Decision Entropy: A New Theory for Representing Uncertainty in Managing Natural Hazard Risks

University Of Texas At Austin, Austin TX

Investigators

Abstract

The goal of this research is to develop a new theoretical basis to rationally and defensibly manage risks from rare natural hazards that cause large consequences. If successful, this research will benefit society by optimizing how public and private resources are invested in mitigating or accepting risks from natural hazards. In addition, it has the potential to improve decision making in a wide variety of fields from medicine to economics to public policy. It will increase awareness about uncertainty and the dangers and tendencies to think we know more than we really do in making decisions, it will improve critical thinking and decision skills in primary school students and foster excitement about opportunities in engineering This research will develop a theoretical basis, Decision Entropy Theory, to rationally and defensibly manage risks from rare natural hazards that cause large consequences. Decision Entropy Theory is a new theory developed by the Principal Investigators to establish an objective (non-informative) starting point for assessing probabilities in the context of making decisions. This starting point is obtained by maximizing the entropy of the decision, which is defined concerning the possible decision outcomes. The following objectives will be addressed: 1. Finalize axiomatic descriptions of the theory. These mathematical axioms establish the starting point (sample space) used to assess probabilities based on any and all available information (objective and subjective) through Bayes' Theorem. 2. Produce analytical or non-dimensional numerical solutions for a set of simplified risk management problems. 3. Develop numerical means to implement the theory on more complicated and realistic risk management problems. 4. Integrate Decision Entropy Theory into the Natural Hazards Engineering Research Infrastructure (NHERI) Cyberinfrastructure DesignSafe-ci.org to support the analysis of data, the valuation of critical data needs and risk-management decision making. 5. Apply the theory to real-world case histories to demonstrate its use and the understanding it provides in managing risks for natural hazards. 6. Create simple games and exercises to illustrate and communicate the theory to the public. 7. Conduct outreach to primary schools to educate students about critical thinking, risk and decision making. This project will be a collaborative effort comprising two departments in engineering at The University of Texas at Austin, the Norwegian Geotechnical Institute and NHERI. This research is a high risk, high reward endeavor. For centuries, a variety of extremely distinguished theoreticians, including Bernoulli, Keynes, Jaynes, and Raiffa, have unsuccessfully attempted to address this problem. This research has the potential to make a transformative advancement in knowledge and decision-making under uncertainty. First, it suggests that the starting point in assessing probabilities depends on the decision in which these probabilities will be used, meaning that probability is not an absolute but a relative concept. Adopting this perspective of relativity provides insights in representing uncertainty and managing risk that are thought-provoking, not always intuitive, and comforting in some cases but disconcerting in others. Second, this research will produce analytical or non-dimensional numerical solutions for simplified risk-management decision problems. These solutions will provide both general insights and practical means for applying the theory. Third, this research will advance innovative numerical methods to maximize "decision entropy" in realistic, multi-dimensional decision problems. Finally, this research will be integrated into the NHERI Cyberinfrastructure DesignSafe-ci.org web portal so that users will be able to apply it with real data to practical problems of managing risks from natural hazards.