Inequality and Social
Justice
Master 2 course, AMSE – 2015-2016
Nicolas Gravel
« The importance of the formal
results lies ultimately in their
relevance to normal
communication, and to things
that people argue about and fight
for »
Amartya K. Sen
What are the things that people
argue about and fight for ?



People argue about and fight for
the defense of their private interest
(much too often perhaps)
People argue about and fight for
the construction of a « better »
world
A better world = a world with less
suffering, less exploitation,
more…justice
What are the things that people
argue about and fight for ?



People argue about and fight for
the defense of their private interest
(much too often perhaps)
People argue about and fight for
the construction of a « better »
world
A better world = a world with less
suffering, less exploitation,
more…justice
What are the things that people
argue about and fight for ?



People argue about and fight for
the defense of their private interest
(much too often perhaps)
People argue about and fight for
the construction of a « better »
world
A better world = a world with less
suffering, less exploitation,
more…justice
« Justice is the first virtue of
social institutions, as truth is of
systems of thought. A theory
however elegant and economical
must be rejected or revised if it is
untrue; likewise laws and
institutions no matter how
efficient and well-arranged must
be reformed or abolished if they
are unjust. »
John Rawls
But what is justice ?


When can we say that a particular
social arrangement is « just » and
another « unjust » ?
When can we say that a social
institution is more just than another ?
Purpose of the course



To present answers proposed by
economists to these questions
More specifically, to present methods
used by economists to compare
societies on the basis of their
performance in achieving justice
Many methods discussed here are
ethically robust
Comparing societies ?




Comparing two different societies at a
given moment (is France more just than
the US ?)
Comparing a given society at different
points of time (is India better now than
fifteen years ago ?)
Comparing a society after a tax reform
with the same society without the tax
reform
etc.
Comparing societies ?




Society = A list of individuals
Approaches focus on specific attributes
of these individuals
Attributes: Income, health, education,
access to public good, etc.
Comparing societies amount to
comparing distributions of these
attributes across individuals
Robust methods of
normative appraisal ?




Method: we want it to be routinely and
« easily » implementable
Based on explicit ethical principles
Robustness: ethical principles that
justify the methods are widely
acceptable
Price to pay for robustness:
Incompleteness. The methods may fail
to provide answers to the questions
above. Ethical principles may conflict.
Comparing societies: some
examples





Comparing 12 OECD countries (+ India) based on
their distribution of disposable income and some
public goods (based on Gravel, Moyes and
Tarroux (2008)
Sample of some 20 000 households in each
country (1998-2002)
Disposable income: income available after all
taxes and social security contributions have been
paid and all transfers payment have been received
Incomes are made comparable across households
by equivalence scale adjustment
Incomes are made comparable across countries
by adjusting for purchasing power differences
80000
70000
60000
Australia
50000
France
Germany
disposable income 40000
Italy
Spain
30000
sweden
UK
USA
20000
India
10000
0
1
2
3
4
5
6
individual rank
7
8
9
10
What are these data saying on
justice ?



Except for the 10% poorest, americans in every income
group have larger income than French, swedish and
German. Does that mean that US is a « better » society
than France, Sweden or Germany?
Americans in every income group have larger income
than British, Australians, Italians, spanish and Indians.
Does that mean that US is a better society than UK,
Australia, Italy, Spain or India ?
It would seem so if income was the only relevant
attribute. But is that so ?
Another attribute: regional
infant mortality


Infant mortality (number of children who die
before the age of one per thousand births) is a
good indicator of the overall working of the
medical system of the region where individuals
live
How do countries compare in terms of the
different infant mortality rate that they offer to
their citizens on the basis of their place of
residence ?
70.00
65.00
60.00
55.00
50.00
45.00
40.00
Number of deads per
35.00
1000
30.00
25.00
20.00
15.00
10.00
5.00
0.00
Australia
France
Germany
Italy
Spain
Sweden
UK
US
India
1
2
3
infant mortality groups
4
5
Other attribute: average class
size in public schools


How do countries compare in
terms of the distribution of the
class sizes at public school ?
Class size: a good indicator of the
school quality
20.00
18.00
16.00
14.00
Australia
France
Germany
Italy
Spain
Sweden
UK
US
12.00
Class sizes (number of
10.00
children/class)
8.00
6.00
4.00
2.00
0.00
1
2
3
Groups of Class size
4
5
General principles that can be
derived from these comparisons



Countries differ by the total amount of each
attribute they allocate to their citizens
:« size of the cake »
They also differ by the way they share this
cake
Less obviously, they also differ by the way
they correlate the attribute between
people (are individuals who are « rich » in
income also those who are « rich » in
health, or education? )
2 cakes of different sizes: US & Sweden
Sweden
US
Sharing the US cake
2%
4%
5%
29%
6%
8%
9%
15%
10%
12%
Sharing the Swedish cake
4%
19%
6%
7%
8%
14%
9%
10%
12%
11%
Ethical principles examined in
this course consider that:



For a given distribution, a larger cake is
better than a smaller one
Given the size, a « more equal »
distribution of the cake is better than a less
equal one (requires a definition of what is
meant by « more equal »)
Given sizes and distributions of several
« cakes », less correlation between cakes
is better
Modern theory of economic justice



A difficult birth: An impossibility theorem
(Arrow 1951)
It is impossible to define a consistent and
informationally parcimonious ranking of
societies that is respectful of individual
preferences
Escape out of this theorem have taken
two routes: welfarist and non-welfarist
What is justice ? A welfarist
answer (1)




Welfarism: The only thing that matters for
evaluating a society is the distribution of
welfare – happiness - between individuals
Individual preferences are important insofar
as they are connected to individual welfare
A just society is a society that maximises
an increasing function of individual
happiness
Philosophical foundations: Hume,
Bentham, Beccaria
What is justice ? A welfarist
answer (2)




Fundamental assumption: individual happiness
can be measured and compared (necessary to
escape from Arrow’s theorem)
We don’t need to know how to measure
happiness but we have to accept the idea that
we can measure it in a meaningful way.
Individual welfare is assumed to depend upon
the individual attributes
The relationship between welfare and attributes
is assumed to satisfy basic properties
Specifically, we assume:



Happiness is increasing with respect to each
attribute (more income makes people happier,
so does more health, smaller class sizes, etc.)
The extra pleasure brought about by an extra
unit of an attribute decreases with the level of
the attribute (a rich individual gets less extra
pleasure from an extra euro than does an
otherwise identical poorer individual)
The rate of increase in happiness with respect
to a particular attribute is decreasing with
respect to every other attribute
Which function of individual
happiness should we maximize ?



Classical Utilitarianism (Bentham): the sum
Modern view point: a function that exhibits
some aversion with respect to happinessinequality
Extreme form of aversion toward happinessinequality (John Rawls): Maxi-Min, we should
focus only on the welfare of the less happy
person in the society.
Contrasting Maxi-min and Utilitarianism
80000
70000
60000
50000
disposable income 40000
France
UK
30000
USA
20000
10000
0
1
2
3
4
5
6
individual rank
7
8
9
10
Contrasting Maxi-min and Utilitarianism
80000
70000
60000
50000
disposable income 40000
France
UK
30000
USA
20000
10000
0
1
2
3
4
5
6
individual rank
7
8
9
10
Contrasting Maxi-min and Utilitarianism
80000
sum of income is larger in US
than in UK and in UK than in
France
70000
60000
50000
disposable income 40000
France
UK
30000
USA
20000
10000
0
1
2
3
4
5
6
individual rank
7
8
9
10
Contrasting Maxi-min and Utilitarianism
80000
sum of income is larger in US
than in UK and in UK than in
France but the poorest individual
is richer in France than in the US
or in the UK
70000
60000
50000
disposable income 40000
France
UK
30000
USA
20000
10000
0
1
2
3
4
5
6
individual rank
7
8
9
10
To sum up, for welfarism:



1: A society = a list of combinations of
observable attributes (one such combination
for every individual)
2: Each combination of attributes is
transformed into (unobservable) happiness
3: Societies are compared on the basis of their
distributions of happiness
Society A is better than society B if
the distribution of happiness in A is
considered better than that in B by
any function that exhibits aversion
to happiness-inequality, under the
assumption that the relationship
between unobservable individual
happiness and obervable individual
attributes satisfies the above
properties (Welfarist dominance)
non-welfarist principles



Some philosophers and economists object to
welfarism
They claim that individual happiness is not the
only thing that matters, that individual happiness
can not be meaningfully measured, and/or that it
is not society’s business to be concerned with
individual’s happiness
Other individual attributes are considered
intrinsically important: freedom, ressources,
preferences,…
Object of the course





Propose operational methods for comparing societies
that are tightly connected to ethical principles (welfarist
or not)
Because of the difficulty of accepting a specific ethical
theory, look for methods that are agreed upon by a
wide spectrum of ethical theories (robustness)
To the extent possible, try to connect the rankings of
societies to elementary operations having a clear
meaning
Theory of this is well-established when attention is
restricted to distributions of one attribute (income)
A lot of research is needed to develop robust methods
for the multi-attributes case
When can we say that one society is better
than another ? (the one attribute case)




n individuals identical in every respect
other than the considered attribute
(income)
y = (y1,…,yn) an income distribution
y(.) = (y(1),…,y(n)) the ordered permutation of
y (considered equivalent to y if the ethics
used is « anonymous »)
Q: When are we « sure » that y is « more
just » than z ?
Anwer no 1: Mana and Robin Hood



When y(.) has been obtained from z(.)
by giving mana to some, or all, the
individuals
When y(.) has been obtained from z(.)
by a finite sequence of bilateral PigouDalton (Robin Hood) transfers between
a donator that is richer than the
recipient.
When y(.) has been obtained from z(.) by
both manas and Robin Hood transfers
Mana ?
80000
70000
60000
50000
40000
UK
USA
30000
20000
10000
0
1
2
3
4
5
6
7
8
9
10
Mana ?
80000
70000
60000
50000
US
40000
UK
30000
20000
10000
0
1
2
3
4
5
6
7
8
9
10
Robin Hood and Mana ?
60000
50000
40000
30000
Australi
Canada
20000
10000
Robin Hood and Mana ?
12000
10000
8000
Australia
6000
Canada
4000
2000
0
1
2
3
Robin Hood and Mana ?
12000
10000
8000
Australia
6000
Canada
4000
2000
0
1
2
3
Robin Hood and Mana ?
12000
10000
8000
Australia
6000
Canada
4000
2000
0
1
2
3
Robin Hood and Mana ?
12000
10000
8000
Australia
6000
Canada
4000
2000
0
1
2
3
Robin Hood and Mana ?
60000
50000
40000
Australia
30000
Canada
20000
10000
0
1
2
3
4
5
6
7
8
9
10
Robin Hood and Mana ?
60000
50000
40000
Australia
30000
Canada
20000
10000
0
1
2
3
4
5
6
7
8
9
10
Robin Hood and Mana ?
60000
50000
40000
Australia
30000
Canada
20000
10000
0
1
2
3
4
5
6
7
8
9
10
Answer no 2: Poverty dominance



Important issue: poverty
How do we define poverty ?
Basic principle: You define a (poverty)
line that partitions the population into 2
groups: poor and rich
2 measures of poverty


1) Headcount: Count the number (or the
fraction) of people below the line
2) poverty gap: Calculate the minimal
amount of money needed to eliminate
poverty as defined by the line
Contrasting headcount and
poverty gap
Australia
Austria
Canada
France
Germany
Italy
Portugal
Spain
sweden
Switz.
UK
USA
India
4733
6815
4285
6170
5855
3554
2546
2747
5808
8679
4898
5403
789
9237
10730
8977
9555
10012
6575
4602
5407
9056
14615
8598
11025
1019
11795
12850
11935
11793
12024
8059
6110
7045
10540
17334
10883
14687
1168
14580
14725
14338
13441
13229
13337
18142
1309
17377
16588
16839
15092
15854
21581
1462
20456
18665
19494
16966
18579
25206
1649
24203
20921
22382
19169
21574
29387
1859
28467
24042
25955
22382
21221
17342
13930
16535
18140
32095
25188
34819
2167
34592
28069
30958
26834
25201
20743
18113
20968
21091
38254
30190
43373
2694
54537
38539
44457
40175
39217
31174
32047
35457
30818
61849
49022
79030
4735
Line = 9 600
There9438are 27549poor 8646
in France
11982
19806
and 1 poor in germany
14857
10933
8666
10113
13371
22044
but poverty gap in Germany
16614
12629
10028
is 3745
while
it is11656only14723 24554
18376
11415
13639
16147
27696
346514769
in France
Poverty dominance


Problem with poverty measurement: how
do we draw the line ?
Criterion: society A is better than society
B if, no matter how the line is drawn,
poverty is lower in A than in B for the
poverty gap (poverty gap dominance)
Answer no 3: Lorenz dominance



Lorenz dominance criterion: Society A
is better than society B if the total
income held by individuals below a
certain rank is higher in A than in B no
matter what the rank is.
Easy to see with Lorenz curves.
Let us draw Lorenz curves with our data.
250000
200000
cumulated total income
Australia
France
150000
Germany
Italy
Spain
Sweden
100000
UK
US
India
50000
0
1
2
3
4
5
6
individual rank
7
8
9
10
Cool! the 3 answers are all equivalent
to the welfarist dominance answer





It is equivalent to say :
society A is more just than society B for
any welfarist ethics
One can go from B to A by a finite
sequence of Robin Hood transfers and/or
mana
Poverty gap in A is lower than in B for all
poverty lines
Lorenz curve in A is everywhere above
that in B.
This result is a beautiful one



Comes from mathematics: Hardy, Littlewood &
Polya (1936), Berge (1959),
Adapted to economics by Kolm (1966;1969),
Dasgupta, Sen and Starett (1973) and Sen (1973)
It provides a solid justification for the use of Lorenz
curves
Lorenz dominance chart
Switzerland
US
Austria
UK
France
Germany
Australia
Canada
Sweden
Italy
Spain
Portugal
India
Important challenge: to extend
to many attributes




Same welfarist ethics
Suitable generalization of poverty notions
(poverty in several dimensions)
No Lorenz curves
New issue: Correlation between
attributes
Aversion to correlation ?
a red society
Literacy rate (%)
70
60
50
40
400 500 600 700
Income (rupees/month)
Aversion to correlation ?
a red society
Literacy rate (%)
and a white society
70
60
50
40
400 500 600 700
Income (rupees/month)
Aversion to correlation ?
a red society
Literacy rate (%)
and a white society
white society is more
just
70
60
50
40
400 500 600 700
Income (rupees/month)
Bidimensional dominance chart
Germany
Switzerland
Australia
Canada
UK
France
Sweden
US
Austria
Spain
Portugal
India
Italy