Ordered Weighted Average Life Expectancy

Abstract This study develops an aggregation framework for life expectancy based on the ordered weighted average (OWA) operator. The framework governs how already-estimated values (subgroup estimates, forecast quantiles, or institutional projections) are aggregated into a single representative value for policy planning, making the attitude toward uncertainty and the degree of compensability across population subgroups explicit and reportable. We introduce the OWA life expectancy (OWALE) operator and its induced, generalized, and quasi-arithmetic extensions, analyze the interaction between the generalization parameter and the weight vector, and determine weights by maximum entropy for a specified orness level. The framework is applied by education level across 19 European countries and to the quantiles of the United Nations probabilistic life expectancy projections, with sampling uncertainty propagated by bootstrap. The attitudinal parameter has a large effect: increasing the orness from 0.2 to 0.8 shifts education-aggregated LE by a median of 2.6 years (up to 6.8 years), about nine times the half-width of the bootstrap confidence intervals, and the gap between the population-weighted average and its pessimistic OWALE (the deprivation discount) reaches 5.5 years. When aggregating forecast quantiles, the orness effect increases with the forecast horizon, reflecting forecast uncertainty. OWALE provides a transparent, preference-sensitive aggregation framework on top of established demographic estimates and stochastic mortality forecasts, making visible the compensability choice that is implicit in any average.