Dominance rankings illustrations Some illustrations Australia Austria Canada

Australia Austria Canada France Germany Italy Portugal Spain sweden Switz. UK USA India 4733

Another attribute: regional infant mortality n n Infant mortality (number of children who die

Other attribute: average class size in publicschools n n How do countries compare in

General principlesthat can be derived from these comparisons n n n Countries differ by

2 cakes of different sizes: US & Sweden US

Mean income rankings vs efficiency principles

Mean income rankings vs efficiency principles Mean income is larger in US than in

Mean Income ranking vs efficiency principles Mean income is larger in US than in

Mean income country ranking country Mean income US 28 265 Switzerland 26 693 Australia

Generalized Lorenz dominance chart Switzerland US Austria UK France Germany Australia Canada Sweden Italy

Efficiency-equalitydominance chart US Sweden Austria India Germany France Switz. Italy Spain Portugal Canada Australia

Important challenge: toextend to many attributes n n Same welfarist ethics Suitable generalization of

Aversion to correlation ? a red society Literacy rate (%) 70 60 50 40

Aversion to correlation ? a red society Literacy rate (%) and a white society

Bidimensionaldominance chart Germany Switzerland Australia Canada UK Sweden US Austria Portugal India France Spain

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Dominance rankings: illustrations Some illustrations

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 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

Another attribute: regional infant mortality n n 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 publicschools n n 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

General principlesthat can be derived from these comparisons n n n 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 US

Sharing the US cake

Sharing the Swedish cake

Mean income rankings vs efficiency principles

Mean Income rankings vs efficiency principles

Mean income rankings vs efficiency principles Mean income is larger in US than in UK and in UK than in France

Mean Income ranking vs efficiency principles Mean income is larger in US than in UK and in UK than in France but US and UK do not dominate France for the Suppes principle

Suppes efficiency

Robin Hood and Mana ?

Generalized Lorenz

Relative Lorenz curves

Mean income country ranking country Mean income US 28 265 Switzerland 26 693 Australia 21 998 Canada 19 962 UK 19 812 Austria 19 194 France 18 158 Germany 17 661 Sweden 15 168 Italy 13 522 Spain 13 221 Portugal 11 501 India 1 885

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

Efficiency-equalitydominance chart US Sweden Austria India Germany France Switz. Italy Spain Portugal Canada Australia

Important challenge: toextend to many attributes n n 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 is more just 70 60 50 40 400 500 600 700 Income (rupees/month)

Bidimensionaldominance chart Germany Switzerland Australia Canada UK Sweden US Austria Portugal India France Spain Italy