Decision engineering: Deriving and applying an entropy model for quantifying risk perception

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2021-05

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Abstract

It has been well established that standard models for analyzing programmatic risk do not align with real-life behavior when choosing between alternatives, resulting in inconsistencies between mental models formed by decision-makers and the outcomes of formal risk analyses using normative models. This misalignment results in devaluation of risk assessments by decision-makers when making discrete choices, a problem also observed in the financial risk community. Disparate risks are evaluated independently rather than as a risk system so interrelationships between risk and projections cannot be evaluated. Contributing to this problem is the lack of a global fungible unit of programmatic risk, which would allow for modeling and pattern analysis across different risk systems. This dissertation seeks to first explain the differences between conventional risk analyses and decision making through the development of a new positive decision model consistent with Prospect Theory and based upon Jeremy Bentham’s original definition of utility and information theory entropy by relating subjective and objective probabilities for quantifying and assessing risks. This new a priori model accurately predicts results from several landmark behavioral economics studies, including Prospect Theory and Cumulative Prospect Theory. Next, this research addresses the magnitude component of utility by merging subjective probabilities from the entropy-based model into expected utility theory, thereby enabling prediction of risk choices over wide ranges of values and creating harmony between positive and normative decision theories Through the process of conducting this research, it was learned that while prior efforts have attempted to quantify risk itself, the real goal should be to quantify the perception of the decision-maker who is evaluating and making risk decisions. As a result, risk perception of an individual or a group in terms of risk aversion (of which loss aversion is a subset) and risk sensitivity can now be deduced to enable prediction of subject choice or the engineering of sets of decisions to achieve a desired outcome.

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Keywords

Entropy, Risk, Subjective Probability, Proximity, Decision Engineering, Risk Perception, Prospect Theory, Information Theory

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