On the value of life

The national budget affects life and death via its allocations in areas such as traffic safety, flood control, public health and the like. When the cost-effectiveness of an intervention is evaluated, common effect measures are the number of lives extended (saved) and the expected life-years gained. The latter are usually adjusted for quality of life, giving QALYs, and discounted. In models that support decision making on the national aggregates, the subjects can be reduced to representative agents that are scored only on these dimensions. The lives extended measure is impartial to age and sex. The life-years measures however are biased in age and sex, since young people have a higher life expectancy than the old and women have a higher life expectancy than men, and policy advice might reflect that bias. It seems advisable to devise a measure that is more impartial and fair with respect to the age groups and the sexes. An alternative is to value a single life at 100%, and to measure the life-years gain with respect to that 100%. In addition, rather than fine-tune policy with interpersonal utility comparisons, one could choose a utility norm for the representative agent. A possible norm for time preference and diminishing marginal utility of life is the square root. The square root is easier to communicate than logarithmic utility or some rate of discount, but has comparable effect. A life of 100 years then has value 10, a life of 25 years has value 5, so that by age 25 half of life is passed. The considerations of both 100% range and square root utility lead to the following age & sex adjusted gain measure. When a person has age a, experiences an event (accident, disease) with a life expectancy of d years, but might have an intervention such that the life expectancy could become e, then the current effect measures are the single life saved and the absolute life-years gain x = e - d, but the proposed compromise gain measure is g[x | a, d] = Sqrt[x] / Sqrt[a + d + x]. The square root gives the utility of the representative agent, g gives the impact for interpersonal comparison, and aggregate utility is found by summing the gi over the individuals i. For example, saving (from acute death, d = 0) a baby (a = 0) has the same value, namely 1, whether it is a boy (life expectancy at birth, x = 75.94) or girl (x = 80.71) (data Statistics Netherlands 2002). As another example, let the unit share s = x / (a + e) be 25% for one person and 81% for another person so that the last person would weigh more than three times as much in this respect. For above gain measure, g = Sqrt[s] and the weight ratio becomes 50% / 90%, so that the last person now weighs less than half so that there is more equality. The paper compares various gain measures within the context of social welfare maximization. The update in 2020 has a more explicit discussion of Fair Innings (FI) and Proportional Shortfall (PS), and it is shown in a better manner that the UnitSqrt can be an acceptable compromise.