An info-gap model to examine the robustness of cost-efficient budget allocations

Benefit cost ratios (BCR) have been applied to conservation decisions for two reasons: cost-efficiency and transparency in decision making. Because BCRs are ratios of benefits to costs, the uncertainties associated with the two components (benefits and costs) are compounded. Therefore, BCRs can potentially involve more uncertainty than allocation strategies based solely on maximizing benefits. The robustness of decisions, defined here as the inverse of the number of misallocations due to uncertainties in benefits and costs of projects, is an unexplored component of applying BCRs to conservation decision making. To investigate the robustness to uncertainty of conservation investment with BCRs, we developed an information-gap model (info-gap) for using BCRs in selecting "portfolios" of conservation projects. Our model allows us to explore how uncertain we can be in our estimates of benefit and cost parameters while still selecting a portfolio that performs better than a critical threshold of misallocations perceived to be unacceptable. We first give a full theoretical description of our info-gap model formulation and then explore applications of the model to several hypothetical data sets.