The Limits to Equity in Water Allocation Under Scarcity

Equitable water allocation in real-world irrigation systems is hampered by supply fluctuations, posing a significant challenge to the goal of promoting fairness among consumers. In this paper, we concern ourselves with the limits of equity achievable for any water allocation scheme across the entire spectrum of water supply conditions. In the process, we develop a typology of canonical water allocation mechanisms that categorizes mechanisms w.r.t. the distribution of fulfilled demand across the users. Adopting specific notions of supply reliability and distribution equity, we derive the theoretical performance limits for all canonical mechanisms and extend the analysis to arbitrary allocation mechanisms. We show that for any value of supply reliability, the best possible equity is realized by mechanisms that uniformly distribute water among users, whereas the worst possible equity is associated with mechanisms that prioritize the demand of some users before allocating water to others. We also show that any intermediate equity level can be realized by adjusting the initial entitlements prior to allocating water to fulfill demands, in an approach we categorize as hybrid allocation. We parameterize the performance boundaries for such allocation schemes based on the fraction of supply allocated to initial entitlements. We discuss how this parameter can serve as a policy tool to balance the goals of equitable water access with other system-level objectives. In the end, we complement the analytical results with numerical simulations of a selected agricultural district from a real-world irrigation system and speculate about the application of our study to large-scale hierarchical systems.