Flat Maxima in Linear Optimization Models
MICHIGAN UNIV ANN ARBOR ENGINEERING PSYCHOLOGY LAB
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Expected value functions as functions of decisions and decision strategies are flat around their maxima. This so called flat maximum phenomenon has been discovered in sensitivity analyses in virtually all decision theoretic paradigms. But until now most of the research on flat maxima explored more or less general examples and limiting considerations. Two basic questions remained unanswered what are the mathematical reasons for the restricted shape of the evaluation functions and can these restrictions be interpreted as flatness in a psychological sense. While the second question calls for psychological experimentation, the first question can be answered with mathematical tools. The present article shows that the mathematical characteristics of linear optimization models impose severe restrictions on the functions evaluating choice alternatives such as gambles, multi-attributed outcomes, or consumption streams.
- Operations Research