Battling Arrow’s Paradox to Discover Robust Water Management Alternatives

Abstract

This study demonstrates how Arrow’s Impossibility Theorem, a theory of social choice, is of direct concern when formulating water-resources systems planning problems. Traditional strategies for solving multiobjective water resources problems typically aggregate multiple performance measures into single composite objectives (e.g., a priori preference weighting or grouping-like measures by category). Arrow’s Impossibility Theorem, commonly referred to as Arrow’s Paradox, implies that a subset of performance concerns will inadvertently dictate the properties of the optimized design alternative in unpredictable ways when using aggregated objectives. This study shows how many-objective planning can aid in battling Arrow’s Paradox. Many-objective planning explicitly disaggregates measures of performance while supporting the discovery of planning tradeoffs, using tools such as multiobjective evolutionary algorithms (MOEAs). An urban water portfolio planning case study for the Lower Rio Grande Valley, Texas is used to demonstrate how aggregate, lower objective-count formulations can adversely bias risk-based decision support. Additionally, this study employs a comprehensive diagnostic assessment of the Borg MOEA’s ability to address Arrow’s Paradox by enabling users to explore problem formulations with increasing numbers of objectives and decisions. Counter to conventional assumptions, the diagnostic analysis carefully documents that for modern self-adaptive MOEA searches, increasing objective counts can lead to more effective, efficient, reliable, and controllable searches. The increased objective counts are also shown to directly reduce decision biases that can emerge from problem formulation aggregation and simplification, related to Arrow’s Paradox.