How do changes in local or global policy affect fundamentally uncertain phenomena? For example, what is the best way to reduce negligent injury in medical encounters? Will sanctioning at-fault physicians reduce this type of injury? RAND, a U.S.-based nonprofit think tank, seeks out practical solutions to such public policy-related questions by developing and employing mathematical models to help understand social behavior, resource management, and decision-making under deep uncertainty. In this talk I will give a brief background of RAND, then consider two examples of previous research that draw on simple mathematical and statistical models to give meaningful insight into complex social issues. I will then briefly explore two areas of mathematics that have promising potential for academic research exploration and application to public policy research.