What does decision making with intervals really assume? The relationship between the Hurwicz decision rule and prescriptive decision analysis

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Sivaprasad, Sarat
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Cameron A. MacKenzie
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Industrial and Manufacturing Systems Engineering
The Department of Industrial and Manufacturing Systems Engineering teaches the design, analysis, and improvement of the systems and processes in manufacturing, consulting, and service industries by application of the principles of engineering. The Department of General Engineering was formed in 1929. In 1956 its name changed to Department of Industrial Engineering. In 1989 its name changed to the Department of Industrial and Manufacturing Systems Engineering.
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Decision analysis can be defined as a discipline where a decision maker chooses the best alternative by considering the decision maker’s values and preferences and by breaking down a complex decision problem into simple or constituent ones. Decision analysis helps an individual make better decisions by structuring the problem. Non-probabilistic approaches to decision making have been proposed for situations in which an individual does not have enough information to assess probabilities over an uncertainty. One non-probabilistic method is to use intervals in which an uncertainty has a minimum and maximum but nothing is assumed about the relative likelihood of any value within the interval. The Hurwicz decision rule in which a parameter trades off between pessimism and optimism generalizes the current rules for making decisions with intervals. This thesis analyzes the relationship between intervals based on the Hurwicz rule and traditional decision analysis using probabilities and utility functions. This thesis shows that the Hurwicz decision rule for an interval is logically equivalent to: (i) an expected value decision with a triangle distribution over the interval; (ii) an expected value decision with a beta distribution; and (iii) an expected utility decision with a uniform distribution. The results call into question whether decision making based on intervals really assumes less information than subjective expected utility decision making. If an individual is using intervals to select an alternative—for which the interval decision rule can be described with the Hurwicz equation—then the individual is implicitly assuming a probability distribution such as a triangle or beta distribution or a utility function expressing risk preference.

Sun Jan 01 00:00:00 UTC 2017