Classical Decision Theory Research Articles

Uncertainty and denial: a resource-rational model of the value of information.

Classical decision theory predicts that people should be indifferent to information that is not useful for making decisions, but this model often fails to describe human behavior. Here we investigate one such scenario, where people desire information about whether an event (the gain/loss of money) will occur even though there is no obvious decision to be made on the basis of this information. We find a curious dual trend: if information is costless, as the probability of the event increases people want the information more; if information is not costless, people's desire for the information peaks at an intermediate probability. People also want information more as the importance of the event increases, and less as the cost of the information increases. We propose a model that explains these results, based on the assumption that people have limited cognitive resources and obtain information about which events will occur so they can determine whether to expend effort planning for them.

A Survey of Multi-Agent Decision Making

In this article we give a high-level overview of various aspects relevant to multi-agent decision making. Classical decision theory makes the start. Then, we introduce multi-agent decision making, focussing on game theory, complex decision making, and on intelligent agents. Afterwards, we discuss methods for reaching agreements interactively, e.g. by negotiation, bargaining, and argumentation, followed by approaches to coordinate and to control agents’ decision making.

SELF-ORGANIZATION IN COMPLEX SYSTEMS AS DECISION MAKING

The idea is advanced that self-organization in complex systems can be treated as decision making (as it is performed by humans) and, vice versa, decision making is nothing but a kind of self-organization in the decision maker nervous systems. A mathematical formulation is suggested based on the definition of probabilities of system states, whose particular cases characterize the probabilities of structures, patterns, scenarios, or prospects. In this general framework, it is shown that the mathematical structures of self-organization and of decision making are identical. This makes it clear how self-organization can be seen as an endogenous decision making process and, reciprocally, decision making occurs via an endogenous self-organization. The approach is illustrated by phase transitions in large statistical systems, crossovers in small statistical systems, evolutions and revolutions in social and biological systems, structural self-organization in dynamical systems, and by the probabilistic formulation of classical and behavioral decision theories. In all these cases, self-organization is described as the process of evaluating the probabilities of macroscopic states or prospects in the search for a state with the largest probability. The general way of deriving the probability measure for classical systems is the principle of minimal information, that is, the conditional entropy maximization under given constraints. Behavioral biases of decision makers can be characterized in the same way as analogous to quantum fluctuations in natural systems.

A connection between quantum decision theory and quantum games: The Hamiltonian of Strategic Interaction

Experimental economics and studies in psychology show incompatibilities between human behavior and the perfect rationality assumption which do not fit in classical decision theory, but a more general representation in terms of Hilbert spaces can account for them. This paper integrates previous theoretical works in quantum game theory, Yukalov and Sornette’s quantum decision theory and Pothos and Busemeyer’s quantum cognition model by postulating the Hamiltonian of Strategic Interaction which introduces entanglement in the strategic state of the decision-maker. The Hamiltonian is inherited from the algebraic structure of angular momentum in quantum mechanics and the only required parameter, θ̃∈[0,π], represents the strength of the interaction. We consider it as a non-revealed type of the decision-maker. Considering θ̃ to be a continuous random variable, phenomena like learning when participating in repeated games and the influence of the amount of disposable information could be considered as an evolution in the mode and shape of the distribution function fθ̃(t,I). This modeling is motivated by the Eisert–Wilkens–Lewenstein quantization scheme for Prisoner’s Dilemma game and then it is applied in the Ultimatum game, which is not a simultaneous but a sequential game. Even when this non-revealed type θ̃ cannot be directly observed, we can compute observable outcomes: the probabilities of offering different amounts of coins and the probability of the different offers being accepted or not by the other player.

Making decisions in an ever-changing environment - A research agenda

Simon recognized the limitations of the classical normative decision theory and established descriptive theory. His concept of bounded rationality and administrative behavior was a big step ahead, but the world has changed dramatically since then. Multiple, continuous changes have become normal, which brings up new problems on the decision maker’s and on the organization’s level as well. It became usual that the decision maker is not able to define preferences for lack of knowledge and have to learn or delegate much more frequently than before. In the same time the organization should be more resilient or nimble in this ever-changing environment. The authors outline a research agenda on both levels: some about the continuous learning and frequent delegating, and some about the HRM and IT-management issues of organizational nimbleness.

OR Forum—Quantum Mechanics and Human Decision Making

In physics, at the beginning of the twentieth century it was recognized that some experiments could not be explained by the conventional classical mechanics, but the same could be explained by the newly discovered quantum theory. It resulted in a new mechanics called quantum mechanics that revolutionized scientific and technological developments. Again, at the beginning of the twenty-first century, it is being recognized that some experiments related to the human decision-making processes could not be explained by the conventional classical decision theory but the same could be explained by the models based on quantum mechanics. It is now recognized that we need quantum mechanics in psychology as well as in economics and finance. In this paper we attempt to advance and explain the present understanding of applicability of quantum mechanics to the human decision-making processes. Using the postulates analogous to the postulates of quantum mechanics, we show the derivation of the quantum interference equation to illustrate the quantum approach. The explanation of disjunction effect experiments of Tversky and Shafir (Tversky A, Shafir E (1992) The disjunction effect in choice under uncertainty. Psych. Sci. 3(5):305–309) has been chosen to demonstrate the necessity of a quantum model. Further, to suggest the possibility of application of the quantum theory to the business-related decisions, some terms such as price operator, state of mind of the acquiring firm, etc., are introduced and discussed in context of the merger/acquisition of business firms. The possibility of the development in areas such as quantum finance, quantum management, application of quantum mechanics to the human dynamics related to healthcare management, etc., is also indicated.

Neurocomputational account of how the human brain decides when to have a break

No pain, no gain: cost-benefit trade-off has been formalized in classical decision theory to account for how we choose whether to engage effort. However, how the brain decides when to have breaks in the course of effort production remains poorly understood. We propose that decisions to cease and resume work are triggered by a cost evidence accumulation signal reaching upper and lower bounds, respectively. We developed a task in which participants are free to exert a physical effort knowing that their payoff would be proportional to their effort duration. Functional MRI and magnetoencephalography recordings conjointly revealed that the theoretical cost evidence accumulation signal was expressed in proprioceptive regions (bilateral posterior insula). Furthermore, the slopes and bounds of the accumulation process were adapted to the difficulty of the task and the money at stake. Cost evidence accumulation might therefore provide a dynamical mechanistic account of how the human brain maximizes benefits while preventing exhaustion.

BETTING MARKET: Rank Dependent Expected Utility

In Pelota matches, games with two mutually exclusive and exhaustive outcomes, bets on the winner are made through a middleman who receives 16% of the finally paid amount. The classical decision theory of expected utility maximization can not explain this market assuming bettors are identical. Llorente and Aizpurua (2007) explain the existence of bets in the market under Quiggin’s rank dependent expected utility (RDEU) model. They find that bettors have to be optimistic in order to explain the existence of a bet. Analyzing the way odds are fixed in the market Llorente (2006) finds that assuming equal return on bets there are inefficiencies in the market. In this paper we show that, given an assumption that bettors are rank dependent expected utility maximizers, these inefficiencies tend to disappear.

Optimum building energy retrofits under technical and economic uncertainty

In a prior study, the authors showed that decomposing holistic, blackbox building energy models into discrete components can increase the computational efficiency of large-scale retrofit analysis. This paper presents an extension of that methodology to include an economic cost-benefit model. The entire framework now comprises an integrated modelling procedure for the simulation and optimisation of retrofit decisions for individual buildings. Potential decisions can range from the installation of demand-side measures to the replacement of energy supply systems and combinations therewithin. The classical decision theories of Wald, Savage, and Hurwicz are used to perform non-probabilistic optimisation under both technical and economic uncertainty. Such techniques, though simple in their handling of uncertainty, may elucidate robust decisions when the use of more intensive, probabilistic assessments of uncertainty is either infeasible or impractical.

Quantum Decision Making by Social Agents

The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social interactions, which influence the decisions of individual agents, leads to a generalization of the quantum decision theory developed earlier by the authors for separate individuals. The generalized approach is free of the standard paradoxes of classical decision theory. This approach also explains the error attenuation effects observed for the paradoxes occurring when decision makers, who are members of a society, consult with each other, increasing in this way the available mutual information. A precise correspondence between quantum decision theory and classical utility theory is formulated via the introduction of an intermediate probabilistic version of utility theory of a novel form, which obeys the requirement that zero-utility prospects should have zero probability weights.

On Improved Loss Estimation for Shrinkage Estimators

Let X be a random vector with distribution Pθ where θ is an unknown parameter. When estimating θ by some estimator φ(X) under a loss function L(θ, φ), classical decision theory advocates that such a decision rule should be used if it has suitable properties with respect to the frequentist risk R(θ, φ). However, after having observed X = x, instances arise in practice in which φ is to be accompanied by an assessment of its loss, L(θ, φ(x)), which is unobservable since θ is unknown. A common approach to this assessment is to consider estimation of L(θ, φ(x)) by an estimator δ, called a loss estimator. We present an expository development of loss estimation with substantial emphasis on the setting where the distributional context is normal and its extension to the case where the underlying distribution is spherically symmetric. Our overview covers improved loss estimators for least squares but primarily focuses on shrinkage estimators. Bayes estimation is also considered and comparisons are made with unbiased estimation.

Risky Decisions

Decision behavior in realistic risky scenarios is quite different from that in gambles: Decision makers in the former are less interested in probability information than they are in the latter. Instead, they often attempt to actively manipulate the risk in an otherwise attractive alternative using a risk-defusing operator (RDO). An RDO is an action intended by the decision maker to be performed in addition to the risky but otherwise attractive alternative, and it is expected to decrease the risk (e.g., vaccination, insurance). The search for an RDO and the incorporation of a detected RDO into the alternative cannot be modeled with classical decision theories or heuristics. In this article I present risk-management-decision theory, which describes the decision process with and without RDOs, and give an overview about experimental research with RDOs. I discuss the consequences of the RDO concept for theories of decision behavior.

Neural network and classification approach in identifying customer behavior in the banking sector: A case study of an international bank

The customer relationship focus for banks is in development of main competencies and strategies of building strong profitable customer relationships through considering and managing the customer impression, influence on the culture of the bank, satisfactory treatment, and assessment of valued relationship building. Artificial neural networks (ANNs) are used after data segmentation and classification, where the designed model register records into two class sets, that is, the training and testing sets. ANN predicts new customer behavior from previously observed customer behavior after executing the process of learning from existing data. This article proposes an ANN model, which is developed using a six-step procedure. The back-propagation algorithm is used to train the ANN by adjusting its weights to minimize the difference between the current ANN output and the desired output. An evaluation process is conducted to determine whether the ANN has learned how to perform. The training process is halted periodically, and its performance is tested until an acceptable result is obtained. The principles underlying detection software are grounded in classical statistical decision theory.

A classical decision theoretic perspective on worst-case analysis

We examine worst-case analysis from the standpoint of classical Decision Theory. We elucidate how this analysis is expressed in the framework ofWald’s famous Maximin paradigm for decision-making under strict uncertainty. We illustrate the subtlety required in modeling this paradigm by showing that information-gap’s robustness model is in fact a Maximin model in disguise.

The Interplay of Routine and Decision-Making in Action: A Literature Review and Proposed Synthesis

What precisely is the relation between routine and decision-making? How do actors’ decisions affect routine – and, in turn, how does the development of routine affect decision-making? Over the last few decades, research into routine has been increasingly disconnected from classical decision theory. The main aim of this paper is to bridge this ‘schism’ and find a new synthesis. A review of the literature shows that many of the basic insights into action and repetition are surprisingly uncontroversial. Building on these insights, the main contribution of this paper is to offer a ‘cognitive’ adaptation of routine that re-connects both concepts and serves as a conceptual foundation for an investigation of the interplay of routine and decision-making in action. This investigation throws a completely new light on what Feldman (2000) and Pentland/Feldman (2005) call the ostensive aspect of routine.

Are Monkeys Sensitive to the Regularity of Pay-off?

Animals commonly face fluctuations in their environment and resources. To maximize their benefits,they need to integrate the risks attached to potential pay-offs. We do not know, however, to what extent individuals account for irregularity in the latter. We tested the sensitivity of monkeys (Cebusapella, Macaca tonkeana, M. fascicularis) to the irregularity of pay-offs in two different tasks. In a first experiment, the subjects were given an exchange task where the reward probability varied between different conditions, but yielded the same average pay-off. There was no evidence of subjects favoring either condition, meaning that they behaved in accordance with the predictions ofthe classical decision theory (Expected Utility Theory). In a second experiment, we offered to subjects a choice between two options involving different pay-off regularity. In this case, a wide range of inter-individual variation was found in the choices of individuals. Whereas monkeys accepted irregular pay-off in a rational way, there were individual biases in their preferences. These results indicate that the preferences of animals in a risky situation were not unequivocally shaped by the environment in which species have evolved.

MATHEMATICAL STRUCTURE OF QUANTUM DECISION THEORY

One of the most complex systems is the human brain whose formalized functioning is characterized by decision theory. We present a "Quantum Decision Theory" of decision-making, based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to explain a variety of interesting fallacies and anomalies that have been reported to particularize the decision-making of real human beings. The theory describes entangled decision-making, non-commutativity of subsequent decisions, and intention interference of composite prospects. We demonstrate how the violation of the Savage's sure-thing principle (disjunction effect) can be explained as a result of the interference of intentions, when making decisions under uncertainty. The conjunction fallacy is also explained by the presence of the interference terms. We demonstrate that all known anomalies and paradoxes, documented in the context of classical decision theory, are reducible to just a few mathematical archetypes, all of which allow the finding of straightforward explanations in the frame of the developed quantum approach.

Adaptive utility and trial aversion

Decision making with adaptive utility provides a generalisation to classical Bayesian decision theory, allowing the creation of a normative theory for decision selection when preferences are initially uncertain. In this paper we address some of the foundational issues of adaptive utility as seen from the perspective of a Bayesian statistician. The implications that such a generalisation has upon the traditional utility concepts of value of information and risk aversion are also explored, with a new concept of trial aversion introduced that is similar to risk aversion, but which concerns a decision maker's aversion to selecting decisions with high uncertainty over resulting utility.

Quantum Mechanics and Human Decision Making

In physics, at the beginning of the twentieth century it was recognized that some experiments could not be explained by the conventional classical mechanics but the same could be explained by the newly discovered quantum theory. It resulted into a new mechanics called quantum mechanics that revolutionized the scientific and technological developments. Again at the beginning of the twenty-first century, it is being recognized that some experiments related with the human decision making processes could not be explained by the conventional classical decision theory but the same could be explained by the models based on quantum mechanics. It is now recognized that we need quantum mechanics in psychology as well as in economics and finance. In this paper we attempt to advance and explain the present understanding of applicability of quantum mechanics to the human decision making processes. Using the postulates analogous to the postulates of quantum mechanics, we show the derivation of the quantum interference equation to illustrate the quantum approach. The explanation of disjunction effect experiments of Tversky and Shafir (1992) has been chosen to demonstrate the necessity of a quantum model. Further to suggest the possibility of application of the quantum theory to the business related decisions, some terms such as price operator, state of mind of the acquiring firm, etc. are introduced and discussed in context of the merger/acquisition of business firms. The possibility of the development in the areas such as quantum finance, quantum management, application of quantum mechanics to the human dynamics related with health care management, etc. is also indicated.

A bird's view of info‐gap decision theory

Purpose – The purpose of this paper is to clarify a number of important facts about info‐gap decision theory.Design/methodology/approach – Theorems are put forward to rebut claims made about info‐gap decision theory in papers published in this journal and elsewhere.Findings – Info‐gap's robustness model is a simple instance of the most famous model in classical decision theory for the treatment of decision problems subject to severe uncertainty, namely Wald's maximin model. This simple instance is the equivalent of the well‐established model known universally as radius of stability. Info‐gap's robustness model has an inherent local orientation. Therefore, it is in principle unable to address the fundamental difficulties presented by the type of severe uncertainty that is postulated by info‐gap decision theory.Practical implications – These findings caution against accepting the assertions made in the info‐gap literature about: info‐gap decision theory's role and place in decision making under severe uncer...