Discussing an Expected Utility and Weighted Entropy Framework

Theoretical Economics Letters, 2015

We present and discuss a conceptual decision-making procedure supported by a mathematical device combining expected utility and a generalized information measure: the weighted Gini-Simpson index, linked to the scientific fields of information theory and ecological diversity analysis. After a synthetic review of the theoretical background relative to those themes, such a devicean EU-WGS framework denoting a real function defined with positive utility values and domain in the simplex of probabilities-is analytically studied, identifying its range with focus on the maximum point, using a Lagrange multiplier method associated with algorithms, exemplified numerically. Yet, this EU-WGS device is showed to be a proper analog of an expected utility and weighted entropy (EU-WE) framework recently published, both being cases of mathematical tools that can be referred to as non-expected utility methods using decision weights, framed within the field of decision theory linked to information theory. This kind of decision modeling procedure can also be interpreted to be anchored in Kurt Lewin utility's concept and may be used to generate scenarios of optimal compositional mixtures applied to generic lotteries associated with prospect theory, financial risk assessment, security quantification and natural resources management. The epistemological method followed in the reasoned choice procedure that is presented in this paper is neither normative nor descriptive in an empirical sense, but instead it is heuristic and hermeneutical in its conception.

Theory and Decision, 2012

Expected utility maximization problem is one of the most useful tools in mathematical finance, decision analysis and economics. Motivated by statistical model selection, via the principle of expected utility maximization, Friedman and Sandow (J Mach Learn Res 4:257–291, 2003a) considered the model performance question from the point of view of an investor who evaluates models based on the performance of

Physica A-statistical Mechanics and Its Applications, 2008

The maximum entropy principle can be used to assign utility values when only partial information is available about the decision maker's preferences. In order to obtain such utility values it is necessary to establish an analogy between probability and utility through the notion of a utility density function. According to some ] the maximum entropy utility solution embeds a large family of utility functions. In this paper we explore the maximum entropy principle to estimate the utility function of a risk averse decision maker.

Entropy weight method (EWM) is a commonly used weighting method that measures value dispersion in decision-making. e greater the degree of dispersion, the greater the degree of differentiation, and more information can be derived. Meanwhile, higher weight should be given to the index, and vice versa. is study shows that the rationality of the EWM in decision-making is questionable. One example is water source site selection, which is generated by Monte Carlo Simulation. First, too many zero values result in the standardization result of the EWM being prone to distortion. Subsequently, this outcome will lead to immense index weight with low actual differentiation degree. Second, in multi-index decision-making involving classification, the classification degree can accurately reflect the information amount of the index. However, the EWM only considers the numerical discrimination degree of the index and ignores rank discrimination. ese two shortcomings indicate that the EWM cannot correctly reflect the importance of the index weight, thus resulting in distorted decision-making results.

Communications in Statistics - Theory and Methods, 2019

Cross entropy is an important index for determining the divergence between two sets or distributions. Most existing cross entropy are proposed in a fuzzy environment and undefined in some uncertain situations (e.g., Dempster-Shafer theory). This study proposes an extended cross entropy measure of belief values based on a belief degree using available evidence. Thus, a new aspect of belief functions represents in the name of a belief set. Then, a new cross entropy measure between two belief sets is defined. Furthermore, the application of the cross-entropy measure in multi-criteria decision making (MCDM) is provided with belief valued information.

Entropy, 2007

We review a decision theoretic, i.e., utility-based, motivation for entropy and Kullback-Leibler relative entropy, the natural generalizations that follow, and various properties of these generalized quantities. We then consider these generalized quantities in an easily interpreted special case. We show that the resulting quantities, share many of the properties of entropy and relative entropy, such as the data processing inequality and the second law of thermodynamics. We formulate an important statistical learning problem-probability estimation-in terms of a generalized relative entropy. The solution of this problem reflects general risk preferences via the utility function; moreover, the solution is optimal in a sense of robust absolute performance.

Operations Research, 2006

This paper presents a method to assign utility values when only partial information is available about the decision maker’s preferences. We introduce the notion of a utility density function and a maximum entropy principle for utility assignment. The maximum entropy utility solution embeds a large family of utility functions that includes the most commonly used functional forms. We discuss the implications of maximum entropy utility on the preference behavior of the decision maker and present an application to competitive bidding situations where only previous decisions are observed by each party. We also present minimum cross entropy utility, which incorporates additional knowledge about the shape of the utility function into the maximum entropy formulation, and work through several examples to illustrate the approach.

2003

We introduce an axiomatic approach to the problem of inferring a complete and transitive weak ordering representing the agent's preferences given a set of observed constraints. The axioms characterize a unique inference rule, which amounts to the constrained maximization of a certain formula we derive. The formula can be interpreted as the entropy of the agent's preference ordering, and its unique maximand identifies the simplest rationalization of the observed behavior.

Systems, 2020

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.

The Journal of Defense Modeling and Simulation: Applications, Methodology, Technology, 2019

This article compares the entropy weight scheme to other subjective weighting schemes using various multi-attribute decision making criteria. We apply the entropy weighting scheme to improve the CARVER center of gravity analysis and targeting analysis that are currently used by Special Operations Forces. We also compare the entropy weighing schemes to other weighting schemes using the ranking of terrorist for targeting. Next, we apply several multi-attribute decision making (MADM) methods using our suggested various weighting schemes to obtain the rankings of the alternatives. We compare the results and provide sensitivity analysis to examine the robustness of each MADM analysis. We conclude that any decision methodology for CARVER and terrorist ranking that used the actual data collected to compute the weights might be a better method than subjective weights.