The social welfare function

Social welfare function

In economics, a social welfare function is a real-valued function that ranks conceivable social states from lowest to highest. Inputs of the function include any variables considered to affect the economic welfare of a society...

, proposed by Amartya Sen

Amartya Sen

Amartya Sen, CH is an Indian economist who was awarded the 1998 Nobel Prize in Economic Sciences for his contributions to welfare economics and social choice theory, and for his interest in the problems of society's poorest members...

 in 1973, is a measure of a society's overall welfare calculated as the product of GDP per capita and the difference between 1 and the society's gini coefficient

Gini coefficient

The Gini coefficient is a measure of statistical dispersion developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper "Variability and Mutability" ....

:
The table below shows Sen's social welfare function using data from the CIA and another version using data from the IMF and UN. The GDP per capita numbers are adjusted for purchasing power parity

Purchasing power parity

In economics, purchasing power parity is a condition between countries where an amount of money has the same purchasing power in different countries. The prices of the goods between the countries would only reflect the exchange rates...

.

Country	IMFgdpPC	CIAgdpPC	UN gini	CIA gini	SenIMF_UN	Sen_CIA
Zimbabwe	188	200	0.501	0.568	93.81	86.4
Burundi	372	300	0.424	0.424	214.27	172.8
Sierra Leone	693	600	0.629	0.629	257.1	222.6
Central African Republic	726	700	0.613	0.613	280.96	270.9
Niger	667	700	0.505	0.505	330.17	346.5
Mozambique	843	800	0.473	0.473	444.26	421.6
Rwanda	899	800	0.468	0.468	478.27	425.6
Madagascar	979	900	0.475	0.475	513.98	472.5
Malawi	793	800	0.390	0.390	483.73	488
Ethiopia	807	700	0.300	0.300	564.9	490
Lesotho	1286	1400	0.632	0.632	473.25	515.2
Nepal	1078	1000	0.472	0.472	569.18	528
Haiti	1292	1300	0.592	0.592	527.14	530.4
Uganda	1059	1000	0.457	0.457	575.04	543
Mali	1038	1100	0.401	0.401	621.76	658.9
Guinea	974	1100	0.386	0.381	598.04	680.9
Zambia	1323	1400	0.508	0.508	650.92	688.8
Burkina Faso	1206	1200	0.395	0.395	729.63	726
Ghana	1426	1400	0.408	0.408	844.19	828.8
Tanzania	1256	1300	0.346	0.346	821.42	850.2
Benin	1548	1400	0.365	0.365	982.98	889
Bangladesh	1311	1400	0.334	0.334	873.13	932.4
Côte d'Ivoire	1737	1700	0.446	0.446	962.3	941.8
Kenya	1673	1700	0.425	0.445	961.98	943.5
Senegal	1692	1700	0.413	0.413	993.2	997.9
Papua New Guinea	1974	2100	0.509	0.509	969.23	1031.1
Tajikistan	1843	1600	0.326	0.326	1242.18	1078.4
Mauritania	2011	1800	0.390	0.390	1226.71	1098
Cambodia	1818	1900	0.417	0.417	1059.89	1107.7
Nigeria	2028	2100	0.437	0.437	1141.76	1182.3
Cameroon	2094	2200	0.446	0.446	1160.08	1218.8
Laos	2054	2000	0.346	0.346	1343.32	1308
Kyrgyzstan	2000	2000	0.303	0.303	1394	1394
Uzbekistan	2390	2400	0.368	0.368	1510.48	1516.8
Namibia	5250	5200	0.743	0.707	1349.25	1523.6
Moldova	2897	2300	0.332	0.332	1935.2	1536.4
East Timor	2506	2500		0.380		1550
Nicaragua	2629	2800	0.431	0.431	1495.9	1593.2
Vietnam	2589	2600	0.344	0.370	1698.38	1638
India	2563	2600	0.368	0.368	1619.82	1643.2
Paraguay	4510	4000	0.584	0.584	1876.16	1664
Yemen	2343	2500	0.334	0.334	1560.44	1665
Pakistan	2594	2400	0.306	0.306	1800.24	1665.6
Philippines	3383	3200	0.445	0.445	1877.57	1776
Bolivia	4084	4400	0.601	0.592	1629.52	1795.2
Mongolia	3222	2900	0.328	0.328	2165.18	1948.8
Honduras	4085	4300	0.538	0.538	1887.27	1986.6
Sri Lanka	4265	4000	0.402	0.500	2550.47	2000
Guyana	3841	3700		0.432		2101.6
Morocco	4094	3700	0.395	0.400	2476.87	2220
Guatemala	4702	5100	0.551	0.551	2111.2	2289.9
Indonesia	3728	3600	0.343	0.363	2449.3	2293.2
Swaziland	5401	4700	0.504	0.504	2678.9	2331.2
Georgia (country)	4694	4400	0.404	0.404	2797.62	2622.4
El Salvador	5847	6000	0.524	0.524	2783.17	2856
Jordan	4906	4700	0.388	0.388	3002.47	2876.4
Turkmenistan	5172	5300	0.408	0.408	3061.82	3137.6
Dominican Republic	8116	6600	0.516	0.516	3928.14	3194.4
Egypt	5495	5000	0.344	0.344	3604.72	3280
Colombia	7968	7400	0.586	0.538	3298.75	3418.8
Armenia	4946	5800	0.338	0.410	3274.25	3422
Peru	7809	7600	0.520	0.520	3748.32	3648
Ecuador	7242	7200	0.536	0.460	3360.29	3888
Jamaica	7688	7400	0.455	0.455	4189.96	4033
South Africa	9767	9700	0.578	0.578	4121.67	4093.4
Brazil	9703	9500	0.570	0.567	4172.29	4113.5
Albania	6298	5800	0.311	0.267	4339.32	4251.4
Algeria	6539	6700	0.353	0.353	4230.73	4334.9
Tunisia	7535	7400	0.398	0.400	4536.07	4440
Bosnia and Herzegovina	7074	6100	0.262	0.262	5220.61	4501.8
Thailand	7907	8000	0.420	0.420	4586.06	4640
Panama	10351	10700	0.561	0.561	4544.09	4697.3
Ukraine	6968	7000	0.281	0.310	5009.99	4830
Azerbaijan	7618	8000	0.365	0.365	4837.43	5080
Botswana	16516	14300	0.605	0.630	6523.82	5291
Costa Rica	10358	11100	0.498	0.498	5199.72	5572.2
Uruguay	11674	10800	0.449	0.452	6432.37	5918.4
Chile	13921	14300	0.549	0.549	6278.37	6449.3
Venezuela	12176	12800	0.482	0.482	6307.17	6630.4
Iran	10570	11700	0.430	0.430	6024.9	6669
Argentina	13318	13100	0.513	0.490	6485.87	6681
Mexico	14120	12400	0.461	0.461	7610.68	6683.6
Turkey	12858	12000	0.436	0.436	7251.91	6768
Mauritius	11126	11300		0.370		7119
Kazakhstan	10837	11000	0.339	0.339	7163.26	7271
Serbia	10071	10400		0.300		7280
Belarus	10949	10600	0.297	0.297	7697.15	7451.8
Kingdom of Romania	11401	11100	0.310	0.310	7866.69	7659
Malaysia	13385	14500	0.492	0.461	6799.58	7815.5
Kingdom of Bulgaria	11311	11800	0.292	0.316	8008.19	8071.2
Russia	14705	14800	0.399	0.410	8837.71	8732
Poland	16316	16200	0.345	0.360	10686.98	10368
Lithuania	17733	16800	0.360	0.360	11349.12	10752
Independent State of Croatia	15532	15500	0.290	0.290	11027.72	11005
Latvia	17488	17700	0.377	0.377	10895.02	11027.1
Portugal	21779	21800	0.385	0.380	13394.09	13516
Hungary	19020	19300	0.269	0.280	13903.62	13896
Estonia	20584	21800	0.358	0.340	13214.93	14388
Slovakia	20268	20200	0.258	0.260	15038.86	14948
Israel	27147	26600	0.392	0.386	16505.38	16332.4
Malta	23026	23400		0.280		16848
New Zealand	26611	27200	0.362	0.362	16977.82	17353.6
Czech Republic	24229	24500	0.254	0.260	18074.83	18130
Cyprus	27171	27100		0.290		19241
Hong Kong	42124	42000	0.434	0.523	23842.18	20034
Greece	29146	30600	0.343	0.330	19148.92	20502
Italy	30365	30900	0.360	0.330	19433.6	20703
Japan	33596	33500	0.249	0.381	25230.6	20736.5
Slovenia	27227	28000	0.284	0.240	19494.53	21280
Spain	30118	33600	0.347	0.320	19667.05	22848
United Kingdom	35634	35000	0.360	0.340	22805.76	23100
Early Modern France	33509	32600	0.327	0.280	22551.56	23472
Australia	36226	37300	0.352	0.352	23474.45	24170.4
Germany	34212	34100	0.283	0.280	24530	24552
United States	45725	45800	0.408	0.450	27069.2	25190
Belgium	35388	36200	0.330	0.280	23709.96	26064
Canada	38614	38600	0.326	0.321	26025.84	26209.4
Switzerland	41265	40100	0.337	0.337	27358.7	26586.3
Finland	35349	36000	0.269	0.260	25840.12	26640
Netherlands	38995	39000	0.309	0.309	26945.55	26949
Denmark	37265	37200	0.247	0.240	28060.55	28272
Singapore	49754	49900	0.425	0.425	28608.55	28692.5
Sweden	36578	37500	0.250	0.230	27433.5	28875
Austria	38181	39300	0.291	0.260	27070.33	29082
Iceland	39168	40400		0.250		30300
Republic of Ireland	43414	46600	0.343	0.320	28523	31688
Norway	53152	53300	0.258	0.280	39438.78	38376
Luxembourg	79660	79400		0.260		58756
Guinea-Bissau	484	600	0.470		256.52
Trinidad and Tobago	18385	25400	0.389		11233.24