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Asymptotic Maximum Entropy Principle for Utility Elicitation under High Uncertainty and Partial Information

Last modified: 2012-05-16

#### Abstract

Decision making has proposed multiple methods to help the decision maker in his analysis, by suggesting ways of formalization of the preferences as well as the assessment of the uncertainties. Although these techniques are established and proven to be mathematically sound, experience has shown that in certain situations we tend to avoid the formal approach by acting intuitively. Especially, when the decision involves a large number of attributes and outcomes, and where we need to use pragmatic and heuristic simplifications such as considering only the most important attributes and omitting the others. In this paper, we provide a model for decision making in situations subject to a large predictive uncertainty with a small learning sample. The high predictive uncertainty is concretized by a countably infinite number of prospects, making the preferences assessment more difficult. Our main result is an extension of the Maximum Entropy utility (MEU) principle into an asymptotic maximum entropy utility principle for preferences elicitation. This will allow us to overcome the limits of the existing MEU method to the extend that we focus on utility assessment when the set of the available discrete prospects is countably infinite. Furthermore, our proposed model can be used to analyze situations of high-cognitive load as well as to understand how humans handle these problems under Ceteris Paribus assumption.

#### Keywords

Decision Theory; Uncertainty; Maximum Entropy; Ceteris Paribus; Bounded Rationality

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