August 31, 2010 at 15:08Nonlinear Quality of Life Index
Alexander Gorban (Department of Mathematics, University of Leicester, Great Britain) and Andrei Zinoviev (Curie Institute, France) compiled a non-linear index of quality of life in 171 countries of the world.
They took four standard indicators from the Gapminder online database.for 2005 (GDP per capita at purchasing power parity, life expectancy for newborns, mortality per 1000 newborns, tuberculosis incidence per 100 thousand people) and analyzed the resulting structure. In this 4D space, there is a main curve that best passes through the “middle” of the data set. Accordingly, scientists projected the values from the tables onto this curve and received a relatively objective rating of countries, taking into account all four indicators.
Such ratings are usually compiled by the sum of indicators, taking into account the weight coefficient of each of them. The problem is that international organizations usually attract experts to determine the weight for each indicator - a certain subjective coefficient (as a result, according to Gorban and Zinoviev, the same Russia is lower than Kyrgyzstan and Turkmenistan in the rating of the quality of life of The Economist). A nonlinear index is most objective from a mathematical point of view. According to the scientists, the best linear index explains 75% of the variations in the data set, while their non-linear index explains 86%.
With regard to specific results, the maximum non-linear index of quality of life was shown by Luxembourg (0.892) and Norway (0.647). The United States was only in fifth place (0.575), Belarus - in 69th (0.105), Russia - in 79th (0.073).
They took four standard indicators from the Gapminder online database.for 2005 (GDP per capita at purchasing power parity, life expectancy for newborns, mortality per 1000 newborns, tuberculosis incidence per 100 thousand people) and analyzed the resulting structure. In this 4D space, there is a main curve that best passes through the “middle” of the data set. Accordingly, scientists projected the values from the tables onto this curve and received a relatively objective rating of countries, taking into account all four indicators.
Such ratings are usually compiled by the sum of indicators, taking into account the weight coefficient of each of them. The problem is that international organizations usually attract experts to determine the weight for each indicator - a certain subjective coefficient (as a result, according to Gorban and Zinoviev, the same Russia is lower than Kyrgyzstan and Turkmenistan in the rating of the quality of life of The Economist). A nonlinear index is most objective from a mathematical point of view. According to the scientists, the best linear index explains 75% of the variations in the data set, while their non-linear index explains 86%.
With regard to specific results, the maximum non-linear index of quality of life was shown by Luxembourg (0.892) and Norway (0.647). The United States was only in fifth place (0.575), Belarus - in 69th (0.105), Russia - in 79th (0.073).