| 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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