scholarly journals Derivation and Application of the Subjective–Objective Probability Relationship from Entropy: The Entropy Decision Risk Model (EDRM)

Systems ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 46 ◽  
Author(s):  
Thomas Monroe ◽  
Mario Beruvides ◽  
Víctor Tercero-Gómez
Keyword(s):  
Prospect Theory ◽  
Subjective Probability ◽  
Risk Model ◽  
Energy State ◽  
Evaluation Model ◽  
A Priori ◽  
Ideal Gas ◽  
Objective Probability ◽  
Power Utility ◽  
Decision Weights

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.

scholarly journals Quantifying Risk Perception: The Entropy Decision Risk Model Utility (EDRM-U)

Systems ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 51
Author(s):  
Thomas Monroe ◽  
Mario Beruvides ◽  
Víctor Tercero-Gómez
Keyword(s):  
Risk Perception ◽  
Expected Utility ◽  
Risk Model ◽  
A Priori ◽  
Expected Utility Theory ◽  
Power Utility ◽  
Initial Wealth ◽  
The Subject ◽  
Conducting Research ◽  
Exponential Power

Risk perception can be quantified in measurable terms of risk aversion and sensitivity. While conducting research on the quantization of programmatic risk, a bridge between positive and normative decision theories was discovered through the application of a novel a priori relationship between objective and subjective probabilities and the application of Bernoulli’s expected utility theory. The Entropy Decision Risk Model (EDRM) derived using the Kullback–Liebler entropy divergence from certainty serves as a translation between objective and subjective probability, referred to as proximity, and has proven its applicability to various positive decision theories related to Prospect Theory. However, EDRM initially assumes the validity of the standard exponential power utility function ubiquitous to positive decision theory models as the magnitude of a choice to isolate and validate proximity. This research modifies the prior model by applying Daniel Bernoulli’s expected utility as the measure of choice magnitude in place of power utility. The revised model, EDRM Utility (EDRM-U), predicts the subject choices for both small and large ranges of values and shows that Prospect Theory’s neutral reference point is actually centered about an assumed initial wealth value, called neutral wealth, that correlates to a power utility exponent value. This hypothesis is confirmed by demonstrating that EDRM-U presents an equivalent or better correlation with prior research in eleven landmark studies of college students spanning more than 26 years and comprising over 300 problems, including those with widely varying values. This research contributes to the fields of risk management and decision engineering by proposing a decision model that behaves according to both positive and normative decision theories and provides measures of risk perception.

scholarly journals The measure problem in no-collapse (many worlds) quantum mechanics

2017 ◽  
Vol 26 (03) ◽  
pp. 1730008 ◽  
Author(s):  
Stephen D. H. Hsu
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Probability Measure ◽  
Ab Initio ◽  
Subjective Probability ◽  
State Vector ◽  
A Priori ◽  
Born Rule ◽  
Many Worlds ◽  
Measure Problem

We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold — these branches exhibit highly improbable behaviors, including possibly the breakdown of decoherence or even the absence of an emergent semi-classical reality. Derivations of the Born rule which originate in decision theory or subjective probability (i.e. the reasoning of individual observers) do not resolve this problem, because they are circular: they assume, a priori, that the observer occupies a non-maverick branch. An ab initio probability measure is sometimes assumed to explain why we do not occupy a maverick branch. This measure is constrained by, e.g. Gleason’s theorem or envariance to be the usual Hilbert measure. However, this ab initio measure ultimately governs the allocation of a self or a consciousness to a particular branch of the wave function, and hence invokes primitives which lie beyond the Everett wave function and beyond what we usually think of as physics. The significance of this leap has been largely overlooked, but requires serious scrutiny.

scholarly journals Subjective Values Theory: The Psychology of Value and Preferential Choice

2019 ◽  
Author(s):  
Dale Cohen ◽  
Amanda R. Cromley ◽  
Katelyn E. Freda ◽  
Madeline White
Keyword(s):  
Random Walk ◽  
Behavioral Economics ◽  
Prospect Theory ◽  
Utility Theory ◽  
Human Life ◽  
Sequential Sampling ◽  
A Priori ◽  
Decision Mechanism ◽  
Preferential Choice ◽  
Social Decisions

Here, we proposed Subjective Values Theory, a theory of the perception of value, andhow that perception drives preferential choice. Utility Theory, Prospect Theory, and traditional implementations of sequential sampling theory derive value from observers’ preferential choices. Subjective Values Theory goes beyond these theories by (a) precisely defining and measuring value independent of preferential choice, and (b) using these independent measurements of value to a priori predict preferential choice. We instantiate the decision mechanism proposed by Subjective Values Theory in a new Robust Random Walk (RRW) procedure. We evaluate the validity of Subjective Values Theory and the RRW in six experiments that measure the value of human lives and predict participants’ RTs and preferential choices in complex social decisions. In these experiments, we demonstrate that the process of perceiving Psychological Value is the same for objects and human lives, social status influences the perceived Psychological Value of a human life, and quantity has little or no influence on the perceived Psychological Value of human lives or objects. We discuss the implications of these findings in relation to decision theory, behavioral economics, and the psychology of morality.

Physical Probability

1990 ◽  
Author(s):  
John L. Pollock
Keyword(s):  
General Theory ◽  
Decision Theory ◽  
Everyday Life ◽  
Subjective Probability ◽  
Relative Frequency ◽  
Probabilistic Reasoning ◽  
Objective Probability ◽  
Problem Of Induction ◽  
Philosophical Foundations ◽  
Statistical Induction

Probability theorists divide into two camps-the proponents of subjective probability and the proponents of objective probability. Opinion has it that subjective probability has carried the day, but I think that such a judgment is premature. I have argued elsewhere that there are deep incoherencies in the notion of subjective probability. Accordingly, I find myself in the camp of objective probability. The consensus is, however, that the armies of objective probability are in even worse disarray. The purpose of this book is to construct a theory of objective probability that rectifies that. Such a theory must explain the meaning of objective probability, show how we can discover the values of objective probabilities, clarify their use in decision theory, and demonstrate how they can be used for epistemological purposes. The theory of nomic probability aims to do all that. This book has two main objectives. First, it will propose a general theory of objective probability. Second, it will, in a sense to be explained, propose a solution to the problem of induction. These two goals are intimately connected. I will argue that a solution to the problem of induction is forthcoming, ultimately, from an analysis of probabilistic reasoning. Under some circumstances, probabilistic reasoning justifies us in drawing non-probabilistic conclusions, and this kind of reasoning underlies induction. Conversely, an essential part of understanding probability consists of providing an account of how we can ascertain the values of probabilities, and the most fundamental way of doing that is by using a species of induction. In statistical induction we observe the relative frequency (the proportion) of A's in a limited sample of B's, and then infer that the probability of a B being an A is approximately the same as that relative frequency. To provide philosophical foundations for probability we must, among other things, explain precisely how statistical induction works and what justifies it. Probability is important both in and out of philosophy. Much of the reasoning of everyday life is probabilistic. We look at the clouds and judge whether it is going to rain by considering how often clouds like that have spawned rain in the past.

Theory of Knowledge

2016 ◽  
pp. 136-161
Author(s):  
Martha Bolton
Keyword(s):  
First Principles ◽  
A Priori ◽  
Natural Sciences ◽  
Theory Of Knowledge ◽  
Objective Probability ◽  
Mathematical Science ◽  
Human Beings ◽  
Degree Of Certainty ◽  
Structural Principles ◽  
Areas Of Concern

Leibniz’s theory of knowledge is an investigation of the conditions that enable human beings to have that degree of certainty which is appropriate to our various areas of concern. This chapter concerns demonstrative certainty in the sciences of mathematics, which contain necessary a priori truths, and the natural sciences, which are based on the senses and structural principles drawn from reason. According to Leibniz, we rarely attain maximum certainty even in mathematical science. One main problem is to establish first principles with certainty. In lieu of that, Leibniz proposes to convert less than certain theorems to more certain conditionals with axioms as antecedents and theorems as consequents. This is worthwhile because the agreed upon results may prove useful or beneficial. In natural sciences, Leibniz gauges hypotheses on the basis of a theory of objective probability grounded in metaphysics.

scholarly journals Using Improved Prospect Theory to Develop a Partner Selection Method for Virtual Enterprises with Unknown Weight

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Nina Su ◽  
Xianqi Zhu ◽  
Yunsheng Xin
Keyword(s):  
Prospect Theory ◽  
Evaluation Model ◽  
Virtual Enterprise ◽  
Risk Attitude ◽  
Virtual Enterprises ◽  
Market Demand ◽  
Fuzzy Language ◽  
Effective Organization ◽  
Language Environment

A “virtual enterprise” is an effective organization formed by enterprises and partners under market opportunity which can flexibly adapt to the dynamic market demand and improve the competitiveness of enterprises. To select virtual enterprise partners objectively and scientifically, this study proposes the evaluation model of the innovation resource capability of the alternative enterprises under the unknown weight. In the multigranularity hesitation fuzzy language environment, the unknown weight is solved by using fuzzy entropy theory. The risk attitude of decision-making enterprises is introduced by using the improved prospect theory and the selection of partners is comprehensively considered. Finally, a case study is presented to demonstrate the effectiveness of the proposed approach. The research intends to enable the virtual enterprise to choose the partners swiftly such that they can compensate for the shortcomings and optimize the allocation of innovation resources.

Feedback Produces Divergence From Prospect Theory in Descriptive Choice

2008 ◽  
Vol 19 (10) ◽  
pp. 1015-1022 ◽  
Author(s):  
Ryan K. Jessup ◽  
Anthony J. Bishara ◽  
Jerome R. Busemeyer
Keyword(s):  
Model Comparison ◽  
Objective Probability ◽  
Decision Making Process ◽  
Probability Weighting ◽  
Critical Component ◽  
Gambling Task ◽  
Individual Subject ◽  
Decision Weights ◽  
The Individual ◽  
Small Probabilities

A recent study demonstrated that individuals making experience-based choices underweight small probabilities, in contrast to the overweighting observed in a typical descriptive paradigm. We tested whether trial-by-trial feedback in a repeated descriptive paradigm would engender choices more correspondent with experiential or descriptive paradigms. The results of a repeated gambling task indicated that individuals receiving feedback underweighted small probabilities, relative to their no-feedback counterparts. These results implicate feedback as a critical component during the decision-making process, even in the presence of fully specified descriptive information. A model comparison at the individual-subject level suggested that feedback drove individuals' decision weights toward objective probability weighting.

Humans, Econs and Portfolio Choice

2016 ◽  
Vol 07 (02) ◽  
pp. 1750001 ◽  
Author(s):  
Michael J. Best ◽  
Robert R. Grauer
Keyword(s):  
Prospect Theory ◽  
Portfolio Choice ◽  
Loss Aversion ◽  
Asset Allocation ◽  
Power Utility ◽  
Numerical Example ◽  
Portfolio Choices ◽  
Out Of Sample ◽  
Finance Theory ◽  
Mean Variance

We compare the portfolio choices of Humans — prospect theory investors — to the portfolio choices of Econs — power utility and mean-variance (MV) investors. In a numerical example, prospect theory portfolios are decidedly unreasonable. In an in-sample asset allocation setting, the prospect theory results are consistent with myopic loss aversion. However, the portfolios are extremely unstable. The power utility and MV results are consistent with traditional finance theory, where the portfolios are stable across decision horizons. In an out-of-sample asset allocation setting, the power utility and portfolios outperform the prospect theory portfolios. Nonetheless the prospect theory portfolios with loss aversion coefficients of 2.25 and 2 perform well.

scholarly journals Salience Theory of Choice Under Risk

2012 ◽  
Vol 127 (3) ◽  
pp. 1243-1285 ◽  
Author(s):  
Pedro Bordalo ◽  
Nicola Gennaioli ◽  
Andrei Shleifer
Keyword(s):  
Prospect Theory ◽  
Decision Maker ◽  
Preference Reversals ◽  
Allais Paradox ◽  
Risk Seeking ◽  
Seeking Behavior ◽  
Context Dependent ◽  
Decision Weights

Abstract We present a theory of choice among lotteries in which the decision maker's attention is drawn to (precisely defined) salient payoffs. This leads the decision maker to a context-dependent representation of lotteries in which true probabilities are replaced by decision weights distorted in favor of salient payoffs. By specifying decision weights as a function of payoffs, our model provides a novel and unified account of many empirical phenomena, including frequent risk-seeking behavior, invariance failures such as the Allais paradox, and preference reversals. It also yields new predictions, including some that distinguish it from prospect theory, which we test.

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