A quantum probability explanation for violations of ‘rational’ decision theory

Pothos, Emmanuel M.; Busemeyer, Jerome R.

doi:10.1098/rspb.2009.0121

Cited by 404 publications

(446 citation statements)

References 43 publications

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“…In particular, for any model with two incompatible events A and B we expect to observe violations of the law of total probability, e.g. Busemeyer, 2009). Therefore, for example, while the 4D CC model may not display some of the non-normative behavioral properties we examine (i.e., Reciprocity, Memorylessness, Violations of the Markov condition, and Anti-Discounting), it is able to account for situations where p(Y 1 ) is judged less likely than p(Y 1 |E 1 )p(E 1 ), for example.…”

Section: Other Non-normative Effectsmentioning

confidence: 99%

A quantum probability framework for human probabilistic inference.

Trueblood

Yearsley

Pothos

2017

Journal of Experimental Psychology: General

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractThere is considerable variety in human inference (e.g., a doctor inferring the presence of a disease, a juror inferring the guilt of a defendant, or someone inferring future weight loss based on diet and exercise). As such, people display a wide range of behaviors when making inference judgments.Sometimes, people's judgments appear Bayesian (i.e., normative), but in other cases, judgments deviate from the normative prescription of classical probability theory. How can we combine bothBayesian and non-Bayesian influences in a principled way? We propose a unified explanation of human inference using quantum probability theory. In our approach, we postulate a hierarchy of mental representations, from 'fully' quantum to 'fully' classical, which could be adopted in different situations. In our hierarchy of models, moving from the lowest level to the highest involves changing assumptions about compatibility (i.e., how joint events are represented). Using results from three experiments, we show that our modeling approach explains five key phenomena in human inference including order effects, reciprocity (i.e., the inverse fallacy), memorylessness, violations of the Markov condition, and anti-discounting. As far as we are aware, no existing theory or model can explain all five phenomena. We also explore transitions in our hierarchy, examining how representations change from more quantum to more classical. We show that classical representations provide a better account of data as individuals gain familiarity with a task.We also show that representations vary between individuals, in a way that relates to a simple measure of cognitive style, the Cognitive Reflection Test.Keywords: Human judgment, quantum probability theory, Bayes' rule, order effects, Markov condition A Quantum Framework for Probabilistic Inference 3 A Quantum Probability Framework for Human Probabilistic InferenceEveryday we face situations where we must make inferences about the world around us. For example, a doctor must determine the likelihood that a patient has a disease based on a set of symptoms. A juror must decide the probability that a defendant is guilty after hearing the cases made by the prosecution and defense. Or, maybe you want to judge the likelihood that you will weigh less next month if you start exercising more regularly and you improve your diet. In general, the inference problem involves judging the likelihood of some hypothesis (e.g., presence of a disease, guilt of a defendant, future weight loss) based on a series of evidence (e.g., medicalsymptoms, prosecution and defense cases, changes in your diet and exercise).Bayesian inference is widely accepted as the normative approach to inference. However, decades of research in human judgment and decision-making have suggested that people's judgments often violate the rules of Bayesian inference and classical probability theory (Tversky...

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Section: Other Non-normative Effectsmentioning

confidence: 99%

A quantum probability framework for human probabilistic inference.

Trueblood

Yearsley

Pothos

2017

Journal of Experimental Psychology: General

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“…Applications of QP theory have been presented in decision making (Blutner et al, in press;Busemeyer, Wang, & Townsend, 2006;Bordley, 1998;Lambert-Mogiliansky, Zamir, & Zwirn, 2009;Pothos & Busemeyer, 2009;Wang & Busemeyer, in press;Yukalov & Sornette, 2010), conceptual combination (Aerts, 2009;Aerts & Gabora, 2005;Blutner, 2008;Bruza et al, under review), memory (Bruza, 2010;, and perception (Atmanspacher, Filk, & Romer, 2004). Psychological models based on quantum probability seem to work well (for overviews see Busemeyer & Bruza, 2009;Khrennikov, 2004;Pothos & Busemeyer, in press) and add to the increasing realization that the application of QP need not be restricted to physics.…”

Section: Introductionmentioning

confidence: 99%

A quantum geometric model of similarity.

Pothos¹,

Busemeyer²,

Trueblood³

2013

Psychological Review

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent repository link: AbstractNo other study has had as great an impact on the development of the similarity literature as that of Tversky (1977), which provided compelling demonstrations against all the fundamental assumptions of the popular, and extensively employed, geometric similarity models. Notably, similarity judgments were shown to violate symmetry and the triangle inequality, and also be subject to context effects, so that the same pair of items would be rated differently, depending on the presence of other items. Quantum theory provides a generalized geometric approach to similarity and can address several of Tversky's (1997) main findings. Similarity is modeled as quantum probability, so that asymmetries emerge as order effects, and the triangle equality violations and the diagnosticity effect can be related to the context-dependent properties of quantum probability. We so demonstrate the promise of the quantum approach for similarity and discuss the implications for representation theory in general.Keywords: similarity, metric axioms, symmetry, triangle inequality, diagnosticity, quantum probability 3 a quantum geometric model of similarity

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“…Khrennikov and Haven 2009;Yukalov and Sornette 2010;Aerts et al 2011); for asymmetry judgments in similarity, i.e. that "A is like B" is not equivalent to "B is like A" ; for paradoxical strategies in game theory such as in the prisoner's dilemma (Piotrowski and Stadkowski 2003;Landsburg 2004;Pothos and Busemeyer 2009;Brandenburger 2010). More generally, new theoretical frameworks with quantum-like models have been offered in decision theory and bounded rationality Lambert-Mogiliansky 2008, 2010;Lambert-Mogiliansky et al 2009;Yukalov and Sornette 2011).…”

Section: Introductionmentioning

confidence: 99%

Quantum-like models cannot account for the conjunction fallacy

2016

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Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities-this is the conjunction fallacy. One of the most discussed accounts of this fallacy is currently the quantum-like explanation, which relies on models exploiting the mathematics of quantum mechanics. The aim of this paper is to investigate the empirical adequacy of major quantum-like models which represent beliefs with quantum states. We first argue that they can be tested in three different ways, in a question order effect configuration which is different from the traditional conjunction fallacy experiment. We then carry out our proposed experiment, with varied methodologies from experimental economics. The experimental results we get are at odds with the predictions of the quantum-like models. This strongly suggests that this quantum-like account of the conjunction fallacy fails. Future possible research paths are discussed.

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A quantum probability explanation for violations of ‘rational’ decision theory

Cited by 404 publications

References 43 publications

A quantum probability framework for human probabilistic inference.

A quantum probability framework for human probabilistic inference.

A quantum geometric model of similarity.

Quantum-like models cannot account for the conjunction fallacy

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