Incorporating probabilistic policy adoption within bilevel optimization solution methods for targeting environmental policies

Much research has focused on the use of optimization algorithms to derive a set of optimal solutions that exhibit trade-offs among multiple objectives. In the context of targeting environmental policies to improve water quality, bilevel optimization solution methods are particularly advantageous because, similar to principle-agent theory, they account for the optimizing behavior of both policy makers and policy followers. That is, bilevel methods generate the Pareto set of optimal policy solutions that both optimize the objectives of a policy maker (e.g., improve water quality over large scales) and the objectives of the policy followers (e.g., improve efficient use of resources at local scales). While the vast majority of optimization studies neglect uncertainty entirely, some studies have incorporated the impacts of weather variability on the resulting Pareto optimal solution set and derived robust frontiers. In this work, we focus on probabilistic policy adoption, wherein we characterize the decision-making process of the policy followers as a probabilistic likelihood of adoption rather than deterministic resource optimization (e.g., profit maximization). Different probabilistic forms (e.g., Gaussian, Heaviside) for the likelihood of adoption are tested and used to generate optimal frontiers that are robust to adoption uncertainty. We demonstrate the utility of the approach using a case study in the Tully catchment (Queensland, Australia), which is dominated by sugarcane farming and contributes to nitrogen pollution to the Great Barrier Reef, but the methods are generally applicable to targeting environmental policies amidst uncertain stakeholder adoption.