How to Deal with High-Impact Low-Probability Events: Theoretical Explanation of the Empirically Successful Fuzzy-Like Technique

Authors

Juan Ulloa, The University of Texas at El PasoFollow
Aaron Velasco, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

1-1-2025

Comments

Technical Report: UTEP-CS-25-2

Abstract

When making decisions, it is important to take into account high-impact low-probability events. For such events, traditional probability-based approach -- which considers the product of the probability p that this event happens and the probability P that a randomly selected building will be destroyed -- often underestimates risks. Available data has lead to an empirical table that provides a more adequate risk estimate. Most of the entries in this table correspond to the fuzzy-like formula min(p,P). This paper explains this empirical result. Specifically, it explains both the effectiveness of the min formula -- and also explains deviations from this formula.