We present progress towards a novel theoretical approach for\nunderstanding Tversky’s famous ‘diagnosticity’ effect in similarity\njudgments, and an initial empirical validation. Our approach\nuses a model for similarity judgments based on quantum\nprobability theory. The model predicts a diagnosticity effect\nunder certain conditions only. Our model also predicts that\nchanges to the set of stimuli to be compared can cause the diagnosticity\neffect to break down or reverse. In one experiment,\nwe test and confirm one of our key predictions
We present progress towards a novel theoretical approach for\nunderstanding Tversky’s famous ‘diagnosticity’ effect in similarity\njudgments, and an initial empirical validation. Our approach\nuses a model for similarity judgments based on quantum\nprobability theory. The model predicts a diagnosticity effect\nunder certain conditions only. Our model also predicts that\nchanges to the set of stimuli to be compared can cause the diagnosticity\neffect to break down or reverse. In one experiment,\nwe test and confirm one of our key predictions
A model of similarity is presented which is based on Quantum Probability (QP) theory. The model is applied to the case of violations of symmetry in similarity judgments, as demonstrated by Tversky (1977). The QP similarity model can predict such violations, on the basis of the same underlying intuitions as Tversky (1977). Moreover, we discuss how the model can be extended to account for violations of the triangle inequality and also the empirical findings in relation to Tversky’s diagnosticity principle.
Lately, so-called 'quantum models' based on parts of the mathematics of quantum mechanics, have been developed in decision theory and cognitive sciences to account for seemingly irrational or paradoxical human judgments. In this paper, we limit ourselves to such quantum-like models that address order effects. It has been argued that such models are able to account for existing and new empirical data, and meet some a priori predictions. From the quantum law of reciprocity, we derive new empirical predictions that we call the Grand Reciprocity equations, that must be satisfied by quantum-like models on the condition that they are non-degenerate. We show that existing non-degenerate quantum-like models for order effects fail this test on several existing data sets. We take it to suggest that degenerate quantum-like models should be the focus of forthcoming research in the area.
Recent findings show that human inferences and decisions interfere in ways analogous to incompatible quantum observables, and conceptual judgments are inseparable in ways similar to entangled quantum states.This discovery has led a group of physicists and psychologists to form a new field called "quantum cognition," which uses mathematical principles of quantum theory to explain human cognitive behavior.The power of this new theoretical approach is illustrated here by testing an a priori and precise prediction derived from quantum theory regarding question order effects commonly observed in survey research.The test of quantum theory was statistically satisfied across a set of 26 national surveys on presidential job approval and country satisfaction in past 10 years.These results suggest that quantum theory, initially invented to explain order effects on measurements in physics, provides a powerful prediction for measurement order effects in social and behavioral sciences too.
The quantum cognition research programme concerns the application of quantum probability theory(the rules for how to assign probabilities to events from quantum mechanics, without the physics) tocognitive modeling. We review quantum cognitive models in several areas of psychology, includingconjunction/ disjunction fallacies in probabilistic judgment, conceptual combinations, similarity, order effects on judgments, causal inference, the disjunction effect in decision making, measurement and interference effects on judgments and decisions, memory, perception, and other judgment anddecision-making applications. For each area, we first present the empirical findings that have motivated the application of quantum models, emphasizing any characteristics which are particularly puzzling or have resisted coherent theoretical explanations previously; we then discuss the quantum cognitive models, noting the key features of the models that help explain the empirical data; we finally cast a critical eye on the models and explore comparisons with non-quantum models.
People can often outperform statistical methods and machine learning algorithms in situations that involve making inferences about the relationship between causes and effects. While people are remarkably good at causal reasoning in many situations, there are several instances where they deviate from expected responses. This paper examines three situations where judgments related to causal inference problems produce unexpected results and describes a quantum inference model based on the axiomatic principles of quantum probability theory that can explain these effects. Two of the three phenomena arise from the comparison of predictive judgments (i.e., the conditional probability of an effect given a cause) with diagnostic judgments (i.e., the conditional probability of a cause given an effect). The third phenomenon is a new finding examining order effects in predictive causal judgments. The quantum inference model uses the notion of incompatibility among different causes to account for all three phenomena. Psychologically, the model assumes that individuals adopt different points of view when thinking about different causes. The model provides good fits to the data and offers a coherent account for all three causal reasoning effects thus proving to be a viable new candidate for modeling human judgment.
Since Tversky (1977) argued that similarity judgments violate the three metric axioms, asymmetrical similarity judgments have been offered as particularly difficult challenges for standard, geometric models of similarity, such as multidimensional scaling. According to Tversky (1977), asymmetrical similarity judgments are driven by differences in salience or extent of knowledge. However, the notion of salience has been difficult to operationalize to different kinds of stimuli, especially perceptual stimuli for which there are no apparent differences in extent of knowledge. To investigate similarity judgments between perceptual stimuli, across three experiments we collected data where individuals would rate the similarity of a pair of temporally separated color patches. We identified several violations of symmetry in the empirical results, which the conventional multidimensional scaling model cannot readily capture. Pothos et al. (2013) proposed a quantum geometric model of similarity to account for Tversky’s (1977) findings. In the present work, we extended this model to a more general framework that can be fit to similarity judgments. We fit several variants of quantum and multidimensional scaling models to the behavioral data and concluded in favor of the quantum approach. Without further modifications of the model, the best-fit quantum model additionally predicted violations of the triangle inequality that we observed in the same data. Overall, by offering a different form of geometric representation, the quantum geometric framework of similarity provides a viable alternative to multidimensional scaling for modeling similarity judgments, while still allowing a convenient, spatial illustration of similarity.