Optimality versus stability in water resource allocation.

Water allocation is a growing concern in a developing world where limited resources like fresh water are in greater demand by more parties. Negotiations over allocations often involve multiple groups with disparate social, economic, and political status and needs, who are seeking a management solution for a wide range of demands. Optimization techniques for identifying the Pareto-optimal (social planner solution) to multi-criteria multi-participant problems are commonly implemented, although often reaching agreement for this solution is difficult. In negotiations with multiple-decision makers, parties who base decisions on individual rationality may find the social planner solution to be unfair, thus creating a need to evaluate the willingness to cooperate and practicality of a cooperative allocation solution, i.e., the solution's stability. This paper suggests seeking solutions for multi-participant resource allocation problems through an economics-based power index allocation method. This method can inform on allocation schemes that quantify a party's willingness to participate in a negotiation rather than opt for no agreement. Through comparison of the suggested method with a range of distance-based multi-criteria decision making rules, namely, least squares, MAXIMIN, MINIMAX, and compromise programming, this paper shows that optimality and stability can produce different allocation solutions. The mismatch between the socially-optimal alternative and the most stable alternative can potentially result in parties leaving the negotiation as they may be too dissatisfied with their resource share. This finding has important policy implications as it justifies why stakeholders may not accept the socially optimal solution in practice, and underlies the necessity of considering stability where it may be more appropriate to give up an unstable Pareto-optimal solution for an inferior stable one. Authors suggest assessing the stability of an allocation solution as an additional component to an analysis that seeks to distribute water in a negotiated process.