1. Inequality and Social Justice
Master 2 course, AMSE –
Nicolas Gravel

2. « 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

3. 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

4. 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

5. 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

6. « 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

7. 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 ?

8. 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

9. 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.

10. 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

11. 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.

12. 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 households in each country ( )
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

14. 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 ?

15. 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 ?

20. 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

22. 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? )

23. 2 cakes of different sizes: US & Sweden

24. Sharing the US cake

25. Sharing the Swedish cake

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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 happiness-inequality
Extreme form of aversion toward happiness-inequality (John Rawls): Maxi-Min, we should focus only on the welfare of the less happy person in the society.

32. Contrasting Maxi-min and Utilitarianism

33. Contrasting Maxi-min and Utilitarianism

34. Contrasting Maxi-min and Utilitarianism
sum of income is larger in US
than in UK and in UK than in
France

35. Contrasting Maxi-min and Utilitarianism
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

36. 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

37. 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)

38. 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,…

39. 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

40. When can we say that one society is better than another
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 ?

41. 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 Pigou-Dalton (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

42. Mana ?

43. Mana ?

44. Robin Hood and Mana ?

45. Robin Hood and Mana ?

46. Robin Hood and Mana ?

47. Robin Hood and Mana ?

48. Robin Hood and Mana ?

49. Robin Hood and Mana ?

50. Robin Hood and Mana ?

51. Robin Hood and Mana ?

52. 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
Pour commencer, faites ressortir l'intérêt du sujet pour l'assistance. Donnez une brève vue d'ensemble de la présentation. Tenez compte de l'intérêt de l'assistance pour le sujet ainsi que de leurs connaissances en la matière pour choisir votre vocabulaire, des exemples et des illustrations. Insistez sur l'importance du sujet pour capter l'attention des auditeurs.

53. 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
Pour commencer, faites ressortir l'intérêt du sujet pour l'assistance. Donnez une brève vue d'ensemble de la présentation. Tenez compte de l'intérêt de l'assistance pour le sujet ainsi que de leurs connaissances en la matière pour choisir votre vocabulaire, des exemples et des illustrations. Insistez sur l'importance du sujet pour capter l'attention des auditeurs.

54. 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
9438
7549
8646
11982
19806
13337
18142
1309
17377
16588
16839
15092
14857
10933
8666
10113
13371
22044
15854
21581
1462
20456
18665
19494
16966
16614
12629
10028
11656
14723
24554
18579
25206
1649
24203
20921
22382
19169
18376
14769
11415
13639
16147
27696
21574
29387
1859
28467
24042
25955
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
There are 2 poor in France
and 1 poor in germany
but poverty gap in Germany
is 3745 while it is only
3465 in France
Pour commencer, faites ressortir l'intérêt du sujet pour l'assistance. Donnez une brève vue d'ensemble de la présentation. Tenez compte de l'intérêt de l'assistance pour le sujet ainsi que de leurs connaissances en la matière pour choisir votre vocabulaire, des exemples et des illustrations. Insistez sur l'importance du sujet pour capter l'attention des auditeurs.

55. 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)

56. 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.

58. 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.

59. 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
Si vous avez plusieurs points, étapes ou idées-clé à traiter, utilisez plusieurs diapositives. Déterminez si l'assistance est censée comprendre un nouveau concept, apprendre une procédure ou approfondir un concept déjà connu. Choisissez l'explication appropriée pour étayer chacun des points traités. Vous pouvez accompagner votre présentation de données techniques supplémentaires sous formes de copies papier, disquettes, messages électroniques ou sites Internet. Développez chaque point de façon à communiquer avec l'assistance.

60. Lorenz dominance chart
Switzerland US
Austria
Australia UK
France
Germany
Canada
Sweden
Italy
Spain
Portugal
India

61. 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

62. Aversion to correlation ?
a red society
Literacy rate (%) 70 60 50 40
400
500
600
700
Income (rupees/month)

63. Aversion to correlation ?
a red society
Literacy rate (%)
and a white society 70 60 50 40
400
500
600
700
Income (rupees/month)

64. 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)

65. Bidimensional dominance chart
Germany
Switzerland
France
Sweden US
Australia
Canada UK
Austria
Spain
Italy
Portugal
India