Fair social orderings for the sharing of international rivers: A leximin based approach  

We consider the problem of sharing water among agents located along a river. A vector of entitlements specifies the amount of water each agent is entitled to. A social welfare function provides a complete ranking of the allocations based on the vector of r-equivalents. The r-equivalent of an agent at an allocation is the amount of money that, when consumed with the agent's entitlement, leaves the agent indifferent to its bundle assigned by the allocation. Using axioms of efficiency and fairness, a social welfare function called the r-leximin is characterized. The r-leximin ranks an allocation over another if the vector of r-equivalents of the former leximin dominates the vector of r- equivalents of the latter. We further show that maximizing the r-leximin over the set of acceptable allocations (defined in the sense of the core) leads to a class of solutions that meet the three key objectives of international river management: efficiency, fairness, and stability. We show that this class contains new solutions as well as the downstream incremental solution of Ambec and Sprumont (2002). Finally, we present an application of our approach to the case of the Blue Nile River Basin, shared among Ethiopia, Sudan and Egypt.