Quantifying Risk Perception: The Entropy Decision Risk Model Utility (EDRM-U)

Abstract

Risk perception can be quantified in measurable terms of risk aversion and sensitivity. While conducting research on the quantization of programmatic risk, a bridge between positive and normative decision theories was discovered through the application of a novel a priori relationship between objective and subjective probabilities and the application of Bernoulli’s expected utility theory. The Entropy Decision Risk Model (EDRM) derived using the Kullback–Liebler entropy divergence from certainty serves as a translation between objective and subjective probability, referred to as proximity, and has proven its applicability to various positive decision theories related to Prospect Theory. However, EDRM initially assumes the validity of the standard exponential power utility function ubiquitous to positive decision theory models as the magnitude of a choice to isolate and validate proximity. This research modifies the prior model by applying Daniel Bernoulli’s expected utility as the measure of choice magnitude in place of power utility. The revised model, EDRM Utility (EDRM-U), predicts the subject choices for both small and large ranges of values and shows that Prospect Theory’s neutral reference point is actually centered about an assumed initial wealth value, called neutral wealth, that correlates to a power utility exponent value. This hypothesis is confirmed by demonstrating that EDRM-U presents an equivalent or better correlation with prior research in eleven landmark studies of college students spanning more than 26 years and comprising over 300 problems, including those with widely varying values. This research contributes to the fields of risk management and decision engineering by proposing a decision model that behaves according to both positive and normative decision theories and provides measures of risk perception.