 1,...,m, where m is the number of indicators, can be compared
to another country (y), characterized by the indicators r j (y), when
r j (y) ≤ r j (x) for all j = 1, . . . , m
( 1 )
Equation 1 is a very hard and strict requirement for establishing a comparison.
It demands that all indicators of x should be better (or at least equal) than those
of y. Further, let X be the subset of countries included in the analyses, x will be
ordered higher (better) than y, i.e., x > y, if at least one of the indicator values for
L. Carlsen
partial ordering techniques, disclosing, among other features that on an average
basis the following 10 countries were found as the happiest countries: Iceland, Australia, Switzerland, Norway, New Zealand, Denmark, the Netherlands, Finland and
Austria, whereas the bottom of the list displays Madagascar, Congo (Brazzaville),
Egypt, Benin, Chad, Gabon, Burundi, Angola, Armenia and Yemen as the least
happy countries, results that is somewhat different from the original study where
the index is generated by a simple arithmetic aggregation of the 7 indicator values
(HI 2016, 2017, 2018).
In today’s world nothing is free, so the obvious question that arises is now: who
is paying for our happiness? To some extent a study of the Happy Planet Index,
which is focused on sustainable wellbeing for all and is based on 4 indicators, i.e.,
experienced wellbeing (EWB), life expectancy (LEX), inequality of outcomes (IoO)
and the ecological footprint (EFP) (Jeffrey et al. 2016) may give some answers.
The present study focus on answering the above question by partial order
analyses of the World Happiness Index and the Happy Planet index in parallel.
2 Methodology
The present paper describes how selected partial order tools may be applied in
the evaluation of a series of countries taking several indicators simultaneously into
account as an alternative to conventional methods to study MIS (Bruggemann and
Carlsen 2012).
2.1 The Basic Equation of Partial Ordering
In its basis partial ordering appears pretty simple as the only mathematical relation
among the objects is “≤” (Bruggemann and Carlsen 2006a, b Bruggemann and
Patil 2011). The basis for a comparison of objects, here countries, characterized
by the subset of indicators describing their performance in relation a) to happiness
as well as b) to the planetary ‘happiness’ (vide infra). This series of indicators, r j ,
characterizes the single countries. Thus, characterizing one country (x) by a set of
indicators r j (x), j = 1,...,m, where m is the number of indicators, can be compared
to another country (y), characterized by the indicators r j (y), when
r j (y) ≤ r j (x) for all j = 1, . . . , m
( 1 )
Equation 1 is a very hard and strict requirement for establishing a comparison.
It demands that all indicators of x should be better (or at least equal) than those
of y. Further, let X be the subset of countries included in the analyses, x will be
ordered higher (better) than y, i.e., x > y, if at least one of the indicator values for