| 1. |
- Angelov, Angel G., et al.
(författare)
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Four-decision tests for stochastic dominance, with an application to environmental psychophysics
- 2019
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier. - 0022-2496 .- 1096-0880. ; 93
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Tidskriftsartikel (refereegranskat)abstract
- If the survival function of a random variable X lies to the right of the survival function of a random variable Y, then X is said to stochastically dominate Y. Inferring stochastic dominance is particularly complicated because comparing survival functions raises four possible hypotheses: identical survival functions, dominance of X over Y, dominance of Y over X, or crossing survival functions. In this paper, we suggest four-decision tests for stochastic dominance suitable for paired samples. The tests are permutation-based and do not rely on distributional assumptions. One-sided Cramér–von Mises and Kolmogorov–Smirnov statistics are employed but the general idea may be utilized with other test statistics. The power to detect dominance and the different types of wrong decisions are investigated in an extensive simulation study. The proposed tests are applied to data from an experiment concerning the individual’s willingness to pay for a given environmental improvement.
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| 2. |
- Asano, Masanari, et al.
(författare)
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A quantum-like model of selection behavior
- 2017
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier. - 0022-2496 .- 1096-0880. ; 78, s. 2-12
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach that employs the state representation specific to quantum theory, which has the mathematical framework beyond the classical probability theory. We show that our quantum approach can clearly explain the famous examples of anomalies for the expected utility theory, the Ellsberg paradox, the Machina paradox and the disparity between WTA and WTP. Further, we point out that our model mathematically specifies the characteristics of the probability weighting function and the value function, which are basic concepts in the prospect theory. (C) 2016 Elsevier Inc. All rights reserved.
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| 3. |
- Bagarello, Fabio, et al.
(författare)
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Quantum field inspired model of decision making : Asymptotic stabilization of belief state via interaction with surrounding mental environment
- 2018
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Ingår i: Journal of mathematical psychology (Print). - : Academic Press. - 0022-2496 .- 1096-0880. ; 82, s. 159-168
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to a justification of quantum-like models of the process of decision making based on the theory of open quantum systems, i.e. decision making is considered as decoherence. This process is modeled as interaction of a decision maker, Alice, with a mental (information) environment R, surrounding her. Such an interaction generates "dissipation of uncertainty" from Alice's belief-state rho(t) into R, and asymptotic stabilization of rho(t) to a steady belief-state. The latter is treated as the decision state. Mathematically the problem under study is about finding constraints on 72, guaranteeing such stabilization. We found a partial solution of this problem (in the form of sufficient conditions). We present the corresponding decision making analysis for one class of mental environments, the so-called "almost homogeneous environments", with the illustrative examples: (a) behavior of electorate interacting with the mass-media "reservoir"; (b) consumers' persuasion. We also comment on other classes of mental environments. (C) 2017 Elsevier Inc. All rights reserved.
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| 4. |
- Bagarello, Fabio, et al.
(författare)
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Quantum like modeling of decision making : Quantifying uncertainty with the aid of Heisenberg-Robertson inequality
- 2018
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier. - 0022-2496 .- 1096-0880. ; 84, s. 49-56
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Tidskriftsartikel (refereegranskat)abstract
- This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg's uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for "incompatible questions" used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions respectively. Our construction unifies the two different situations (compatible versus incompatible mental observables), by means of a single Hilbert space and of a deformation parameter which can be tuned to describe these opposite cases. One of the main foundational consequences of this paper for cognitive psychology is formalization of the mutual uncertainty about incompatible questions with the aid of Heisenberg's uncertainty principle implying the mental state dependence of (in)compatibility of questions. (C) 2018 Elsevier Inc. All rights reserved.
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| 5. |
- Basieva, Irina, 1974-, et al.
(författare)
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Quantum probability updating from zero priors (by-passing Cromwell's rule)
- 2017
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier. - 0022-2496 .- 1096-0880. ; 77, s. 58-69
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Tidskriftsartikel (refereegranskat)abstract
- Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a straightforward implication of how Bayes' rule works). Relatedly, hypotheses with a very low prior cannot be updated to have a very high posterior without a tremendous amount of new evidence to support them (or to make other possibilities highly improbable). Cromwell's rule appears at odds with our intuition of how humans update probabilities. In this work, we report two simple decision making experiments, which seem to be inconsistent with Cromwell's rule. Quantum probability theory, the rules for how to assign probabilities from the mathematical formalism of quantum mechanics, provides an alternative framework for probabilistic inference. An advantage of quantum probability theory is that it is not subject to Cromwell's rule and it can accommodate changes from zero or very small priors to significant posteriors. We outline a model of decision making, based on quantum theory, which can accommodate the changes from priors to posteriors, observed in our experiments. (C) 2016 Elsevier Inc. All rights reserved.
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| 6. |
- Bleichrodt, Han, et al.
(författare)
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Probability Weighting and Utility Curvature in QALY-Based Decision Making
- 1999
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Ingår i: Journal of mathematical psychology. - : Elsevier Inc. - 1096-0880 .- 0022-2496. ; 43:2, s. 238-260
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Tidskriftsartikel (refereegranskat)abstract
- Quality-Adjusted Life-Years (QALYs) are currently the most important utility model in medical decision making. QALYs are calculated by adjusting years of life for the utility of the health state in which these years are spent. For normative reasons the standard gamble is the preferred method to measure health state utilities, but concern exists about its descriptive properties. Recent theoretical work has suggested that probability weighting can explain anomalies in standard gamble measurement. This paper shows that applying probability weighting in standard gamble measurement increases the consistency of QALYs with individual preferences. The consistency of QALYs with individual preferences is not significantly increased further if utility curvature is also taken into account.
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| 7. |
- Bleichrodt, Han, et al.
(författare)
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Time Preference for Health: A Test of Stationarity versus Decreasing Timing Aversion
- 2001
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Ingår i: Journal of mathematical psychology. - : Elsevier Inc. - 1096-0880 .- 0022-2496. ; 45:2, s. 265-282
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Tidskriftsartikel (refereegranskat)abstract
- This paper provides a new and more robust test of the descriptive validity of the constant rate discounted utility model in medical decision analysis. The constant rate discounted utility model is compared with two competing theories, Harvey's (1986) proportional discounting model and Loewenstein and Prelec's (1992) hyperbolic discounting model. To compare the various intertemporal models, previous studies on intertemporal preferences for health assumed a specific parametric form of the utility function for life-years and no discounting within the time periods that health states are experienced. The present study avoids such confounding assumptions by focusing on the axiomatic structure of the discounting models. The present study further differs by using choices instead of matching to elicit intertemporal preferences. The experimental results provide support for decreasing timing aversion, the condition underlying the proportional and the hyperbolic discounting model, but they violate stationarity, the central condition of the constant rate discounted utility model. There is some ambiguity whether the violations of stationarity are primarily caused by an immediacy effect. The results confirm violations of stationarity in choice-based elicitations tasks, in contrast with the results from Ahlbrecht and Weber (1997) which supported stationarity in choices over monetary outcomes.
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| 8. |
- Carlson, Erik, 1961-
(författare)
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Extensive measurement with incomparability
- 2008
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier BV. - 0022-2496 .- 1096-0880. ; 52:4, s. 250-259
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Tidskriftsartikel (refereegranskat)abstract
- Standard theories of extensive measurement assume that the objects to be measured form a complete order with respect to the relevant property. In this paper, representation and uniqueness theorems are presented for a theory that departs radically from this completeness assumption. It is first shown that any quasi-order on a countable set can be represented by vectors of real numbers. If such an order is supplemented by a concatenation operator, yielding a relational structure that satisfies a set of axioms similar to the standard axioms for an extensive structure, we obtain a scale possessing the crucial properties of a ratio scale. Incomparability is thus compatible with extensive measurement. The paper ends with a brief discussion on some possible applications and developments of this result.
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| 9. |
- Carlson, Erik
(författare)
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Generalized extensive measurement for lexicographic orders
- 2010
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier BV. - 0022-2496 .- 1096-0880. ; 54:4, s. 345-351
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Tidskriftsartikel (refereegranskat)abstract
- Theories of extensive measurement usually assume an "Archimedean axiom", designed to exclude the possibility of infinite or infinitesimal differences among the objects of measurement. The standard theories are therefore not applicable to structures containing lexicographic orders In this paper, a generalized theory of extensive measurement is developed, which allows infinite and infinitesimal differences The theory has potential applications in areas such as value and preference research, where lexicographically ordered structures are common. Our result is fully analogous to the standard representation and uniqueness theorem of extensive measurement, and only simple and familiar mathematical concepts are assumed.
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| 10. |
- Dzhafarov, Ehtibar, et al.
(författare)
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Foreword
- 2017
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Ingår i: Journal of mathematical psychology (Print). - USA : Elsevier BV. - 0022-2496 .- 1096-0880. ; 78, s. 1-1
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Tidskriftsartikel (refereegranskat)
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| 11. |
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| 12. |
- Dzhafarov, Ehtibar N.
(författare)
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Dissimilarity, Quasidistance, Distance
- 2010
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Ingår i: Journal of mathematical psychology (Print). - Amsterdam : Elsevier. - 0022-2496 .- 1096-0880. ; 54:2, s. 334-337
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Tidskriftsartikel (refereegranskat)
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| 13. |
- Dzhafarov, Ehtibar N., et al.
(författare)
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Mental architectures with selectively influenced but stochastically interdependent components
- 2004
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier BV. - 0022-2496 .- 1096-0880. ; 48:1, s. 51-64
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Tidskriftsartikel (refereegranskat)abstract
- The way external factors influence distribution functions for the overall time required to perform a mental task (such as responding to a stimulus, or solving a problem) may be informative as to the underlying mental architecture, the hypothetical network of interconnected processes some of which are selectively influenced by some of the external factors. Under the assumption that all processes contributing to the overall performance time are stochastically independent, several basic results have been previously established. These results relate patterns of response time distribution functions produced by manipulating external factors to such questions as whether the hypothetical constituent processes in the mental architecture enter AND gates or OR gates, and whether pairs of processes are sequential or concurrent. The present study shows that all these results are also valid for stochastically interdependent component times, provided the selective dependence of these components upon external factors is understood within the framework of a recently proposed theory of selective influence. According to this theory each component is representable as a function of three arguments: the factor set selectively influencing it, a component-specific source of randomness, and a source of randomness shared by all the components.
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| 14. |
- Dzhafarov, Ehtibar N., et al.
(författare)
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Notes on selective influence, probabilistic causality, and probabilistic dimensionality
- 2006
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier BV. - 0022-2496 .- 1096-0880. ; 50:4, s. 390-401
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Tidskriftsartikel (refereegranskat)abstract
- The paper provides conceptual clarifications for the issues related to the dependence of jointly distributed systems of random entities on external factors. This includes the theory of selective influence as proposed in Dzhafarov [(2003a). Selective influence through conditional independence. Psychometrika, 68, 7–26] and generalized versions of the notions of probabilistic causality [Suppes, P., & Zanotti, M. (1981). When are probabilistic explanations possible? Synthese, 48, 191–199] and dimensionality in the latent variable models [Levine, M. V. (2003). Dimension in latent variable models. Journal of Mathematical Psychology, 47, 450–466]. One of the basic observations is that any system of random entities whose joint distribution depends on a factor set can be represented by functions of two arguments: a single factor-independent source of randomness and the factor set itself. In the case of random variables (i.e., real-valued random entities endowed with Borel sigma-algebras) the single source of randomness can be chosen to be any random variable with a continuous distribution (e.g., uniformly distributed between 0 and 1).
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| 15. |
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| 16. |
- Dzhafarov, Ehtibar N., et al.
(författare)
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Psychophysics without physics : extension of Fechnerian scaling from continuous to discrete and discrete-continuous stimulus spaces
- 2005
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier BV. - 0022-2496 .- 1096-0880. ; 49:2, s. 125-141
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Tidskriftsartikel (refereegranskat)abstract
- The computation of subjective (Fechnerian) distances from discrimination probabilities involves cumulation of appropriately transformed psychometric increments along smooth arcs (in continuous stimulus spaces) or chains of stimuli (in discrete spaces). In a space where any two stimuli that are each other's points of subjective equality are given identical physical labels, psychometric increments are positive differences ψ(x,y)-ψ(x,x) and ψ(y,x)-ψ(x,x), where x≠y and ψ is the probability of judging two stimuli different. In continuous stimulus spaces the appropriate monotone transformation of these increments (called overall psychometric transformation) is determined uniquely in the vicinity of zero, and its extension to larger values of its argument is immaterial. In discrete stimulus spaces, however, Fechnerian distances critically depend on this extension. We show that if overall psychometric transformation is assumed (A) to be the same for a sufficiently rich class of discrete stimulus spaces, (B) to ensure the validity of the Second Main Theorem of Fechnerian Scaling in this class of spaces, and (C) to agree in the vicinity of zero with one of the possible transformations in continuous spaces, then this transformation can only be identity. This result is generalized to the broad class of “discrete-continuous” stimulus spaces, of which continuous and discrete spaces are proper subclasses.
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| 17. |
- Franco, Vithor Rosa, et al.
(författare)
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Nondecomposable item response theory models : fundamental measurement in psychometrics
- 2023
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Ingår i: Journal of mathematical psychology (Print). - : Academic Press. - 0022-2496 .- 1096-0880. ; 114
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Tidskriftsartikel (refereegranskat)abstract
- The main aim of the current paper is to propose Item Response Theory (IRT) models derived from the nondecomposable measurement theories presented in Fishburn (1974). More specifically, we aim to: (i) present the theoretical basis of the Rasch model and its relations to psychophysics’ models of utility; (ii) give a brief exposition on the measurement theories presented in Fishburn (1974, 1975), some of which do not require an additive structure; and (iii) derive IRT models from these measurement theories, as well as Bayesian implementations of these models. We also present two empirical examples to compare how well these IRT models fit to real data. In addition to deriving new IRT models, we also discuss theoretical interpretations regarding the models’ capability of generating fundamental measures of the true scores of the respondents. The manuscript ends with prospects for future studies and practical implications.
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| 18. |
- Ghirlanda, Stefano
(författare)
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On elemental and configural models of associative learning
- 2015
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier BV. - 0022-2496 .- 1096-0880. ; 64-65, s. 8-16
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Tidskriftsartikel (refereegranskat)abstract
- The elemental and configural approaches to associative learning are considered fundamentally distinct, with much theoretical and empirical work devoted to determining which one can better account for empirical data. Elemental models assume that each perceptual element is capable of acquiring associative strength independently of other elements. Configural models, on the other hand, assume that associative strength accrues to percepts as wholes. Here I derive a necessary and sufficient condition for an elemental and a configural model to be equivalent, i.e., to always make the same predictions. I then ask when the condition can be fulfilled. I show that it is always possible to construct a configural model equivalent to a given elemental model, provided we broaden somewhat the customary definition of a configural model. Constructing an elemental model equivalent to a given elemental one is possible provided the generalization function of the configural model is positive definite. The latter condition is satisfied by existing configural models. The arguments leading to these conclusions clarify the relationship between elemental and configural models, and show that both approaches have heuristic value for associative learning theory.
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| 19. |
- Ghirlanda, Stefano
(författare)
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Studying associative learning without solving learning equations
- 2018
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier BV. - 0022-2496 .- 1096-0880. ; 85, s. 55-61
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Tidskriftsartikel (refereegranskat)abstract
- I introduce a simple mathematical method to calculate the associative strengths of stimuli in many models of associative learning, without solving the models' learning equations and without simulating the learning process. The method applies to many models, including the Rescorla and Wagner (1972) model, the replaced elements model of Brandon et al. (2000), and Pearce's (1987) configural model. I illustrate the method by calculating the predictions of these three models in summation and blocking experiments, allowing for a degree of similarity between the training stimuli as well as for the effects of contextual stimuli. The method clarifies the models' predictions and suggests new empirical tests.
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| 20. |
- Haven, Emmanuel, et al.
(författare)
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Statistical and subjective interpretations of probability in quantum-like models of cognition and decision making
- 2016
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier BV. - 0022-2496 .- 1096-0880. ; 74, s. 82-91
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Tidskriftsartikel (refereegranskat)abstract
- The paper starts with an introduction to the basic mathematical model of classical probability (CP), i.e. the Kolmogorov (1933) measure-theoretic model. Its two basic interpretations are discussed: statistical and subjective. We then present the probabilistic structure of quantum mechanics (QM) and discuss the problem of interpretation of a quantum state and the corresponding probability given by Born’s rule. Applications of quantum probability (QP) to modeling of cognition and decision making (DM) suffer from the same interpretational problems as QM. Here the situation is even more complicated than in physics. We analyze advantages and disadvantages of the use of subjective and statistical interpretations of QP. The subjective approach to QP was formalized in the framework of Quantum Bayesianism (QBism) as the result of efforts from C. Fuchs and his collaborators. The statistical approach to QP was presented in a variety of interpretations of QM, both in nonrealistic interpretations, e.g., the Copenhagen interpretation (with the latest version due to A. Plotnitsky), and in realistic interpretations (e.g., the recent Växjö interpretation). At present, we cannot make a definite choice in favor of any of the interpretations. Thus, quantum-like DM confronts the same interpretational problem as quantum physics does.
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| 21. |
- Haven, Emmanuel, et al.
(författare)
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The use of action functionals within the quantum-like paradigm
- 2017
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier. - 0022-2496 .- 1096-0880. ; 78, s. 13-23
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Tidskriftsartikel (refereegranskat)abstract
- Arbitrage is a key concept in the theory of asset pricing and it plays a crucial role in financial decision making. The concept of the curvature of so-called 'fibre bundles' can be used to define arbitrage. The concept of 'action' can play an important role in the definition of arbitrage. In this paper, we connect the probabilities emerging from a (non) zero linear action with so-called risk neutral probabilities. The paper also shows how arbitrage/non arbitrage can be well defined within a quantum-like paradigm. We also discuss briefly the behavioural dimension of arbitrage. (C) 2016 Elsevier Inc. All rights reserved.
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| 22. |
- Kalish, Michael L., et al.
(författare)
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A statistical test of the equality of latent orders
- 2016
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Ingår i: Journal of mathematical psychology (Print). - : Academic Press. - 0022-2496 .- 1096-0880. ; 70, s. 1-11
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Tidskriftsartikel (refereegranskat)abstract
- It is sometimes the case that a theory proposes that the population means on two variables should have the same rank order across a set of experimental conditions. This paper presents a test of this hypothesis. The test statistic is based on the coupled monotonic regression algorithm developed by the authors. The significance of the test statistic is determined by comparison to an empirical distribution specific to each case, obtained via non-parametric or semi-parametric bootstrap. We present an analysis of the power and Type I error control of the test based on numerical simulation. Partial order constraints placed on the variables may sometimes be theoretically justified. These constraints are easily incorporated into the computation of the test statistic and are shown to have substantial effects on power. The test can be applied to any form of data, as long as an appropriate statistical model can be specified.
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| 23. |
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| 24. |
- Khrennikov, Andrei, et al.
(författare)
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Possibility to agree on disagree from quantum information and decision making
- 2014
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Ingår i: Journal of mathematical psychology (Print). - : Elsevier BV. - 0022-2496 .- 1096-0880. ; 62-63, s. 1-15
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Tidskriftsartikel (refereegranskat)abstract
- The celebrated Aumann theorem states that if two agents have common priors, and their posteriors for a given event E are common knowledge, then their posteriors must be equal; agents with the same priors cannot agree to disagree. The aim of this note is to show that in some contexts agents using a quantum probability scheme for decision making can agree to disagree even if they have the common priors, and their posteriors for a given event E are common knowledge. We also point to sufficient conditions guaranteeing impossibility to agree on disagree even for agents using quantum(-like) rules in the process of decision making. A quantum(-like) analog of the knowledge operator is introduced; its basic properties can be formulated similarly to the properties of the classical knowledge operator defined in the set-theoretical approach to representation of the states of the world and events (Boolean logics). However, this analogy is just formal, since quantum and classical knowledge operators are endowed with very different assignments of truth values. A quantum(-like) model of common knowledge naturally generalizing the classical set-theoretic model is presented. We illustrate our approach by a few examples; in particular, on attempting to escape the agreement on disagree for two agents performing two different political opinion polls. We restrict our modeling to the case of information representation of an agent given by a single quantum question-observable (of the projection type). A scheme of extending of our model of knowledge/common knowledge to the case of information representation of an agent based on a few question-observables is also presented and possible pitfalls are discussed. (C) 2014 Elsevier Inc. All rights reserved.
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| 25. |
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