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Switch to: References
Citations of:
A closer look at the probabilities of the notorious three prisoners
Cognition 43 (3):197-223 (1992)
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The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions and erroneous (...) |
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Decision making theory in general, and mental models in particular, associate judgment and choice. Decision choice follows probability estimates and errors in choice derive mainly from errors in judgment. In the studies reported here we use the Monty Hall dilemma to illustrate that judgment and choice do not always go together, and that such a dissociation can lead to better decision-making. Specifically, we demonstrate that in certain decision problems, exceeding working memory limitations can actually improve decision choice. We show across (...) |
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In this response, we clarify several misunderstandings of the understanding/acceptance principle and defend our specific operationalization of that principle. We reiterate the importance of addressing the problem of rational task construal and we elaborate the notion of computational limitations contained in our target article. Our concept of thinking dispositions as variable intentional-level styles of epistemic and behavioral regulation is explained, as is its relation to the rationality debate. Many of the suggestions of the commentators for elaborating two-process models are easily (...) |
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Bayesian Conditionalization is a widely used proposal for how to update one’s beliefs upon the receipt of new evidence. This is in part because of its attention to the totality of one’s evidence, which often includes facts about what one’s new evidence is and how one has come to have it. However, an increasingly popular position in epistemology holds that one may gain new evidence, construed as knowledge, without being in a position to know that one has gained this evidence. (...) |
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The Bayesian model is used in psychology as the reference for the study of dynamic probability judgment. The main limit induced by this model is that it confines the study of revision of degrees of belief to the sole situations of revision in which the universe is static (revising situations). However, it may happen that individuals have to revise their degrees of belief when the message they learn specifies a change of direction in the universe, which is considered as changing (...) |
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You know that a two-child family has a son. What is the probability that the family has two sons? And what is this probability if you know that the family has a son born on a Tuesday? The former question has been widely discussed previously. The latter adds a new puzzling twist to the situation. In both cases the answer should depend on the specifics of the assumed underlying procedure by which the given information has been obtained. Quantitative analysis, assuming (...) |
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Cognition is both empowered and limited by representations. The matrix lens model explicates tasks that are based on frequency counts, conditional probabilities, and binary contingencies in a general fashion. Based on a structural analysis of such tasks, the model links several problems and semantic domains and provides a new perspective on representational accounts of cognition that recognizes representational isomorphs as opportunities, rather than as problems. The shared structural construct of a 2 × 2 matrix supports a set of generic tasks (...) |
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Rutherford criticizes the way some people have analyzed the 2-children problem, claiming that slight nuances in the problem’s formulation can change the correct answer. However, his own data demonstrate that even when there is a unique correct answer, participants give intuitive answers that differ from it systematically — replicating the data reported by those he criticizes. Thus, his critique reduces to an admonition to use care in formulating and analyzing this brainteaser — which is always a good idea — but (...) |
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The representational epistemic approach to the design of visual displays and notation systems advocates encoding the fundamental conceptual structure of a knowledge domain directly in the structure of a representational system. It is claimed that representations so designed will benefit from greater semantic transparency, which enhances comprehension and ease of learning, and plastic generativity, which makes the meaningful manipulation of the representation easier and less error prone. Epistemic principles for encoding fundamental conceptual structures directly in representational schemes are described. The (...) |
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This research examined choice behaviour and probability judgement in a counterintuitive reasoning problem called the Monty Hall problem (MHP). In Experiments 1 and 2 we examined whether learning from a simulated card game similar to the MHP affected how people solved the MHP. Results indicated that the experience with the card game affected participants' choice behaviour, in that participants selected to switch in the MHP. However, it did not affect their understanding of the objective probabilities. This suggests that there is (...) |
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Two old problems in probability theory involving the concept of randomness are considered. Data obtained with one of them--Bertrand's chord problem--demonstrate the equivocality of this term in the absence of a definition or explication of assumptions underlying its use. They also support two propositions about probabilistic thinking: (1) upon obtaining an answer to a question of probability, people tend to see it as the answer, overlooking tacit assumptions on which it may be based, and tend not to consider the possibility (...) |
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