Abstract
The uncertainty, or entropy, of an atom of an ideal gas being in a certain energy state mirrors the way people perceive uncertainty in the making of decisions, uncertainty that is related to unmeasurable subjective probability. It is well established that subjects evaluate risk decisions involving uncertain choices using subjective probability rather than objective, which is usually calculated using empirically derived decision weights, such as those described in Prospect Theory; however, an exact objective–subjective probability relationship can be derived from statistical mechanics and information theory using Kullback–Leibler entropy divergence. The resulting Entropy Decision Risk Model (EDRM) is based upon proximity or nearness to a state and is predictive rather than descriptive. A priori EDRM, without factors or corrections, accurately aligns with the results of prior decision making under uncertainty (DMUU) studies, including Prospect Theory and others. This research is a first step towards the broader effort of quantifying financial, programmatic, and safety risk decisions in fungible terms, which applies proximity (i.e., subjective probability) with power utility to evaluate choice preference of gains, losses, and mixtures of the two in terms of a new parameter referred to as Prospect. To facilitate evaluation of the EDRM against prior studies reported in terms of the percentage of subjects selecting a choice, the Percentage Evaluation Model (PEM) is introduced to convert choice value results into subject response percentages, thereby permitting direct comparison of a utility model for the first time.
Highlights
An executive is presented with an engineering risk analysis for a critical decision that involves a potential for loss of life for a failure mode that is highly unlikely and has no history of prior failure, a high-consequence, low-probability event that would take years and tens of millions of dollars to mitigate; the system under consideration itself is a safety system that provides mitigation for other Black Swan events, so its unavailability adds to risk in other interconnected areas
A financial manager is presented with the results of a value at risk analysis from the company’s risk management team for a transaction and chooses to go against their recommendation and make the trade based upon instinct
The uncertainty, or entropy, of a single atom of an ideal gas being in a certain energy state mirrors the way people perceive uncertainty in the making of decisions, uncertainty that is related to unmeasurable subjective probability
Summary
An executive is presented with an engineering risk analysis for a critical decision that involves a potential for loss of life for a failure mode that is highly unlikely and has no history of prior failure, a high-consequence, low-probability event that would take years and tens of millions of dollars to mitigate; the system under consideration itself is a safety system that provides mitigation for other Black Swan events, so its unavailability adds to risk in other interconnected areas. The executive chooses to accept the risk in spite of the grave prediction by the system’s engineers In another example, an individual chooses to buy insurance for their property, but at the same time buys lottery tickets despite the overwhelming odds against success—seemingly a contraction. An individual chooses to buy insurance for their property, but at the same time buys lottery tickets despite the overwhelming odds against success—seemingly a contraction In yet another case, a financial manager is presented with the results of a value at risk analysis from the company’s risk management team for a transaction and chooses to go against their recommendation and make the trade based upon instinct.
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