A quantum probability framework for human probabilistic inference.

Abstract

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...

A Process Model of Causal Reasoning

“…Yet participants judged that instead. This apparent expectation that the causes of a common effect graph are positively correlated has been observed in other studies (Luhmann & Ahn, 2007; Perales, Catena, & Maldonado, 2004; Rehder, 2014, 2015, 2018; Rehder & Burnett, 2005; Rottman & Hastie, 2016; Trueblood, Yearsley, & Pothos, 2017; cf. Von Sydow, Hagmayer, Meder, & Waldman, 2010).…”

“…Trueblood et al (2017) also found differences in the magnitude of Markov violations and, moreover, that those violations correlated with other measures, such as the magnitude of order effects (i.e., the difference between p ( Z | XthenY ) and p ( Z | YthenX )) and measures they referred to as reciprocity and memorylessness . These measures in turn correlated with subjects' performance on the cognitive reflection test (CRT), which is purported to measure differences in reasoners' tendency to emit intuitive versus deliberative responses (Frederick, 2005).…”

“…Recently, Trueblood et al (2017) applied quantum probability theory (QP) to some of the causal reasoning phenomena considered here. While in classic probability theory, probabilities are computed as subsets (of a joint probability distribution), in QP events are represented as subspaces and probabilities are computed by taking the inner product of vectors within those spaces.…”

“…For example, if p ( Z | X , Y ) is interpreted as p ( Z | XthenY ) (i.e., one first learns that X and then that Y ), then QP potentially accounts for the finding that the order of X and Y matters (i.e., that p ( Z | XthenY ) ≠ p ( Z | YthenX ). In fact, Trueblood et al (2017) found order effects in a causal reasoning task such that more recently presented information was weighed more heavily (also see Trueblood & Busemeyer, 2012). They also found that appropriately parameterized QP models could reproduce Markov violations and weak explaining away, phenomena we have taken here as evidence for the mutation sampler.…”

“…Although QP is a potentially important contribution to the understanding of human probabilistic reasoning, as presently formulated its application to causal reasoning is incomplete. Thus far, QP has only been applied to one causal network topology (a three‐variable common effect network, Trueblood & Busemeyer, 2012; Trueblood et al, 2017). More generally, no principles have been specified that determine which variables in a causal network should be treated as compatible or incompatible (and thus the dimensionality of the space) as a function of their causal roles.…”