Conditional probability judgments: Effects of imagining vs experiencing the conditioning event

1991 ◽  
Vol 49 (2) ◽  
pp. 302-325 ◽  
Author(s):  
William S Waller ◽  
Terence R Mitchell
Keyword(s):  
Conditional Probability ◽  
Probability Judgments ◽  
Conditioning Event

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.

Agreeing to Disagree with Conditional Probability Systems

2018 ◽  
Vol 18 (2) ◽  
Author(s):  
Elias Tsakas
Keyword(s):  
Economic Theory ◽  
Conditional Probability ◽  
Dynamic Games ◽  
Interactive Epistemology ◽  
Agreeing To Disagree ◽  
Conditioning Event

Abstract In this note, we extend Aumann’s agreement theorem to a framework where beliefs are modelled by conditional probability systems à la Battigalli, P., and M. Siniscalchi. 1999. “Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games.” Journal of Economic Theory 88: 188–230. We prove two independent generalizations of the agreement theorem, one where the agents share some common conditioning event, and one where they may not.

Evidence for the Jeffrey Table

2019 ◽  
Vol 66 (3) ◽  
pp. 187-194
Author(s):  
Moyun Wang ◽  
Mingyi Zhu
Keyword(s):  
Conditional Probability ◽  
Fundamental Question ◽  
The Other ◽  
Adequate Account ◽  
Natural Languages ◽  
Probability Judgments ◽  
Low Level ◽  
De Finetti

Abstract. Conditionals statements are a common and necessary component in natural languages. The research reported in this paper is on a fundamental question about singular conditionals. Is there an adequate account of people’s truth, falsity, and credibility (probability) judgments about these conditionals when their antecedents are false? Two experiments examined people’s quantitative credibility ratings and qualitative truth and falsity judgments for singular conditionals, if p then q, given false antecedent, not-p, cases. The results demonstrate that, when relevant knowledge about the conditional probability of q given p, P( q|p), is available to participants in not-p cases, they tend to make credibility ratings based on P( q|p), and to make “true” (or “false”) judgments at a high (or low) level of these credibility ratings. These findings favor the Jeffrey table account of these conditionals over the other existing accounts, including that of the de Finetti table.

Causation and the Probability of Causal Conditionals

2017 ◽  
Author(s):  
David E. Over
Keyword(s):  
Natural Language ◽  
Conditional Probability ◽  
Causal Reasoning ◽  
Probability Judgments ◽  
Counterfactual Conditionals ◽  
Bayesian Inferences ◽  
Conditional Inferences

Indicative and counterfactual conditionals are central to reasoning in general and causal reasoning in particular. Normative theorists and psychologists have held a range of views on how natural language indicative and counterfactual conditionals, and probability judgments about them, are related to causation. There is the question of whether “causal” conditionals, referring to possible causes and effects, can be used to explain causation, or whether causation can be used to explain the conditionals. There are questions about how causation, conditionals, Bayesian inferences, conditional probability, and imaging are related to each other. Psychological results are relevant to these questions, including findings on how people make conditional inferences and judgments about possibilities, conditionals, and conditional probability. Deeper understanding of the relation between causation and conditionals will come in further research on people’s reasoning from counterfactuals as premises, and to counterfactuals as conclusions.

Facial Likability and Smiling Enhance Cooperation, but Have No Direct Effect on Moralistic Punishment

2016 ◽  
Vol 63 (5) ◽  
pp. 263-277 ◽  
Author(s):  
Laura Mieth ◽  
Raoul Bell ◽  
Axel Buchner
Keyword(s):  
Conditional Probability ◽  
Direct Effect ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Prisoner’S Dilemma Game ◽  
Costly Punishment ◽  
Prisoner's Dilemma Game ◽  
Moralistic Punishment

Abstract. The present study serves to test how positive and negative appearance-based expectations affect cooperation and punishment. Participants played a prisoner’s dilemma game with partners who either cooperated or defected. Then they were given a costly punishment option: They could spend money to decrease the payoffs of their partners. Aggregated over trials, participants spent more money for punishing the defection of likable-looking and smiling partners compared to punishing the defection of unlikable-looking and nonsmiling partners, but only because participants were more likely to cooperate with likable-looking and smiling partners, which provided the participants with more opportunities for moralistic punishment. When expressed as a conditional probability, moralistic punishment did not differ as a function of the partners’ facial likability. Smiling had no effect on the probability of moralistic punishment, but punishment was milder for smiling in comparison to nonsmiling partners.

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