When can we say than one society is better than another ? Nicolas Gravel (CSH -Delhi & IDEP-GREQAM (Marseille, France)

« 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

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 talk To present answers proposed by economists to answer these questions More specifically, to present methods used by economists to compare societies on the basis of their performance in achieving justice Methods discussed here are 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 a firm answer to the questions above.

Comparing societies: some examples Comparing 12 OECD countries (+ India) based on their distribution of disposable income and some public goods 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

AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia

AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia

AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia

AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia

AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia

AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia

AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia

AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia

AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia

AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia

AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia

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 UK, France, or Sweden ? 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 ?

Other attribute: average class size in public schools How do the countries compare in terms of the distribution of the class sizes at public school ? Class size: a good indicator of the school quality

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 between the different attributes

2 cakes of different sizes: US & Sweden US Sweden

Sharing the US cake

Sharing the Swedish cake

Our ethical principles will 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. Given sizes and distributions, less correlation between cakes is better

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 A just society is a society that maximises a 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 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 additional rupee than 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 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.

Contrasting Maxi-min and Utilitarianism

sum of income is larger in US than in UK and in UK than in France

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

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)

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 = (y 1,…,y n ) an income distribution 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 (Robin Hood) transfers, each transfer taking place between a donator that is richer than the recipient, and each transfer being insufficient to reverse the ranking of the donator and the recipient. When y has been obtained from z by both manas and Robin Hood transfers

Mana ?

Robin Hood and Mana ?

Answer no 2: Poverty dominance Important issue: poverty How do we define poverty ? Basic principle: You define a (poverty) line that partition 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 AustraliaAustriaCanadaFranceGermanyItalyPortugalSpainswedenSwitz.UKUSAIndia Line = There are 2 poor in France and 1 poor in germany but poverty gap in Germany is 3745 while it is only 3475 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.

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 SwitzerlandUS UK Australia Canada Austria FranceGermany Sweden Italy Spain Portugal India

Methodology can be extended 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 ? Literacy rate (%) Income (rupees/month) a red society

Aversion to correlation ? Literacy rate (%) Income (rupees/month) a red society and a white society

Aversion to correlation ? Literacy rate (%) Income (rupees/month) a red society and a white society white society is more just

Bidimensional dominance chart Switzerland US UK AustraliaCanada Austria France Germany Sweden Italy Spain Portugal India