There are presently two leading foreign policy decision-making paradigms in vogue. The first is based on the classical or rational model originally posited by von Neumann and Morgenstern to explain microeconomic decisions. The second is based on the cybernetic perspective whose groundwork was laid by Herbert Simon in his early research on bounded rationality. In this paper we introduce a third perspective — thepoliheuristic theory of decision-making — as an alternative to the rational actor and cybernetic (...) paradigms in international relations. This theory is drawn in large part from research on heuristics done in experimental cognitive psychology. According to the poliheuristic theory, policy makers use poly (many) heuristics while focusing on a very narrow range of options and dimensions when making decisions. Among them, the political dimension is noncompensatory. The paper also delineates the mathematical formulations of the three decision-making models. (shrink)

There are presently two leading foreign policy decision-making paradigms in vogue. The first is based on the classical or rational model originally posited by von Neumann and Morgenstern to explain microeconomic decisions. The second is based on the cybernetic perspective whose groundwork was laid by Herbert Simon in his early research on bounded rationality. In this paper we introduce a third perspective -- the poliheuristic theory of decision-making -- as an alternative to the rational actor and (...) cybernetic paradigms in international relations. This theory is drawn in large part from research on heuristics done in experimental cognitive psychology. According to the poliheuristic theory, policy makers use poly (many) heuristics while focusing on a very narrow range of options and dimensions when making decisions. Among them, the political dimension is noncompensatory. The paper also delineates the mathematical formulations of the three decision-making models. (shrink)

Due to the increasing number of people traveling by air, the passenger flow at the airport is increasing, and the problem of passenger drop-off and pickup has a huge impact on urban traffic. The difficulty of taking a taxi at the airport is still a hot issue in the society. Aiming at the problem of optimizing the allocation of taxi resource, this paper is based on the cost-benefit analysis method to determine the factors that affect the taxi driver’s decision- (...) class='Hi'>making. The mathematical methods such as function equation, BP neural network algorithm, and queuing theory were used to establish a complete decision-making model for taxi drivers and an optimization model of dispatching efficiency at the airport. A conclusion has been drawn that the allocation of airport taxi resource should be arranged closely related to drivers’ revenue and the layout of airport line. (shrink)

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected in such the experiments have “quantum-like” properties, which can not be explained in (...) classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33–59, 1999). (shrink)

This book introduces readers to the concept of the neutrosophic set which can deal with dynamic and complex decision-making problems. With the complexity of the socio-economic environment, today's decision-making is one of the most notable ventures, whose mission is to decide the best alternative under numerous known or unknown criteria. This book provides a large amount of theoretical and practical information about the latest research in the field, allowing readers to gain an extensive understanding of both (...) the fundamentals and applications of neutrosophic sets to solve different kinds of decision-making problems and mathematical programming such as medical diagnosis, pattern recognition, construction problems, technology selection etc. (shrink)

Neuroscience has illuminated the neural basis of decision-making, providing evidence that supports specific models of decision-processes. These models typically are quite mechanical, the realization of abstract mathematical “diffusion to bound” models. While effective decision-making seems to be essential for sophisticated behavior, central to an account of freedom, and a necessary characteristic of self-governing systems, it is not clear how the simple models neuroscience inspires can underlie the notion of self-governance. Drawing (...) from both philosophy and neuroscience I explore ways in which the proposed decision-making architectures can play a role in systems that can reasonably be thought of as “self-governing”. (shrink)

While game theory has been transformative for decision making, the assumptions made can be overly restrictive in certain instances. In this work, we investigate some of the underlying assumptions of rationality, such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-k reasoning and quantal response equilibrium (QRE) respectively. Specifically, we propose an information-theoretic two-parameter model called the quantal hierarchy model, which can relax both mutual consistency and best response while still (...) approximating level-k, QRE, or typical Nash equilibrium behavior in the limiting cases. The model is based on a recursive form of the variational free energy principle, representing higher-order reasoning as (pseudo) sequential decision-making in extensive-form game tree. This representation enables us to treat simultaneous games in a similar manner to sequential games, where reasoning resources deplete throughout the game-tree. Bounds in player processing abilities are captured as information costs, where future branches of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the effectiveness of the quantal hierarchy model in several canonical economic games, both simultaneous and sequential, using out-of-sample modelling. (shrink)

This book provides an overview of behavioral decision theory and related research findings. In brief, behavioral decision theory is a general term for descriptive theories to explain the psychological knowledge related to decision-making behavior. It is called a theory, but actually it is a combination of various psychological theories, for which no axiomatic systems, such as the utility theory widely used in economics, have been established; it is often limited to qualitative knowledge. However, as suggested in (...) the studies of H. A. Simon, who won the Nobel Prize for Economics in 1978, and D. Kahneman, who won the prize in 2002, the psychological methodology and knowledge of behavioral decision theory have been applied widely in such fields as economics, business administration, and engineering, and are expected to become more useful in the future. This book explains various behavioral decision theories related to decision-making processes. Numerous models have been proposed to explain the psychological processes related to such a selection of decision strategies, and this book also introduces some new models that are useful to explain decision-making processes. The book concludes with speculation about the future of modern behavioral decision theories while referring to their relation to fields associated with neuroscience, such as neuroeconomics, that have been developed in recent years. In addition, each chapter includes a bibliography that can be referred to when studying more details related to behavioral decision theory. Reading this book requires no advanced expertise; nonetheless, an introductory knowledge of psychology, business administration, and economics, and approximately a high school graduate’s level of mathematics should facilitate the reader’s comprehension of the content. (shrink)

A reasoned argument or tarka is essential for a wholesome vāda that aims at establishing the truth. A strong tarka constitutes of a number of elements including an anumāna based on a valid hetu. Several scholars, such as Dharmakīrti, Vasubandhu and Dignāga, have worked on theories for the establishment of a valid hetu to distinguish it from an invalid one. This paper aims to interpret Dignāga’s hetu-cakra, called the wheel of grounds, from a modern philosophical perspective by deconstructing it into (...) a simple probabilistic mathematical model. The objective is to understand how and why a vāda based on a probabilistically weaker hetu can degrade into a Jalpa or vitaṇḍā. To do so, the paper maps the concept of ‘Bounded Rationality’ onto the hetu-cakra. Bounded Rationality, an idea coined by the management thinker Herbert Simon, is often employed in understanding decision-making processes of rational agents. In the context of this paper, the concept would state that the prativādin and ālocaka (debater) may not hold unbounded information to back their pratijñā (proposition). The paper argues that within the probabilistically deconstructed hetu-cakra model, most people argue in the ‘Zone of Bounded Rationality’, and thus, the probability of a debate degrading into Jalpa or vitaṇḍā is high. -/- . (shrink)

Legal scholarship exploring the nature of evidence and the process of juridical proof has had a complex relationship with formal modeling. As evident in so many fields of knowledge, algorithmic approaches to evidence have the theoretical potential to increase the accuracy of fact finding, a tremendously important goal of the legal system. The hope that knowledge could be formalized within the evidentiary realm generated a spate of articles attempting to put probability theory to this purpose. This literature was both insightful (...) and frustrating. Much light was shed on the legal system, but it also quickly became evident that the tools of probability theory were in many ways ill-constructed for the task. Fundamental incompatibilities between the structure of legal decision making and the extant formal tools were identified, and it became evident that many of the purported explanations of legal phenomena were internally inconsistent. As a consequence, interest in this type of formal modeling declined, and attention was directed toward different kinds of explanations of the phenomena. Perhaps under the influence of a recent trend toward various types of formal modeling in legal scholarship, a recent burst of articles, rather than attempting to explain the macro structure of trials, which was the previous object of interest, attempts to quantify the probative value of various items of evidence in ways consistent with the formal features of various probability theories, and then to study decision making from that perspective. For example, the value of evidence is often purported to be its likelihood ratio, that is, the probability of discovering or receiving the evidence given a hypothesis (e.g., the defendant did it) divided by the probability of discovering or receiving the evidence given the negation of the hypothesis (the defendant didn't do it). Alternatively, the value of evidence is purported (more contextually) to be the information gain it provides, defined as the increase in probability it provides for a hypothesis above the probability of the hypothesis based on the other available evidence. Both conceptions then assume that all of the various probability assessments conform or ought to conform to the dictates of Bayes' theorem (that maintains consistency among such assessments); empirical studies are then done testing the extent to which this is so and proposing how the law can increase the probability that it is so. The general criticisms of using Bayes' theorem as a formal model of juridical proof are well known and were integral to the last wave of interest in formal modeling of the evidentiary process. This paper thus for the most part puts aside that more general issue, and focuses specifically on mathematical modeling of the value of particular items of evidence. The paper demonstrates that formal modeling has only limited value in explaining the value of legal evidence, much more limited than those constructing and discussing the models assume, and thus that the conclusions they draw about the value of evidence are unwarranted. This is done through a discussion of four recent examples that attempt to quantify evidence relating to, respectively, carpet fibers, infidelity, DNA random-match evidence, and character evidence used to impeach a witness. This article thus makes two contributions. First, and most importantly, it is another demonstration of the complex relationship between algorithmic tools and legal decision making. Second, at a minimum it points out serious pitfalls for analytical or empirical studies of juridical proof. (shrink)

We propose a model of an agent’s probability and utility that is a compromise between Savage (The foundations of statistics, Wiley, 1954) and Jeffrey (The Logic of Decision, McGraw Hill, 1965). In Savage’s model the probability–utility pair is associated with preferences over acts which are assignments of consequences to states. The probability is defined on the state space, and the utility function on consequences. Jeffrey’s model has no consequences, and both probability and utility are defined on the same set (...) of propositions. The probability–utility pair is associated with a desirability relation on propositions. Like Savage we assume a set of consequences and a state space. However, we assume that states are comprehensive, that is, each state describes a consequence, as in Aumann (Econometrica 55:1–18, 1987). Like Jeffrey, we assume that the agent has a preference relation, which we call desirability, over events, which by definition involves uncertainty about consequences. For a given probability and utility of consequences, the desirability relation is presented by conditional expected utility, given an event. We axiomatically characterize desirability relations that are represented by a probability–utility pair. We characterize the family of all the probability–utility pairs that represent a given desirability relation. (shrink)

A recent interpretation of artificial intelligence (AI) (Floridi 2013, 2022) suggests that the implementation of AI demands the investigation of the binding conditions that make it possible to build and integrate artifacts into our lived world. Such artifacts can successfully interact with the world because our environment has been designed to be compatible with intelligent machines (such as robots). As the use of AI becomes ubiquitous in society, possibly leading to the formation of increasingly intelligent bio-technological unions, there will likely (...) be a coexistence of a plethora of micro-environments wrapped and tailored around humans and basic robots. The key element of this pervasive process will be the capacity to integrate biological realms in an infosphere suitable for the implementation of AI technologies. This process will require extensive datafication. This is because data is the basis of the logical-mathematical codes and models that drive and guide AI. This process will have huge consequences on workplaces, on workers, as well as on the decision-making processes required for the functioning of future societies. In this paper we will offer a comprehensive reflection on the moral and social implications of datafication as well as a set of considerations about its desirability, which will be informed by the following insights: (1) full protection of privacy may become structurally impossible, thus leading to undesirable forms of political and social control; (2) worker’s freedom may be reduced; (3) human creativity, imagination, and even divergence from AI logic might be channeled and possibly discouraged; (4) there will likely be a push towards efficiency and instrumental reason, which will become preeminent in production lines as well as in society. (shrink)

This article reviews the strengths and limitations of five major paradigms of medical computer-assisted decision making (CADM): (1) clinical algorithms, (2) statistical analysis of collections of patient data, (3) mathematical models of physical processes, (4) decision analysis, and (5) symbolic reasoning or artificial intelligence (Al). No one technique is best for all applications, and there is recent promising work which combines two or more established techniques. We emphasize both the inherent power of symbolic reasoning and (...) the promise of artificial intelligence and the other techniques to complement each other. (shrink)

The question “How can humans learn efficiently to make decisions in a complex, dynamic, and uncertain environment” is still a very open question. We investigate what effects arise when feedback is given in a computer-simulated microworld that is controlled by participants. This has a direct impact on training simulators that are already in standard use in many professions, e.g., for flight simulators for pilots, and a potential impact on a better understanding of human decision making in general. Our (...) study is based on a benchmark microworld with an economic framing, the IWR Tailorshop. N=94 participants played four rounds of the microworld, each 10 months, via a web interface. We propose a new approach to quantify performance and learning, which is based on a mathematical model of the microworld and optimization. Six participant groups receive different kinds of feedback in a training phase, then results in a performance phase without feedback are analyzed. As a main result, feedback of optimal solutions in training rounds improved model knowledge, early learning, and performance, especially when this information is encoded in a graphical representation. (shrink)

The predictive processing framework includes a broad set of ideas, which might be articulated and developed in a variety of ways, concerning how the brain may leverage predictive models when implementing perception, cognition, decision-making, and motor control. This article provides an up-to-date introduction to the two most influential theories within this framework: predictive coding and active inference. The first half of the paper (Sections 2–5) reviews the evolution of predictive coding, from early ideas about efficient coding in (...) the visual system to a more general model encompassing perception, cognition, and motor control. The theory is characterized in terms of the claims it makes at Marr's computational, algorithmic, and implementation levels of description, and the conceptual and mathematical connections between predictive coding, Bayesian inference, and variational free energy (a quantity jointly evaluating model accuracy and complexity) are explored. The second half of the paper (Sections 6–8) turns to recent theories of active inference. Like predictive coding, active inference models assume that perceptual and learning processes minimize variational free energy as a means of approximating Bayesian inference in a biologically plausible manner. However, these models focus primarily on planning and decision-making processes that predictive coding models were not developed to address. Under active inference, an agent evaluates potential plans (action sequences) based on their expected free energy (a quantity that combines anticipated reward and information gain). The agent is assumed to represent the world as a partially observable Markov decision process with discrete time and discrete states. Current research applications of active inference models are described, including a range of simulation work, as well as studies fitting models to empirical data. The paper concludes by considering future research directions that will be important for further development of both models. (shrink)

This article reviews the strengths and limitations of five major paradigms of medical computer-assisted decision making (CADM): (1) clinical algorithms, (2) statistical analysis of collections of patient data, (3) mathematical models of physical processes, (4) decision analysis, and (5) symbolic reasoning or artificial intelligence (Al). No one technique is best for all applications, and there is recent promising work which combines two or more established techniques. We emphasize both the inherent power of symbolic reasoning and (...) the promise of artificial intelligence and the other techniques to complement each other. Keywords: Diagnosis, Computer Assisted Decision Making, Artificial Intelligence * Current address: Intelligenetics, 124 University Avenue, Palo Alto, CA. 94301, U.S.A. ** Dr. Shortliffe is a Henry J. Kaiser Family Foundation Faculty Scholar in General Internal Medicine and recipient of research career development award LM0048 from the National Library of Medicine. CiteULike Connotea Del.icio.us What's this? (shrink)

In this study I discuss G. W. Leibniz's (1646-1716) views on rational decision-making from the standpoint of both God and man. The Divine decision takes place within creation, as God freely chooses the best from an infinite number of possible worlds. While God's choice is based on absolutely certain knowledge, human decisions on practical matters are mostly based on uncertain knowledge. However, in many respects they could be regarded as analogous in more complicated situations. In addition to (...) giving an overview of the divine decision-making and discussing critically the criteria God favours in his choice, I provide an account of Leibniz's views on human deliberation, which includes some new ideas. One of these concerns is the importance of estimating probabilities – in making decisions one estimates both the goodness of the act itself and its consequences as far as the desired good is concerned. Another idea is related to the plurality of goods in complicated decisions and the competition this may provoke. Thirdly, heuristic models are used to sketch situations under deliberation in order to help in making the decision. Combining the views of Marcelo Dascal, Jaakko Hintikka and Simo Knuuttila, I argue that Leibniz applied two kinds of models of rational decision-making to practical controversies, often without explicating the details. The more simple, traditional pair of scales model is best suited to cases in which one has to decide for or against some option, or to distribute goods among parties and strive for a compromise. What may be of more help in more complicated deliberations is the novel vectorial model, which is an instance of the general mathematical doctrine of the calculus of variations. To illustrate this distinction, I discuss some cases in which he apparently applied these models in different kinds of situation. These examples support the view that the models had a systematic value in his theory of practical rationality. (shrink)

A theoretical structure for multiattribute decision making is presented, based on a dynamical system for interactions in a neural network incorporating affective and rational variables. This enables modeling of problems that elude two prevailing economic decision theories: subjective expected utility theory and prospect theory. The network is unlike some that fit economic data by choosing optimal weights or coefficients within a predetermined mathematical framework. Rather, the framework itself is based on principles used elsewhere to model many (...) other cognitive and behavioral data, in a manner approximating how humans perform behavioral functions. Different, interconnected modules within the network encode (a) attributes of objects among which choices are made, (b) object categories, (c) and goals of the decision maker. An example is utilized to simulate the actual consumer choice between old and new versions of Coca-Cola. Potential applications are also discussed to market decisions involving negotiations between participants, such as international petroleum traders. (shrink)

The globalization in business and tourism becomes crucial more and more for the economical sustainability of local communities. In the presence of an epidemic outbreak, there must be such a decision on the policy by the host community as whether to accept visitors or not, the number of acceptable visitors, or the condition for acceptable visitors. Making use of an SIRI type of mathematical model, we consider the influence of visitors on the spread of a reinfectious disease (...) in a community, especially assuming that a certain proportion of accepted visitors are immune. The reinfectivity of disease here means that the immunity gained by either vaccination or recovery is imperfect. With the mathematical results obtained by our analysis on the model for such an epidemic dynamics of resident and visitor populations, we find that the acceptance of visitors could have a significant influence on the disease’s endemicity in the community, either suppressive or supportive. (shrink)

As a compact representation of joint probability distributions over a dependence graph of random variables, and a tool for modelling and reasoning in the presence of uncertainty, Bayesian networks are of great importance for artificial intelligence to combine domain knowledge, capture causal relationships, or learn from incomplete datasets. Known as a NP-hard problem in a classical setting, Bayesian inference pops up as a class of algorithms worth to explore in a quantum framework. This paper explores such a research direction and (...) improves on previous proposals by a judicious use of the utility function in an entangled configuration. It proposes a completely quantum mechanical decision-making process with a proven computational advantage. A prototype implementation in Qiskit (a Python-based program development kit for the IBM Q machine) is discussed as a proof-of-concept. (shrink)

This paper is an attempt to understand how social knowledge affects human economic decision making. The paper discusses the nature of social knowledge in today’s context with special reference to how social knowledge influences consumers’ sentiments and their economic decisions. Social networks are being continuously flooded with various kinds of information and disinformation. Some of the information becomes knowledge for social network users who browse various kinds of content that are either entertaining or related to products and marketing. (...) Although reliability remains a critical issue regarding online information from social networks, it, however, provides some knowledge about diverse things, goods, and products being in use in different societies around the world. Some products advertised on social networks like Facebook may affect consumer decisions or provide information about new products. This paper presents a formal discussion on what social knowledge is and how it is originated, and what use it might have for such consumers. The paper designs a simplistic mathematical model for a theoretical understanding of the assumption that has practical implications regarding its utility in society. It is found that social networks generate enough social information that can influence user choice and preferences. The study has implications for both the users and the developers of social networking sites. (shrink)

The paper points out that Adam Smith’s famous argument about the “invisible hand” (IH) of markets can be inverted. While the IH argument suggests that the baker and butcher do what is in their costumers’ interests not because they care for their costumers, but out of their own self-interest, one can also defend the converse claim: if one cares for other people and finds a way to satisfy their needs, one can expect that those others will be willing to pay (...) for the satisfaction of their needs. The paper argues that the IH argument has a strong link to the view that the ultimate goal of management should be “profit maximization” and to neo-liberalism’s tenet that in a market economy where companies attempt to maximize profits, a “socially optimal” allocation will be achieved. It is argued, however, that profit maximization is well-defined only within a mathematical model, while real-world decision-making requires one to choose the “relevant set” of options before any assessment of associated profits can be attempted. “Profit maximization” is therefore characterized as a heuristic for managerial decision-making, and it is pointed out that it is by no means essential for management to be successful and sustainable. The inverse IH argument supports natural alternatives, such as Prahalad and Hart’s “bottom-of-the-pyramid” and Yunus’s “social entrepreneurship” approach. Both require the manager to focus on people’s needs first, and regard the “money-making” aspect as secondary. (shrink)

Often in insurance decision making, there are risk factors on which the insurer has an informational advantage over the consumer. But when the insurer sets and posts a premium for the consumer to consider, the consumer can potentially use the premium as an informational cue for the loss probability, and thereby to reduce the insurer’s informational advantage. We study, by means of a behavioral model, how consumers would use the premium as an informational cue in such contexts. The (...) belief formation process in our model assumes that both prior knowledge and the premium might have an impact on the consumer’s estimate of the loss probability. Moreover, the premium impacts the estimate through an anchoring-and-adjustment process. The model potentially leads to violations of rational expectations, with which the consumer overestimates the loss probability beyond what could be inferred from the premium, given the premise that the insurer must seek to break even or earn an expected profit. Our model analysis moreover implies that the frequency of such violations is non-increasing as the premium increases. Last, the model implies a generally inverted-U relationship between insurance demand and the premium so that the demand is upward sloping at low premium levels and downward sloping at high premium levels. A pilot field study and a laboratory experiment provide robust evidence for our model implications and calibrations for its parameters. (shrink)

This paper studies the three kinds of conservativeness in a jury decision-making structure: the voting rule, the threshold of reasonable doubt, and the legal information system. In a model of simultaneous voting, Feddersen and Pesendorfer (The American Political Science Review, 92(1), 23-35, 1998) argue that the unanimity rule is the worst-performing voting rule because voters with strategic behaviour mitigate the bias brought about by the voting rule. If this bias can be offset by an opposing (less conservative) bias (...) in the legal information system, we would be able to restore the rationality of informative voting. The new informative equilibrium is strictly better than the original strategic equilibrium in terms of ex post error probability. When a strategic equilibrium survives, we can lower the probability of convicted defendant being innocent by making the information system more informative or by forming a jury with a higher (more conservative) threshold of reasonable doubt. (shrink)

This work presents a post-positivist research framework to explain any surprising fact in the evolutionary path of a complex, dynamic and contingent social phenomenon. Primarily, it reconciles the ontological and epistemological assumptions of Critical Realism with the principles of American Pragmatism. Then, the research approach is presented: theoretical propositions about a social structure are translated into a set of grammar rules that acknowledges a pattern of sequences of events of either individual action or social interaction between actors within a real (...) social system. The result is a discrete mathematical model for a concrete category of social process based on these rules. Finally, data-grounded refinement of the theory is possible by the comparison between cases belonging to the same category, but differing about some contingent pattern of sequences of event outcomes. Consequently, their grammars differ in some pairs of context-sensitive rules that can explain this surprising fact, such that the derivation of this alternative historical trajectory of event outcomes becomes an extension to the early category of social process. In this sense, the proposed framework suggests there is a hierarchy of classes of grammars for middle-range explanations based upon the ontological assumption of the generative nature of social reality. (shrink)

Looks into evaluation of information provision probability from different sources, based on use of linguistic variables. Formation of functions appurtenant for its unclear variables provides for adoption of decisions by the decision maker, in conditions of nonprobabilistic equivocation. The development of market relations in Ukraine increases the independence and responsibility of enterprises in justifying and making management decisions that ensure their effective, competitive activities. As a result of the analysis, it is determined that the condition of economic facilities (...) can be described and determined by the decision-maker, in the presence of the necessary information. The confidence of the decision-maker in the information received is different and the decisions made have a correspondingly different level of information risk. It is important to substantiate the procedure for assessing the numerical extent of information risk in decision-making based on the information obtained in conditions of uncertainty. The use of a linguistic variable in the processing of expert data presented in the form of a matrix of binary relations of values of the membership function, which allowed to move to further processing of knowledge to support decision-making in the management of industrial, commercial, financial and other activities. As a mathematical model for estimating the numerical measure of information risk when making decisions based on the information obtained in conditions of non-stochastic uncertainty, a model has been developed to model natural language uncertainties, which differs from existing ones by formalizing knowledge taking into account uncertainty of input information. Making such a clear decision in a fuzzy environment has appropriate values of effectiveness and risk. The paper proposes all the functions and accessories of indicators of both quantitative nature and qualitative nature to bring their values in the field of definition to one scale. Then the indicator of the effectiveness of decision-making will be a measure of the clarity of the cross-section of fuzzy subsets, which correspond to the introduced indicators of information risk. The condition of economic facilities can be described and determined by the decision-maker, if the necessary information is available. Decision-making on thenumerical measure of information risk must be determined by a set of basic indicators, which can be both quantitative and qualitative in nature. Predictive values of indicators should be determined in conditions of nonstochastic uncertainty. In this case, the indicators of a quantitative nature can be determined by fuzzy triangular numbers, which implement a high level of confidence in the subjective judgments of experts. Indicators of qualitative nature should be presented in linguistic variables. The values of the indicators of qualitative nature that are predicted must be considered for all fuzzy variable terms-sets of linguistic variables introduced into consideration. For any fuzzy variable, the introduction to the consideration of a clear set of values as carriers of the α-level of its membership function allows to reduce to a single interpretation of the predicted values of indicators of quantitative and qualitative nature in terms of non-stochastic uncertainty. (shrink)

Stability definitions for describing human behavior under conflict when coalitions may form are generalized within the Graph Model for Conflict Resolution and algebraic formulations of these definitions are provided to allow computer implementation. The more general definitions of coalitional stabilities relax the assumption of transitive graphs capturing movements under the control of decision makers, either independently or cooperatively, and allow the convenient expansion to the case of coalitions of the four basic individual stabilities consisting of Nash stability, general metarationality, (...) symmetric metarationality, and sequential stability. To permit the various coalitional stabilities to be efficiently calculated and conveniently encoded within a decision support system, algebraic expressions for the coalitional stabilities are provided in this research. Furthermore, a range of the theorems establish the mathematical credibility of employing the innovative algebraic approach to conflict resolution when coalitions are present. Finally, a conflict over the proposed exportation of bulk water from Lake Gisborne within the Canadian Province of Newfoundland and Labrador is modelled and analyzed to illustrate the practical application of the different coalitional stabilities and the strategic insights they provide. (shrink)

In this study we analyze a recent controversy within the biomedical world, concerning the evaluation of safety of certain vaccines. This specific struggle took place among experts: the Danish epidemiologist Peter Gøtzsche on one side and a respected scientific institution, the Cochrane, on the other. However, given its relevance, the consequences of such a conflict invest a much larger spectrum of actors, last but not least the public itself. Our work is aimed at dissecting a specific aspect happening in this (...) complex scenario: strategy. In other words, we want to highlight the value and the impact of strategic decisions when complex issues, as those analyzed, are at stake. In order to address this we have decided to adopt a game-theoretic approach. Our work will be structured as it follows. First, we will introduce the controversy and the two main actors: Peter Gøtzsche and the Cochrane. Second, we will explain why this controversy is important and its value beyond its academic relevance. Third, we will frame the controversy as a game and will provide several models representing different situations, also furnishing an analysis of these distinct scenarios. In the end we will argue why such game-theoretic approach can be useful in dissecting this type of issues. (shrink)

This work presents a post-positivist research framework for explaining any surprising or anomalous fact in the evolutionary path of a complex, dynamic, and contingent social process. Firstly, it elaborates on the reconciliation betweenthe ontological and epistemological assumptions of Critical Realism with the principles of American Pragmatism. Next, the research method is presented: theoretical propositions about a social structure are translated into a set of grammar rules that acknowledge patterns of sequences of events, either involving individual action or interaction between actors (...) within a real social system. The result is a discrete mathematical model for a concrete category of social process based on these rules. Finally, data-grounded refinement of the theory is possible through comparison between cases belonging to the same category, but differing in some contingent pattern of sequences of event outcomes. Consequently, their grammars differ in some pairs of context-sensitive rules that explain this surprising fact, and the derivation of this alternative historical trajectory of event outcomes becomes an extension to the early category of social process. In this sense, the proposed framework suggests a hierarchy of classes of grammars for middle-range explanations based on the ontological assumption of the generative nature of social reality. (shrink)

This paper attempts to present a formal model for the science of decision where “science of decision” is restricted to the work that has been done in formal models and not those aspects connected with the gathering of empirical data and development of measures for the data. One of the difficulties in treating such a phenomenon as decision-making has been to give a precise statement of the problem. The literature of numerous fields is filled with (...) models and talk about models where various restrictions are imposed. Among all of these it seems that the formalistic or logical, game-theoretic, and statistical decision function conceptual schemas have solved some decision problems largely due to the fact that they could give a mathematical formulation of the problem and its solution. The result is that in these three fields the decision problem can be fed into a computer which grinds out an answer for each particular set of parameters. (shrink)

Individuals make decisions under uncertainty every day based on incomplete information concerning the potential outcome of the choice or chance levels. The choices individuals make often deviate from the rational or mathematically objective solution. Accordingly, the dynamics of human decision-making are difficult to capture using conventional, linear mathematical models. Here, we present data from a two-choice task with variable risk between sure loss and risky loss to illustrate how a simple nonlinear dynamical system can be employed (...) to capture the dynamics of human decision-making under uncertainty (i.e., multi-stability, bifurcations). We test the feasibility of this model quantitatively and demonstrate how the model can account for up to 86% of the observed choice behavior. The implications of using dynamical models for explaining the nonlinear complexities of human decision-making are discussed, as well as the degree to which nonlinear dynamical systems theory might offer an alternative framework for understanding human decision-making processes. (shrink)

Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels of abstraction. Indeed, it is (...) basically impracticable to maintain logic–and–metalogic without paying heed to cognitive theorizing. For it is cognitively irrelevant whether possible conclusions are deduced from some premises before the premises are determined to be true or whether the premises themselves are determined to be true first and, then, the conclusions are deduced from them. In this paper we consider the term metalogic as inherently embodied under the framework referred to as cognitive science and mathematics. We propose a metalogical interpretation of Arrow’s impossibility theorem and, to that end, choice theory is understood as a mental course of action dealing with logic and metalogic issues, in which a possible mathematical approach to model a mental course of action is adopted as a systematic operating method. Nevertheless, if we look closely at the core of Arrow’s impossibility theorem in terms of metalogic, a second fundamental contribution to this framework is represented by the Nash equilibrium. As a result of the foregoing, therefore, we prove the metalogical equivalence between Arrow’s impossibility theorem and the existence of the Nash equilibrium. More specifically, Arrow’s requirements correspond to the Nash equilibrium for finite mixed strategies with no symmetry conditions. To demonstrate this proof, we first verify that Arrow’s set and Nash’s set are isomorphic to each other, both sets being under stated conditions of non–symmetry. Then, the proof is completed by virtue of category theory. Indeed, the two sets are categories that correspond biuniquely to one another and, thus, it is possible to define a covariant functor that preserves their mutual structures. According to this, we show the proof–dedicated metalanguage as a precursor to a special equivalence theorem. (shrink)

This pioneer work in comparative political analysis manifests once more the growing influence of behavioral approaches on the study of politics. In this case the general topic is the voting pattern of justices on the highest courts of several Pacific nations and India. Various heuristic and explanatory models are employed to determine the influence of such variables as age, culture, and political orientation on the adjudicative behavior of these men over a determinate period. Although the articles by twelve different (...) authors are not all of the same analytic caliber as those contributed by the editors themselves, they collectively offer an insight into the possibilities as well as into the pitfalls of behavioral studies of the judiciary. As the editors note, such a work is necessarily hypothetical and exploratory, raising more questions than it answers. Philosophers will be interested mainly in the methodological problems of concept formation and explanation which this book raises and seeks to resolve. The article by Edward J. Weissman, "Mathematical Theory and Dynamic Models," is particularly valuable from that point of view. Moreover, by classifying and comparing the other contributions to this volume, Weissman's article furnishes a certain unity which the book as a whole sorely lacks. Geared primarily for those who are familiar with such techniques as smallest-space analysis and the use of recursive causal models, this work nevertheless can be read with profit by social philosophers, philosophers of law and those interested in general questions of methodology.--T. R. F. (shrink)

An Interdisciplinary Approach to Cognitive Modelling presents a new approach to cognition that challenges long-held views. It systematically develops a broad-based framework to model cognition, which is mathematically equivalent to the emerging 'quantum-like modelling' of the human mind. The book argues that a satisfactory physical and philosophical basis of such an approach is missing, a particular issue being the application of quantization to the mind for which there is no empirical evidence as yet. In response to this issue, the book (...) adopts a COM (classical optical modelling) approach, broad-based but mathematically equivalent to quantum-like modelling while avoiding its problematic features. It presents a philosophically informed and empirically motivated mathematical model of cognition, mainly concerning decision making processes. It also deals with applications to different areas of the social sciences. It will be of interest to scholars and research students interested in the mathematical modelling of cognition and decision making, and also interdisciplinary researchers interested in broader issues of cognition. (shrink)

In commerce, many moral failures are due to narrow mindsets that preclude taking into account the moral dimensions of a decision or action. In turn, sometimes these mindsets are caused by failing to question managerial decisions from a moral point of view, because of a perceived authority of management. In the 1960s, Stanley Milgram conducted controversial experiments to investigate just how far obedience to an authority figure could subvert his subjects' moral beliefs. In this thought-provoking work, the authors examine (...) the prevalence of narrow mental models and the phenomenon of obedience to an authority to analyse and understand the challenges which business professionals encounter in making ethical decisions. Obstacles to Ethical Decision-Making proposes processes - including collaborative input and critique - by which individuals may reduce or overcome these challenges. It provides decision-makers at all levels in an organisation with the means to place ethical considerations at the heart of managerial decision-making. (shrink)

Evidence Theory is a branch of mathematics that concerns combination of empirical evidence in an individual’s mind in order to construct a coherent picture of reality. Designed to deal with unexpected empirical evidence suggesting new possibilities, evidence theory is compatible with Shackle’s idea of decision-making as a creative act. This essay investigates this connection in detail, pointing to the usefulness of evidence theory to formalise and extend Shackle’s decision theory. In order to ease a proper framing of (...) the issues involved, evidence theory is compared with sub-additive probability theory and Ewens’s infinite alleles model. Furthermore, the original version of evidence theory is presented along with its most recent developments. (shrink)

Climate modelling plays a crucial role for understanding and addressing the climate challenge, in terms of both mitigation and adaptation. It is therefore of central importance to understand to what extent climate models are adequate for relevant purposes, such as providing certain kinds of climate change projections in view of decision-making. In this perspective, the issue of the stability of climate models under small relevant perturbations in their structure seems particularly important. Within this framework, a debate (...) has emerged in the philosophy of science literature about the relevance for climate modelling of the mathematical notion of structural stability. This paper adresses several important foundational and epistemological questions that arise in this context, in particular about the the role of abstract mathematical considerations of a qualitative nature for concrete modelling projects with mainly quantitative purposes. (shrink)

A discussion of ethical decision-making literature is overdue. In this article, we summarize the current literature of ethical decision-making models used in mental health professions. Of 1,520 articles published between 2001 and 2020 that met initial search criteria, 38 articles were included. We report on the status of empirical evidence for the use of these models along with comparisons, limitations, and considerations. Ethical decision-making models were synthesized into eight core procedural components (...) and presented based on the composition of steps present in each model. This taxonomy provides practitioners, trainers, students, and supervisors relevant information regarding ethical decision-making models. (shrink)

Medical decision making often utilizes subjective observations to arrive at concrete judgments. The decisions frequently affect who receives scarce medical treatments and, thus, who lives or dies. In this paper, a model health status index is described. It is specific for the problem of choosing patients for hemodialysis or transplantation. Such a health status index may be designed for any medical decision involving such issues as drug treatment priorities, identification of salvageable patients, and selection of patients for (...) scarce medical treatment. This index (1) incorporates a physician''s own medical criteria and values, (2) can be modified as the data base improves, (3) assures consistency from decision to decision, and (4) can be developed and used without the help of a mathematician or computer. (shrink)

The field of quantitative analysis is often mistaken to be a discipline free from ethical burdens. The quantitative financial analyst or “quant” profession holds a position of significant responsibility as the keeper of mathematical models used in complex derivative security pricing and risk management. Despite this responsibility very few postgraduate programs address the teaching of ethics and professional standards in their curriculum, and the credibility of the profession has suffered as a result of several high-profile financial losses. Some (...) of these failures could have been avoided and their impacts diminished if ethical considerations were integrated with quantitative method. Appropriate development in ethics education for quants is needed to identify points in the decision-making process where ethical questions can arise, and to explain how quants can protect stakeholders from the costs of unethical behaviour. An approach to ethics education needs to be flexible and allow for different methods to infuse ethical coverage into the course. Such an approach will go some way towards aligning the profession with other specialisations in banking and avoid the need for complex and unnecessary regulation. (shrink)

Introduction: Nurses who work in an emergency department regularly care for acute patients in a fast-paced environment, being at risk of suffering high levels of burnout. This situation makes them especially vulnerable to be accountable for decisions they did not have time to consider or have been pressured into. Research objective: The objective of this study was to find which factors influence ethical, legal and professional accountability in nursing practice in an emergency department. Research design: Data were analysed, codified and (...) triangulated using qualitative ethnographic content analysis. Participants and research context: This research is set in a large emergency department in the Midlands area of England. Data were collected from 186 nurses using participant observation, 34 semi-structured interviews with nurses and ethical analysis of 54 applicable clinical policies. Ethical considerations: Ethical approval was granted by two research ethics committees and the National Health Service Health Research Authority. Results: The main result was the clinical nursing accountability cycle model, which showed accountability as a subjective concept that flows between the nurse and the healthcare institution. Moreover, the relations among the clinical nursing accountability factors are also analysed to understand which factors affect decision-making. Discussion: The retrospective understanding of the factors that regulate nursing accountability is essential to promote that both the nurse and the healthcare institution take responsibility not only for the direct consequences of their actions but also for the indirect consequences derived from previous decisions. Conclusion: The decision-making process and the accountability linked to it are affected by several factors that represent the holistic nature of both entities, which are organised and interconnected in a complex grid. This pragmatic interpretation of nursing accountability allows the nurse to comprehend how their decisions are affected, while the healthcare institution could act proactively to avoid any problems before they happen. (shrink)

Analogy making from examples is a central task in intelligent system behavior. A lot of real world problems involve analogy making and generalization. Research investigates these questions by building computer models of human thinking concepts. These concepts can be divided into high level approaches as used in cognitive science and low level models as used in neural networks. Applications range over the spectrum of recognition, categorization and analogy reasoning. A major part of legal reasoning could be (...) formally interpreted as an analogy making process. Because it is not the same as reasoning in mathematics or the physical sciences, it is necessary to use a method, which incorporates first the ability to specify likelihood and second the opportunity of including known court decisions. We use for modelling the analogy making process in legal reasoning neural networks and fuzzy systems. In the first part of the paper a neural network is described to identify precedents of immaterial damages. The second application presents a fuzzy system for determining the required waiting period after traffic accidents. Both examples demonstrate how to model reasoning in legal applications analogous to recent decisions: first, by learning a system with court decisions, and second, by analyzing, modelling and testing the decision making with a fuzzy system. (shrink)

Active inference offers a unified theory of perception, learning, and decision-making at computational and neural levels of description. In this article, we address the worry that active inference may be in tension with the belief–desire–intention model within folk psychology because it does not include terms for desires at the mathematical level of description. To resolve this concern, we first provide a brief review of the historical progression from predictive coding to active inference, enabling us to distinguish between (...) active inference formulations of motor control and active inference formulations of decision processes. We then show that, despite a superficial tension when viewed at the mathematical level of description, the active inference formalism contains terms that are readily identifiable as encoding both the objects of desire and the strength of desire at the psychological level of description. We demonstrate this with simple simulations of an active inference agent motivated to leave a dark room for different reasons. Despite their consistency, we further show how active inference may increase the granularity of folk-psychological descriptions by highlighting distinctions between drives to seek information versus reward—and how it may also offer more precise, quantitative folk-psychological predictions. Finally, we consider how the implicitly conative components of active inference may have partial analogues in other systems describable by the broader free energy principle to which it conforms. (shrink)

We argue for a foundational epistemic claim and a hypothesis about the production and uses of mathematical epidemiological models, exploring the consequences for our political and socio-economic lives. First, in order to make the best use of scientific models, we need to understand why models are not truly representational of our world, but are already pitched towards various uses. Second, we need to understand the implicit power relations in numbers and models in public policy, and, (...) thus, the implications for good governance if numbers and models are used as the exclusive drivers of decision making. (shrink)

Facing an increasingly competitive market, enterprises need correct decisions to solve operational problems in a timely manner to maintain their competitive advantages. In this context, insufficient information may lead to an overfitting phenomenon in general mathematical modeling methods, making it difficult to ensure good analytical performance. Therefore, it is important for enterprises to be able to effectively analyze and make predictions using small data sets. Although various approaches have been developed to solve the problem of prediction, their application (...) is often limited by insufficient observations. To further enforce the effectiveness of data uncertainty processing, this study proposed an aggregating prediction model for management decision analysis using small data sets. Compared with six popular approaches, the results from the experiments show that the proposed method can effectively deal with the small data set prediction problem and is thus an appropriate decision analysis tool for managers. (shrink)

Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people's goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty (...) and the reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma–Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information‐theoretic formalism. (shrink)

Philosophers since antiquity have argued the merits of mathematics as a normative aid in ethical decision-making and of the mathematization of ethics a theoretical discipline. Recently, Anagnostopoulos, Annas, Broadie and Hutchinson have probed such issues said to be of interest to Aristotle. Despite their studies, the sense in which Aristotle either opposed or proposed a mathematical ethics in subject-matter and method remains unclear. This paper attempts to clarify the matter. It shows Aristotle’s matrix of exactness and inexactness (...) for ethical subject-matter and ethical method in the Nicomachean Ethics. Then it probes a resultant puzzle from the matrix, namely, the HL model of the happy life without consideration of mathematical justice and the HJL model of the happy life with such consideration. Finally, it examines Aristotle’s twofold rationale for differentiating these two models in his overall moral feedback loop system: differences in the intellectual virtue of good deliberation; the priority of friendship over justice for the happy life. This suggests Aristotle saw no objection either to using mathematics as an aid to ethical decision-making for a happy life, or to mathematizing at least some parts of an ethical theory of eudaimonism. (shrink)