AMultilateral Sustainability Index: Theory, Measurement, and Dynamics

This paper develops a multilateral sustainability index designed to compare heterogeneous production units across multiple sustainability dimensions. The index is grounded in ratio-scale measurement theory, frontier benchmarking, and multilateral index-number methods. We distinguish carefully between production-theoretic distance functions and normalized sustainability measures, and show how the latter can be aggregated consistently using geometric means. We clarify that two natural constructions of the index—one based on input- and contextadjusted ratios, and one based on direct comparison at a common reference technology— answer different questions and coincide only when inputs and contexts are homogeneous across units. The resulting index is scale-invariant, transitive, and interpretable as a measure of relative sustainability performance. We extend the static framework to strong sustainability aggregators imposing minimum thresholds on critical dimensions and to dynamic settings tracking sustainability trajectories over time. Numerical examples illustrate the axiomatic properties and aggregation mechanics of the approach; a full empirical implementation with estimated frontiers is left to future work.