scholarly journals Exploring the Conjunction Fallacy in Probability Judgment: Conversational Implicature or Nested Sets?

2019 ◽  
Vol 10 (2) ◽  
Author(s):  
Amos Pagin
Keyword(s):  
Conjunction Fallacy ◽  
Probability Judgment ◽  
Conversational Implicature ◽  
Nested Sets

scholarly journals The Bayesian Sampler: Generic Bayesian Inference Causes Incoherence in Human Probability Judgments

2018 ◽  
Author(s):  
Jian-Qiao Zhu ◽  
Adam N Sanborn ◽  
Nick Chater
Keyword(s):  
Probabilistic Models ◽  
Conjunction Fallacy ◽  
Probability Judgment ◽  
Noise Model ◽  
Probability Judgments ◽  
Probability Estimates ◽  
Bayesian Models Of Cognition ◽  
Improved Accuracy ◽  
Biases And Heuristics ◽  
The Brain

Human probability judgments are systematically biased, in apparent tension with Bayesian models of cognition. But perhaps the brain does not represent probabilities explicitly, but approximates probabilistic calculations through a process of sampling, as used in computational probabilistic models in statistics. Naïve probability estimates can be obtained by calculating the relative frequency of an event within a sample, but these estimates tend to be extreme when the sample size is small. We propose instead that people use a generic prior to improve the accuracy of their probability estimates based on samples, and we call this model the Bayesian sampler. The Bayesian sampler trades off the coherence of probabilistic judgments for improved accuracy, and provides a single framework for explaining phenomena associated with diverse biases and heuristics such as conservatism and the conjunction fallacy. The approach turns out to provide a rational reinterpretation of “noise” in an important recent model of probability judgment, the probability theory plus noise model (Costello & Watts, 2014, 2016a, 2017, 2019; Costello, Watts, & Fisher, 2018), making equivalent average predictions for simple events, conjunctions, and disjunctions. The Bayesian sampler does, however, make distinct predictions for conditional probabilities, and we show in a new experiment that this model better captures these judgments both qualitatively and quantitatively.

Facilitating Normative Judgments of Conditional Probability: Frequency or Nested Sets?

2003 ◽  
Vol 50 (2) ◽  
pp. 97-106 ◽  
Author(s):  
Kimihiko Yamagishi
Keyword(s):  
Conditional Probability ◽  
Probabilistic Reasoning ◽  
Probability Judgment ◽  
Probability Judgments ◽  
Normative Reasoning ◽  
Roulette Wheel ◽  
Probability Task ◽  
Nested Sets ◽  
Probabilistic Structure ◽  
Inspection Machine

Abstract. Recent probability judgment research contrasts two opposing views. Some theorists have emphasized the role of frequency representations in facilitating probabilistic correctness; opponents have noted that visualizing the probabilistic structure of the task sufficiently facilitates normative reasoning. In the current experiment, the following conditional probability task, an isomorph of the “Problem of Three Prisoners” was tested. “A factory manufactures artificial gemstones. Each gemstone has a 1/3 chance of being blurred, a 1/3 chance of being cracked, and a 1/3 chance of being clear. An inspection machine removes all cracked gemstones, and retains all clear gemstones. However, the machine removes ½ of the blurred gemstones. What is the chance that a gemstone is blurred after the inspection?” A 2 × 2 design was administered. The first variable was the use of frequency instruction. The second manipulation was the use of a roulette-wheel diagram that illustrated a “nested-sets” relationship between the prior and the posterior probabilities. Results from two experiments showed that frequency alone had modest effects, while the nested-sets instruction achieved a superior facilitation of normative reasoning. The third experiment compared the roulette-wheel diagram to tree diagrams that also showed the nested-sets relationship. The roulette-wheel diagram outperformed the tree diagrams in facilitation of probabilistic reasoning. Implications for understanding the nature of intuitive probability judgments are discussed.

Converging evidence supports fuzzy-trace theory's nested sets hypothesis, but not the frequency hypothesis

2007 ◽  
Vol 30 (3) ◽  
pp. 278-280 ◽  
Author(s):  
Valerie F. Reyna ◽  
Britain Mills
Keyword(s):  
Conjunction Fallacy ◽  
Base Rate ◽  
Syllogistic Reasoning ◽  
Class Inclusion ◽  
Trace Theory ◽  
Fuzzy Trace Theory ◽  
Rate Effects ◽  
Nested Sets

AbstractEvidence favors the nested sets hypothesis, introduced by fuzzy-trace theory (FTT) in the 1990s to explain “class-inclusion” effects and extended to many tasks, including conjunction fallacy, syllogistic reasoning, and base-rate effects (e.g., Brainerd & Reyna 1990; Reyna 1991; 2004; Reyna & Adam 2003; Reyna & Brainerd 1995). Crucial differences in mechanisms distinguish the FTT and Barbey & Sloman (B&S) accounts, but both contrast with frequency predictions (see Reyna & Brainerd, in press).

scholarly journals The Linda who skipped the logic classes

2021 ◽  
Author(s):  
Rivka Schlagbaum ◽  
Moshe Szweizer
Keyword(s):  
Critical Analysis ◽  
Conjunction Fallacy ◽  
Probability Judgment ◽  
Original Publication ◽  
Research Papers ◽  
Entire Field

The letter points to a logical mistake found in “The conjunction fallacy in probability judgment” published by Tversky and Kahneman. Currently, at least 5,100 research papers reference this work, and an entire field of associated studies has been created based on the paper. These works assume the correctness of the original publication and reproduce the error without due critical analysis.

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