Balancing equity and efficiency in transboundary water systems with Atkinson’s welfare function

Abstract

Water resources optimization conventionally maximizes system-wide efficiency, treating distributional equity as secondary. Here we present a framework that directly incorporates equity into optimization using Atkinson’s inequality measure. This approach makes distributional value judgements transparent through a single, interpretable inequality aversion parameter that spans principles from utilitarian efficiency to Rawlsian justice, enabling stakeholders to negotiate between efficiency and fairness. Applied to hydropower operations and floating photovoltaic expansion in the Zambezi Watercourse, we demonstrate that substantial equity improvements (3–25 percentage point reduction in the Atkinson index) can be achieved with minimal efficiency sacrifices (1.0–4.2% of total hydropower generation). These gains arise through increases in reliable (‘firm’) power generation, enhancing drought resilience for the most vulnerable riparian states. The framework adapts to changing objectives, prioritizing investments towards disadvantaged actors without requiring predetermined weights or hierarchies. The methodology generalizes to any multi-actor resource allocation problem in which monotonically increasing, concave objectives create scope for welfare-improving redistribution. Despite increasing emphasis on distributional equity in transboundary water negotiations, most water resource models include it only indirectly through embedded assumptions or constraints, if at all. This work uses the Atkinson welfare function to transparently incorporate equity into optimization, enabling systematic evaluation of how changes in fairness priorities affect efficiency.