Surprisingly rational: Probability theory plus noise explains biases in judgment.

Costello, Fintan; Watts, Paul

doi:10.1037/a0037010

Cited by 120 publications

(301 citation statements)

References 60 publications

Supporting

Mentioning

285

Contrasting

Unclassified

Order By: Relevance

“…Their results suggest that deviations from optimality observed in the behavior are not due to a fundamental inability to represent and combine probability distributions, but might instead be due to random noise in this process. A similar argument is made by Costello and Watts, who suggest that biases in probability judgment may arise from a fundamental adherence to probability theory, but corrupted by random approximations (Costello and Watts, 2014). …”

Section: Approximated Probabilistic Computationsmentioning

confidence: 80%

Confidence as Bayesian Probability: From Neural Origins to Behavior

Meyniel

Sigman

Mainen

2015

Neuron

296

305

View full text Add to dashboard Cite

Research on confidence spreads across several sub-fields of psychology and neuroscience. Here, we explore how a definition of confidence as Bayesian probability can unify these viewpoints. This computational view entails that there are distinct forms in which confidence is represented and used in the brain, including distributional confidence, pertaining to neural representations of probability distributions, and summary confidence, pertaining to scalar summaries of those distributions. Summary confidence is, normatively, derived or "read out" from distributional confidence. Neural implementations of readout will trade off optimality versus flexibility of routing across brain systems, allowing confidence to serve diverse cognitive functions.

show abstract

Section: Approximated Probabilistic Computationsmentioning

confidence: 80%

Confidence as Bayesian Probability: From Neural Origins to Behavior

Meyniel

Sigman

Mainen

2015

Neuron

296

305

View full text Add to dashboard Cite

show abstract

“…Informally, if we know about the causes of some event X, then the descendants of X may give us information about X, but the non-descendants cannot give us any more information about X. Recently, various studies (Rottman & Hastie, 2016Park & Sloman, 2013;Rehder, 2014;Fernbach & Sloman, 2009;Waldmann, Cheng, Hagmayer, & Blaisdell, 2008;Hagmayer & Waldmann, 2002) have provided evidence that people often violate the Markov condition when making causal inferences.In another line of research, there has been an attempt to modify existing Bayesian models to explain away erroneous judgments (Costello, 2009;Costello & Watts, 2014). These models are interesting both from a philosophical point of view, because they may shed light on the principles underlying human reasoning, and also from a practical point of view, as an understanding of why we make judgment errors may inform strategies to improve decision making.…”

mentioning

confidence: 99%

A quantum probability framework for human probabilistic inference.

Trueblood

Yearsley

Pothos

2017

Journal of Experimental Psychology: General

View full text Add to dashboard Cite

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...

show abstract

“…A reviewer suggested a slightly more subtle comparison based on the True + Error model (e.g., Costello & Watts, ; Erev et al, ). Assuming that all the judges generate their judgments by anchoring on the true values, but these values are perturbed by individual and independent random errors with possibly different variances but symmetric distributions around a common mean of 0, one can work backwards and associate each mean direct estimate with a corresponding underlying value using the following three steps:

y_{i} ((), X) = normalln \frac{p_{i} ((), X)}{1 - p_{i} ((), X)}

where p i ( X ) = joint estimates of the individual judges for event X.

E ((), Y) = \frac{true {true\sum}_{i}^{n} y_{i} ((), X)}{n}

where n is the total number of judges who estimated P(Event X).

p^{*} = \frac{e^{E (Y)}}{1 + e^{E ((), Y)}}

where p * is the recovered value for P(Event X). The correction brought the direct estimates closer to the true probabilities (Table ).…”

Section: Resultsmentioning

confidence: 99%

“…Judgments of subjective probabilities expressed by individuals often do not obey all the requirements imposed, and implied, by probability theory. The high incidence of conjunction fallacies and internal inconsistency observed in the direct estimates can be explained by the availability and representativeness heuristics and the positivity bias or, alternatively, by the effects of random error on, otherwise accurate, judgments (e.g., Costello & Watts, ). Our work was not guided by one particular theoretical view.…”

Section: Discussionmentioning

confidence: 99%

Eliciting Subjective Probabilities through Pair‐wise Comparisons

Por

Budescu

2016

Behavioral Decision Making

View full text Add to dashboard Cite

We propose and test a novel approach for eliciting subjective joint probabilities. In the proposed approach, judges compare pairs of possible outcomes and identify which of the two is more likely and by how much. These pair‐wise comparative judgments create a matrix of ratio judgments from which the target probabilities are extracted using the rows' (or columns') geometric means. In Study 1, subjects provided direct assessments of the likelihood of joint events (e.g., sunny days and stock market gains) and also made pair‐wise comparisons of the same joint events. Subjects in Study 2 learnt the distribution of hypothetical events pairs and provided direct and ratio estimates. In both studies, the ratio estimates were significantly more accurate than the direct estimates. The results suggest that it is possible to elicit probabilistic estimates without explictly asking for probabilities and that the pair‐wise approach is a candidate for complementing or replacing traditional elicitation approaches. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

Surprisingly rational: Probability theory plus noise explains biases in judgment.

Cited by 120 publications

References 60 publications

Confidence as Bayesian Probability: From Neural Origins to Behavior

Confidence as Bayesian Probability: From Neural Origins to Behavior

A quantum probability framework for human probabilistic inference.

Eliciting Subjective Probabilities through Pair‐wise Comparisons

Contact Info

Product

Resources

About