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The HPI is based on general utilitarian principles — that most people want to live long and fulfilling lives, and the country which is doing the best is the one that allows its citizens to do so, whilst avoiding infringing on the opportunity of future people and people in other countries to do the same. In effect it operationalises the IUCN's (World Conservation Union) call for a metric capable of measuring 'the production of human well-being (not necessarily material goods) per unit of extraction of or imposition upon nature'. Human well-being is operationalised as Happy Life Years. Extraction of or imposition upon nature is proxied for using the ecological footprint per capita, which attempts to estimate the amount of natural resources required to sustain a given country's lifestyle. A country with a large per capita ecological footprint uses more than its fair share of resources, both by drawing resources from other countries, but also by causing permanent damage to the planet which will impact future generations.
As such, the HPI is not a measure of which are the happiest countries in the world. Countries with relatively high levels of life satisfaction, as measured in surveys, are found from the very top (Colombia in 6th place) to the very bottom (the USA in 114th place) of the rank order. The HPI is best conceived as a measure of the environmental efficiency of supporting well-being in a given country. Such efficiency could emerge in a country with a medium environmental impact (e.g. Costa Rica) and very high well-being, but it could also emerge in a country with only mediocre well-being, but very low environmental impact (e.g. Vietnam).
Each country’s HPI value is a function of its average subjective life satisfaction, life expectancy at birth, and ecological footprint per capita. The exact function is a little more complex, but conceptually it approximates multiplying life satisfaction and life expectancy, and dividing that by the ecological footprint. Most of the life satisfaction data is taken from the World Values Survey and World Database of Happiness, but some is drawn from other surveys, and some is estimated using statistical regression techniques.
The Satisfaction with Life Index was created by Adrian G. White, an Analytic Social Psychologist at the University of Leicester, using data from a metastudy. It is an attempt to show life satisfaction (subjective life satisfaction) in different nations.
In this calculation, subjective well being correlates most strongly with health (.7), wealth (.6), and access to basic education (.6).   
This is an example of directly measuring happiness -- asking people how happy they are -- as an alternative to traditional measures of policy success such as GDP or GNP. Some studies suggest that happiness can be measured effectively.