Classical Decision Theory Research Articles

Using ELECTRE to analyse the behaviour of economic agents

According to behavioural finance, economic agents display cognitive bias, heuristics and emotional factors that generate preferences which systematically violate the rationality assumptions of the normative model of classical decision theory. Rather than maximizing the expected utility, representing the optimal choice, they attempt to accept a satisfactory solution. Morton and Fasolo (J Oper Res Soc 60:268–275, 2009) outlined some behavioural findings relevant to the practice of multicriteria approach. In this paper, we propose a multicriteria model for analysing some experiments proposed by Kahneman and Tversky (Econometrica 47:263–29 l, 1979). Our aim is to verify whether a multicriteria tool reduces or minimizes cognitive biases. We focus on ELECTRE due to its main features: it accepts the violation of some mathematical axioms. By a simulation study, we represent a set of prospects by means of decision matrices: the prospects are considered as alternatives, the events as criteria, the probabilities of events as the weights assigned to criteria. Then, we apply ELECTRE to verify whether the preference ranking among the alternatives confirms the results obtained by Kahneman–Tversky, that is, whether it is able to describe the emotional behaviours of economic agents.

Cost-Optimal Maintenance Planning for Defects on Wind Turbine Blades

Due to the considerable increase in clean energy demand, there is a significant trend of increased wind turbine sizes, resulting in much higher loads on the blades. The high loads can cause significant out-of-plane deformations of the blades, especially in the area nearby the maximum chord. This paper briefly presents a discrete Markov chain model as a simplified probabilistic model for damages in wind turbine blades, based on a six-level damage categorization scheme applied by the wind industry, with the aim of providing decision makers with cost-optimal inspection intervals and maintenance strategies for the aforementioned challenges facing wind turbine blades. The in-history inspection information extracted from a database with inspection information was used to calibrate transition probabilities in the discrete Markov chain model. With the calibrated transition probabilities, the damage evolution can be statistically simulated. The classical Bayesian pre-posterior decision theory, as well as condition-based maintenance strategy, was used as a basis for the decision-making. An illustrative example with transverse cracks is presented using a reference wind turbine.

The influence of horizontal and vertical product attribute information on decision making under risk: The role of perceived competence

Classical decision theory assumes that risk is negatively associated with the attractiveness of an option. Thus, it is not surprising that individuals may seek to reduce the level of risk associated with a purchase by choosing a product based on information that allows a direct evaluation of objective value. This research proposes that, under risk, individuals prefer to utilize information that they perceive themselves to be more knowledgeable as a result of a tendency toward favorable perceptions of their own competence, which could lead to choices with negative implications for one's own experienced utility. We demonstrate that, under higher levels of risk, decision makers increase their reliance on attributes that reflect their own personal preference (i.e., horizontal attributes) rather than on attributes that unambiguously indicates a superior product (i.e., vertical attributes) when making a choice. This result is reversed when knowledge about vertical attributes is increased.

Sour grapes and sweet victories: How actions shape preferences.

Classical decision theory postulates that choices proceed from subjective values assigned to the probable outcomes of alternative actions. Some authors have argued that opposite causality should also be envisaged, with choices influencing subsequent values expressed in desirability ratings. The idea is that agents may increase their ratings of items that they have chosen in the first place, which has been typically explained by the need to reduce cognitive dissonance. However, evidence in favor of this reverse causality has been the topic of intense debates that have not reached consensus so far. Here, we take a novel approach using Bayesian techniques to compare models in which choices arise from stable (but noisy) underlying values (one-way causality) versus models in which values are in turn influenced by choices (two-way causality). Moreover, we examined whether in addition to choices, other components of previous actions, such as the effort invested and the eventual action outcome (success or failure), could also impact subsequent values. Finally, we assessed whether the putative changes in values were only expressed in explicit ratings, or whether they would also affect other value-related behaviors such as subsequent choices. Behavioral data were obtained from healthy participants in a rating-choice-rating-choice-rating paradigm, where the choice task involves deciding whether or not to exert a given physical effort to obtain a particular food item. Bayesian selection favored two-way causality models, where changes in value due to previous actions affected subsequent ratings, choices and action outcomes. Altogether, these findings may help explain how values and actions drift when several decisions are made successively, hence highlighting some shortcomings of classical decision theory.

Algorithm of classification based on fuzzy logic with expanding number of outputs

In this article the problem of automatic generation of a knowledge base which consists of production rules for training dataset using fuzzy logic methods and a rule for comparing the values of an output variable is considered. An algorithm for the formation of fuzzy production rules is proposed. An actual problem of development and improvement of artificial intelligence algorithms and fuzzy logic application for solving a wider range of problems is considered. With the help of such systems are possible to eliminate the difficulties of formalizing knowledge about technological processes; also it is possible to organize recognition of nonstandard and emergency situations without using precise mathematical models and classical decision theory based on the tool of mathematical equations. The development of this area is relevant, as the number of tasks are constantly increasing, and the amount of knowledge becomes too large to handle them manually. The construction of an exact mathematical model for poorly formalized objects and processes are very difficult task, due to the lack of complete information. The situation becomes even more complicated if the properties of the object or process change dynamically. Therefore, the development of mathematical methods and algorithms that allow structuring the system of rules and determining the order of their calls to control consistency and completeness to optimize the number of rules, are an actual task. Modern approaches to the automation of these processes are considered. These approaches significantly improve the work of expert systems, but they allow to work only with static knowledge bases, limit the number of logical inferences and are not applicable for cases when it is necessary to add new logical rules to the existing system. In this article, an approach is developed that makes it possible to expand the knowledge base of the expert system with new rules in the process of exploitation. The developed algorithm has following advantages: high speed of problem solving; the ability that allows expanding the number of system responses without changing the scope of the rules and the program itself; expanding the range of application of fuzzy logic algorithms. The developed algorithm has following disadvantages: if the system's response database has objects that are similar to each other, they can have the same center of gravity, which in turn leads to additional checks; the minimum distance for mapping the object should be selected experimentally. The application of this algorithm can be seen on the website of the program, which classifies, maps an arbitrary user in a set of comic book characters database "CMD - Combat Marvel DC" [8]. The approach that was proposed has been successfully implemented using the C/C ++ and JavaScript languages, and JSON open-standard file format that uses human-readable text to transmit data objects consisting of attribute–value pairs and array data types. Software that was used for development: NetBeans IDE, MinGW, GNU Compiler Collection, WhiteStarUML, GitHub, WebGL, Chrome, Mozilla Firefox, Opera

Analysis of Wallace’s Proof of the Born Rule in Everettian Quantum Mechanics: Formal Aspects

To solve the probability problem of the Many Worlds Interpretation of Quantum Mechanics, D.Wallace has presented a formal proof of the Born rule via decision theory, as proposed by D.Deutsch. The idea is to get subjective probabilities from rational decisions related to quantum measurements, showing the non-probabilistic parts of the quantum formalism, plus some rational constraints, ensure the squared modulus of quantum amplitudes play the role of such probabilities. We provide a new presentation of Wallace's proof, reorganized to simplify some arguments, and analyze it from a formal perspective. Similarities with classical decision theory are made explicit, to clarify its structure and main ideas. A simpler notation is used, and details are filled in, making it easier to follow and verify. Some problems have been identified, and we suggest possible corrections.

NEOKLASYCZNE PODEJŚCIE DO TRADYCYJNYCH UBEZPIECZEŃ GOSPODARCZYCH – WSTĘP DO TEORII UBEZPIECZEŃ ROLNYCH

The contemporary agriculture is among the most risky economic activities. In addition to the previously known production, price and market risk, and later also the financial risk, today agricultural producers are increasingly more often confronted with institutional risk and personnel management risk and risk related to climate change. On the other hand, farmers have at their disposal numerous tools and strategies to counteract threats and mitigate their negative effects. Among these risk management instruments and strategies, traditional/ conventional insurance of crops, livestock and tangible assets is still important. In this context, the basic goal of the article is to generalise the theoretical foundations of the above-mentioned insurance, but limited to their historically oldest approach; hence on the basis of neoclassical microeconomics and classical decision theory. According to the convention existing, the essence of the theory/hypothesis of the expected utility of von Neumann–Morgenstern is first analysed. In the last part of the article, the assumptions of the expected utility theory are concretised on the example of agricultural insurance.

Quantum-like model of subjective expected utility

We present a very general quantum-like model of lottery selection based on representation of beliefs of an agent by pure quantum states. Subjective probabilities are mathematically realized in the framework of quantum probability (QP). Utility functions are borrowed from the classical decision theory. But in the model they are represented not only by their values. Heuristically one can say that each value ui=u(xi) is surrounded by a cloud of information related to the event (A,xi). An agent processes this information by using the rules of quantum information and QP. This process is very complex; it combines counterfactual reasoning for comparison between preferences for different outcomes of lotteries which are in general complementary. These comparisons induce interference type effects (constructive or destructive). The decision process is mathematically represented by the comparison operator and the outcome of this process is determined by the sign of the value of corresponding quadratic form on the belief state. This operational process can be decomposed into a few subprocesses. Each of them can be formally treated as a comparison of subjective expected utilities and interference factors (the latter express, in particular, risks related to lottery selection). The main aim of this paper is to analyze the mathematical structure of these processes in the most general situation: representation of lotteries by noncommuting operators.

Local and global optima in decision-making: a sheaf-theoretical analysis of the difference between classical and behavioral approaches

One of the main differences between the traditional and the behavioral approaches to decision-making is that the latter has not yet been captured in a unifying framework. This hampers in a certain way the whole research program and raises the question of whether this competing approach can provide an encompassing alternative to the classical one. We analyze this issue in light of the problem of reconstructing global choices of an agent up from the solutions found for local problems. We show that a representation based on category theory of the conditions for such reconstruction is general and robust enough to represent both the case in which problems are non-contextual and local as well as that, typical in the literature on behavioral decision-making, in which such properties do not hold. In the first case, we show how a sheaf-theoretical representation provides an abstract characterization of the global solution. In the latter case, we show how locality and contextuality generate obstructions toward the reconstruction of global solutions, yielding a possible clue for the intrinsic difference between behavioral and classical decision theory.

On the hierarchical nature of partial preferences over lotteries

In this work we consider preference relations that might not be total. Partial preferences may be helpful to represent those situations where, due to lack of information or vacillating desires, the decision maker would like to maintain different options “alive” and defer the final decision. In particular, we show that, when totality is relaxed, different axiomatizations of classical Decision Theory are no longer equivalent but form a hierarchy where some of them are more restrictive than others. We compare such axiomatizations with respect to theoretical aspects—such as their ability to propagate comparability/incomparability over lotteries and the induced topology—and to different preference elicitation methodologies that are applicable in concrete domains. We also provide a polynomial-time procedure based on the bipartite matching problem to determine whether one lottery is preferred to another.

An approach to decision making based on dynamic argumentation systems

In this paper we introduce a formalism for single-agent decision making that is based on Dynamic Argumentation Frameworks. The formalism can be used to justify a choice, which is based on the current situation the agent is involved. Taking advantage of the inference mechanism of the argumentation formalism, it is possible to consider preference relations, and conflicts among the available alternatives for that reasoning. With this formalization, given a particular set of evidence, the justified conclusions supported by warranted arguments will be used by the agent's decision rules to determine which alternatives will be selected. We also present an algorithm that implements a choice function based on our formalization. Finally, we complete our presentation by introducing formal results that relate the proposed framework with approaches of classical decision theory.

Evaluating gambles using dynamics.

Gambles are random variables that model possible changes in wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but their generality limits predictive power. Expectation value maximizers are defined as rational in economics, but expectation values are only meaningful in the presence of ensembles or in systems with ergodic properties, whereas decision-makers have no access to ensembles, and the variables representing wealth in the usual growth models do not have the relevant ergodic properties. Simultaneously addressing the shortcomings of utility and those of expectations, we propose to evaluate gambles by averaging wealth growth over time. No utility function is needed, but a dynamic must be specified to compute time averages. Linear and logarithmic "utility functions" appear as transformations that generate ergodic observables for purely additive and purely multiplicative dynamics, respectively. We highlight inconsistencies throughout the development of decision theory, whose correction clarifies that our perspective is legitimate. These invalidate a commonly cited argument for bounded utility functions.

On the equivalence between non-factorizable mixed-strategy classical games and quantum games.

A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding mathematical question is to understand the conditions under which a classical game-theoretic setting can be transformed to a quantum game, and under which conditions there is an equivalence. In this paper, we consider quantum games as those that allow non-factorizable probabilities. We discuss two approaches for obtaining a non-factorizable game and study the outcome of such games. We demonstrate how the standard version of a quantum game can be analysed as a non-factorizable game and determine the limitations of our approach.

Role of Information in Decision Making of Social Agents

The influence of additional information on the decision making of agents, who are the 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 (QDT) 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 QDT 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.

Decision-Making and the Barriers to Judicious Antibiotic Use.

Escalating antibiotic resistance is a “multinational public health crisis.”1 As children are heavy consumers of antibiotics and serve as community reservoirs of resistant organisms, promoting judicious pediatric antibiotic use can have high impact.2 Decreasing prescribing rates over the past decade have recently plateaued; young children still receive, on average, >1 antibiotic prescription per year, most for broad-spectrum drugs, with 25% of antibiotics prescribed for diagnoses for which antibiotics are unlikely to be of benefit.3,4 These data seem to defy rational logic; why is this problem so recalcitrant? Vaz et al,5 in this issue of Pediatrics , address this important question by recognizing that antibiotic prescribing decisions take place within the context of the physician–patient relationship, where the perspectives of individual families and physicians often take precedence over potential future risks of resistance for society at large. Classic decision theory and behavioral economics can help to explain how we make flawed choices. Vaz et al5 demonstrate that many parents have imperfect information; they are mistaken about the indications for antibiotic treatment and remain confused about the distinction between bacterial and viral infections. Although … Address correspondence to Sharon B. Meropol, MD, PhD, Rainbow Babies and Children’s Hospital, 11100 Euclid Ave, Mailstop 6019, Cleveland, OH 44106. E-mail: sharon.meropol{at}uhhospitals.org

A Solution To Rational Decision Making Via Compositional Data Analysis: A Case Study Using Students Cellular Phone Tendencies

Decisions can be simple or complex depending on the alternatives available to the decision maker, and also, to the different state of the worlds. In classical decision theory, a pay-off table is analysed in order to make an optimal decision. Here, the decision process involves the definition of different alternatives and state of the worlds, cost or profit calculations of the pay-off table, and probability values, if any, related to state of the worlds. In decision problems, sometimes, it may be necessary to involve emotional attachments in order to create pay-off table. In this setting, rather than using the usual cost or profit values, some satisfaction values can be assigned to the criteria and the rationality of different alternatives can be investigated. In this study, the rationality approach to decision pay-off matrix is demonstrated using a real life example regarding a cellular phone purchase. Furthermore, a compositional data analysis approach is also suggested, and the contributions of the compositional data analysis to decision theory are given.

On Sturdy Policy Evaluation

This paper provides an overview of different approaches to policy evaluation. We focus on how different types of uncertainty should be accounted for in the policy evaluation process. Appropriate incorporation of uncertainty in policy evaluation leads to what we call sturdy decisions. We describe classical Bayesian decision theory and decision theory under ambiguity. We provide examples ranging from the deterrent effect of capital punishment to Food and Drug Administration approval rules to environmental policy to illustrate the conceptual framework we present. Throughout, the role of judgment in any formal approach to policy evaluation is emphasized.

FAIR CHANCE AND MODAL CONSEQUENTIALISM

Abstract:This paper develops aMultidimensional Decision Theoryand argues that it better captures ordinary intuitions about fair distribution of chances than classical decision theory. The theory is an extension of Richard Jeffrey’s decision theory to counterfactual prospect and is a form ofModal Consequentialism, according to which the value of actual outcomes often depends on what could have been. Unlike existing versions of modal consequentialism, the multidimensional decision theory allows us toexplicitlymodel the desirabilistic dependencies between actual and counterfactual outcomes that, I contend, are at the heart of common intuitions about fair distribution of chances.

Maximum Relative Entropy Updating and the Value of Learning

We examine the possibility of justifying the principle of maximum relative entropy (MRE) considered as an updating rule by looking at the value of learning theorem established in classical decision theory. This theorem captures an intuitive requirement for learning: learning should lead to new degrees of belief that are expected to be helpful and never harmful in making decisions. We call this requirement the value of learning. We consider the extent to which learning rules by MRE could satisfy this requirement and so could be a rational means for pursuing practical goals. First, by representing MRE updating as a conditioning model, we show that MRE satisfies the value of learning in cases where learning prompts a complete redistribution of one’s degrees of belief over a partition of propositions. Second, we show that the value of learning may not be generally satisfied by MRE updates in cases of updating on a change in one’s conditional degrees of belief. We explain that this is so because, contrary to what the value of learning requires, one’s prior degrees of belief might not be equal to the expectation of one’s posterior degrees of belief. This, in turn, points towards a more general moral: that the justification of MRE updating in terms of the value of learning may be sensitive to the context of a given learning experience. Moreover, this lends support to the idea that MRE is not a universal nor mechanical updating rule, but rather a rule whose application and justification may be context-sensitive.

Modelling decision making under risk and uncertainty by novel utility measures

In this paper, we will address the classical decision theories (the expected value, EV, and expected utility theories, EUTs) along with their violations, such as the common consequence, common ratio effect, violation of betweenness and the fourfold risk pattern. In particular, a numerical method is proposed to determine the utility function of an individual or group of individuals. The approach depends on the individual's evaluation of the certainty equivalent (CE) of a decision problem under uncertainty. Later, we propose an optimisation model to predict human preference between pairs of reward scenarios in which uncertainty is involved. The optimisation model implements binary logistic regression (BLR). Both SPSS and Excel Solver were used in the optimisation and parameter fitting. The presented model is verified via collected survey and literature studies. It is found that the model is able to explain the violations and serve as a new replica to predict human preferences.