We test contrasting predictions of two recent models of proba-bility judgment: the quantum probability model (Busemeyeret al., 2011) and the probability theory plus noise model(Costello and Watts, 2014). Both models assume that peo-ple estimate probability using formal processes that follow orsubsume standard probability theory. The quantum probabil-ity model predicts people’s estimates should agree with oneset of probability theory identities, while the probability the-ory plus noise model predicts a specific pattern of violation ofthose identities. Experimental results show just the form of vi-olation predicted by the probability theory plus noise model.These results suggest that people’s probability judgments donot follow quantum probability: instead, they follow the rulesof standard probability theory, with the systematic biases seenin those judgments due to the effects of random noise.
We test contrasting predictions of two recent models of proba-bility judgment: the quantum probability model (Busemeyeret al., 2011) and the probability theory plus noise model(Costello and Watts, 2014). Both models assume that peo-ple estimate probability using formal processes that follow orsubsume standard probability theory. The quantum probabil-ity model predicts people’s estimates should agree with oneset of probability theory identities, while the probability the-ory plus noise model predicts a specific pattern of violation ofthose identities. Experimental results show just the form of vi-olation predicted by the probability theory plus noise model.These results suggest that people’s probability judgments donot follow quantum probability: instead, they follow the rulesof standard probability theory, with the systematic biases seenin those judgments due to the effects of random noise.
How can we use quantum theory to model other phenomena of interest to researchers in cognition and decision making? Quantum theory is not easy for researchers in cognition and decision making to accept. In fact, quantum mechanics was not easy for physicists to accept either, but it was forced on them by several paradoxical findings that could not be explained using classical physics. We have a similar problem in cognition and decision making – there are numerous paradoxical findings that just seem irrational according to classic probability theory. For example, under some conditions, people judge the probability of event A and B to be greater than the probability of event B , which is called the conjunction fallacy (Tversky & Kahneman, 1983). Also, under the same conditions, they judge the probability of A or B to be less than the probability of event A (Carlson & Yates, 1989), which is called the disjunction fallacy. In this chapter we examine how quantum probability theory explains these and other puzzling results from human probability judgment research. This chapter has two main parts. In the first part, we use a quantum model to derive qualitative predictions for conjunction errors, disjunction errors, and other closely related findings. The first section provides a general set of predictions that do not depend on specific assumptions about the features used to represent events, and the predictions are parameter free. In the second part, we examine the quantitative predictions of the quantum model for a Bayesian inference task, which we use to explain order effects on inference.
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.
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction and disjunction fallacies, averaging effects, unpacking effects, and order effects on inference. On the one hand, quantum theory is similar to other categorization and memory models of cognition in that it relies on vector spaces defined by features and similarities between vectors to determine probability judgments. On the other hand, quantum probability theory is a generalization of Bayesian probability theory because it is based on a set of (von Neumann) axioms that relax some of the classic (Kolmogorov) axioms. The quantum model is compared and contrasted with other competing explanations for these judgment errors, including the anchoring and adjustment model for probability judgments. In the quantum model, a new fundamental concept in cognition is advanced--the compatibility versus incompatibility of questions and the effect this can have on the sequential order of judgments. We conclude that quantum information-processing principles provide a viable and promising new way to understand human judgment and reasoning.
There 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 both Bayesian 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 3 experiments, we show that our modeling approach explains 5 key phenomena in human inference including order effects, reciprocity (i.e., the inverse fallacy), memorylessness, violations of the Markov condition, and antidiscounting. As far as we are aware, no existing theory or model can explain all 5 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. (PsycINFO Database Record
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning.
This article presents the results of an experiment, called the ABA experiment, designed to test a fundamental prediction of quantum probability theory when applied to human judgments and decisions. The prediction concerns the effect of one measurement on another when the measurements are incompatible (i.e., the answers to the measurements depend on the order of these measurements). After an initial measurement of an opinion on an issue, A, the answer to a second measurement on the same issue A immediately afterwards will certainly be the same as the first. However, according to the uncertainty principle, if a measurement of opinion on issue A is followed by an incompatible measurement on another issue, B, then the answer to a second measurement on issue A will become uncertain. This prediction was tested with 325 participants on a wide range of 12 different set of issues that were previously shown to be incompatible. Contrary to previous claims published in this journal, the empirical findings support the prediction of quantum probability theory applied to human judgments.