Alexander Gorban (Department of Mathematics, University of Leicester, UK) and Andrei Zinoviev (Institute of Curie, France) compiled a nonlinear quality of life index in 171 countries around 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 morbidity per 100 thousand population) 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, the scientists projected the values from the tables onto this curve and obtained a relatively objective rating of countries, taking into account all four indicators. Such ratings are usually compiled by the sum of the indicators, taking into account the weighting factor 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, as Gorban and Zinoviev write, Russia is lower than Kyrgyzstan and Turkmenistan in the ranking of The Economist’s quality of life). The nonlinear index is the most objective from a mathematical point of view.
According to scientists, the best linear index explains 75% of the variations in the data set, while their non-linear index explains 86%.
As for the specific results, Luxembourg (0.892) and Norway (0.647) showed the maximum non-linear quality of life index. The US was only in fifth place (0.575), Belarus - on the 69th (0.105), Russia - on the 79th (0.073).