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Some Notes on Maximum Entropy Utility.

Eun Young Kim¹, Byeong Seok Ahn²

¹Department of Neurosurgery, Gachon University Gil Medical Center, 21 Namdongdaero 774, Namdong, Incheon 21565, Korea.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

The maximum entropy principle can be limited when dealing with partial preferences. A new distance-based method, centralized utility increments, offers a more robust solution for decision-making under uncertainty.

Keywords:

decision analysis maximum entropy utility

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Area of Science:

Decision theory
Utility theory
Mathematical optimization

Background:

The maximum entropy principle is a standard approach for decision-making with incomplete information.
It is used to derive maximum entropy utility for ordered prospects.
However, it faces limitations with partial preferences, ordered utility increments, or uncertain probabilities.

Purpose of the Study:

To address the limitations of the maximum entropy principle in representing partial preferences.
To introduce a novel distance-based method for utility increment calculation.
To compare the proposed method with the existing maximum entropy utility.

Main Methods:

Proposing a distance-based solution termed centralized utility increments.
Minimizing the expected quadratic distance to a set of vertices derived from partial preferences.
Deriving and comparing centralized utility increments with maximum entropy utility.

Main Results:

Centralized utility increments are determined by centering utility increments around the vertices.
The proposed method provides a satisfactory representation for partial preferences where maximum entropy fails.
Demonstrated effectiveness in handling ordered utility increments and uncertain probabilities.

Conclusions:

The centralized utility increments method offers an improvement over the maximum entropy principle for specific decision problems.
This approach enhances the handling of complex preference structures in decision analysis.
Provides a valuable alternative for decision-making under uncertainty with partial information.