This research is motivated by the Hippocratic Paradox and associated hard cases that have been heard by the U.S. Supreme Court. The Hippocratic Paradox refers to ethical dilemmas caused by the conflict of some of the four principles in medical ethics — nonmaleficence, beneficence, autonomy, and justice. Studies in medicine, law, sociology, and philosophy have contributed considerable expertise and narrative insights on an ad hoc basis. This research aims to discover general patterns. It appears to be the first mathematical analysis of the co-evolution of the three domains — ethics, law, and society — in the context of medicine. Previously there has been no research in this direction.

This interdisciplinary research makes several contributions. First, I establish a coordinate system for each of the three domains to understand issues that occur in each domain driven by underlying principles. Second, I apply a novel mathematical approach developed by Saari (2018) to capture the qualitative features of unknown dynamics among the three domains, including the existence, number, and nature of unexpected interior equilibria. Third, I predict and update bifurcations when dynamics evolve from one state to another. Fourth, I identify root causes of bifurcations, i.e., variations in endogenous or exogenous parameters that change the weighing of underlying principles of each domain and hence alter the dynamic outcomes. Fifth, I discover the existence of equivalence classes in which seemingly different issues have similar configurations and hence similar evolutions. Sixth, I conduct policy analyses for contemporary issues such as abortion, the opioid epidemic, healthcare artificial intelligence, stem cell and genome editing research, and find unexpected and undesired outcomes. I also propose effective policies. In sum, I apply a general theory created by Saari (2018) to explain what has happened for existing cases in medical ethics and law, and to predict what can and probably will happen for new cases and what can be done. This research can serve as a prediction and policy tool to assist the ethical and legal aspects of medical decision-making.