The mathematical expression for the Life-Quality Index is: LQI = , showing the LQI as a function of
L, the life expectancy at birth and G, the Gross Domestic Product (GDP) per person. The parameter
q is a constant either defined as , where
w is the fraction of time allocated for economic activities based on time-budget studies available for many countries (approximately equal to for developed nations easily available for all countries and can be updated when necessary.
Societal Capacity to Commit Resources (SCCR) The LQI has been used to determine an acceptable level of expenditure that can be justifiably incurred on behalf of the public interest in exchange for a small reduction in the risk of death that results in improved life-quality for all. This limit of benefit can be considered as the
societal capacity to commit resources to
sustainable risk reduction. Suppose a portion of GDP, dG, is invested in implementing a program that affects public risk, thus modifying the life expectancy by a small amount dL. There is a net benefit if there is a net increase in LQI, dL. This criterion can be derived from the definition of L as: dL/L + qdG/G > 0, from which the limit of benefit, the Societal Capacity to Commit Resources (SCCR) to sustainable risk reduction, follows as: SCCR = G/(qL). In conjunction with an actuarial
life table the SCCR serves to evaluate life-saving interventions in place of the discredited “value of a statistical life.” Using data from the
United Nations Development Programme (UNDP) for years 2000-20 for calibration and growths of L and G[6], Table 1 shows the 2023 values of LQI, dimensionless normalized to equal 1.00 for the World in year 2000, and the LQI rank for the 40 most highly developed countries. Table 2 gives 2023 values for country groupings defined by the UNDP for the HDI. Table1. Life Quality Index 2023 rankings and values (World LQI2000 = 1.000) Table 2. 2023 Data[6], Life Quality Index, and Societal Capacity to Commit Resources to Risk Reduction for regions and other country groupings == Application ==