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16
Updating Probabilities
, 2002
"... As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a "naive space", which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine why. A criterion known as CAR ("coarsening at random") in t ..."
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Cited by 53 (6 self)
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As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a "naive space", which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine why. A criterion known as CAR ("coarsening at random") in the statistical literature characterizes when "naive" conditioning in a naive space works. We show that the CAR condition holds rather infrequently, and we provide a procedural characterization of it, by giving a randomized algorithm that generates all and only distributions for which CAR holds. This substantially extends previous characterizations of CAR. We also consider more generalized notions of update such as Jeffrey conditioning and minimizing relative entropy (MRE). We give a generalization of the CAR condition that characterizes when Jeffrey conditioning leads to appropriate answers, and show that there exist some very simple settings in which MRE essentially never gives the right results. This generalizes and interconnects previous results obtained in the literature on CAR and MRE.
Individuation, counting, and statistical inference: The role of frequency and wholeobject representations in judgment under uncertainty
 Journal of Experimental Psychology: General
, 1998
"... Evolutionary approaches to judgment under uncertainty have led to new data showing that untutored subject reliably produce judgments that conform to may principles of probability theory when (a) they are asked to compute a frequency instead of the probability of a single event, and (b) the relevant ..."
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Cited by 29 (11 self)
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Evolutionary approaches to judgment under uncertainty have led to new data showing that untutored subject reliably produce judgments that conform to may principles of probability theory when (a) they are asked to compute a frequency instead of the probability of a single event, and (b) the relevant information is expressed as frequencies. But are the frequencycomputation systems implicated in these experiments better at operating over some kinds of input than others? Principles of object perception and principles of adaptive design led us to propose the individuation hypothesis: that these systems are designed to produce wellcalibrated statistical inferences when they operate over representations of “whole ” objects, events, and locations. In a series of experiments on Bayesian reasoning, we show that human performance can be systematically improved or degraded by varying whether a correct solution requires one to compute hit and falsealarm rates over “natural ” units, such as whole objects, as opposed to inseparable aspects, views, and other parsings that violate evolved principles of object construal. The ability to make wellcalibrated probability judgments depends, at a very basic level, on the ability to count. The
A logical approach to reasoning about uncertainty: a tutorial
 Discourse, Interaction, and Communication
, 1998
"... I consider a logical framework for modeling uncertainty, based on the use of possible worlds, that incorporates knowledge, probability, and time. This turns out to be a powerful approach for modeling many problems of interest. I show how it can be used to give insights into (among other things) seve ..."
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Cited by 12 (0 self)
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I consider a logical framework for modeling uncertainty, based on the use of possible worlds, that incorporates knowledge, probability, and time. This turns out to be a powerful approach for modeling many problems of interest. I show how it can be used to give insights into (among other things) several wellknown puzzles.
Partitioneditcount: Naïve extensional reasoning in conditional probability judgment
 Journal of Experimental Psychology: General
, 2004
"... The authors provide evidence that people typically evaluate conditional probabilities by subjectively partitioning the sample space into n interchangeable events, editing out events that can be eliminated on the basis of conditioning information, counting remaining events, then reporting probabiliti ..."
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Cited by 10 (5 self)
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The authors provide evidence that people typically evaluate conditional probabilities by subjectively partitioning the sample space into n interchangeable events, editing out events that can be eliminated on the basis of conditioning information, counting remaining events, then reporting probabilities as a ratio of the number of focal to total events. Participants ’ responses to conditional probability problems were influenced by irrelevant information (Study 1), small variations in problem wording (Study 2), and grouping of events (Study 3), as predicted by the partition–edit–count model. Informal protocol analysis also supports the authors ’ interpretation. A 4th study extends this account from situations where events are treated as interchangeable (chance and ignorance) to situations where participants have information they can use to distinguish among events (uncertainty). People are often called on to make judgments of conditional likelihood. For example, a patient might try to assess the likelihood of having a disease, given a positive test result; a litigant might try to estimate the odds of prevailing in court, given a piece of damning evidence. Over the last 30 years, psychologists have shown that people typically judge conditional probabilities using a
Evolutionary Versus Instrumental Goals: How Evolutionary Psychology Misconceives Human Rationality. Evolution and the psychology of thinking
, 2003
"... An important research tradition in the cognitive psychology of reasoningcalled the heuristics and biases approachhas firmly established that people’s responses often deviate from the performance considered normative on many reasoning tasks. For example, people assess probabilities incorrectly, t ..."
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Cited by 6 (0 self)
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An important research tradition in the cognitive psychology of reasoningcalled the heuristics and biases approachhas firmly established that people’s responses often deviate from the performance considered normative on many reasoning tasks. For example, people assess probabilities incorrectly, they display confirmation bias, they test hypotheses inefficiently, they violate the axioms of utility theory, they do not properly calibrate degrees of belief, they overproject their own opinions onto others, they display illogical framing effects, they uneconomically honor sunk costs, they allow prior knowledge to become implicated in deductive reasoning, and they display numerous other information processing biases (for summaries of the large literature, see
Assessing psychology students’ difficulties with conditional probability and bayesian reasoning
 In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics
, 2006
"... Conditional probability and Bayesian reasoning are important to psychology students because they are involved in the understanding of classical and Bayesian inference, regression and correlation, linear models, multivariate analysis and other statistical procedures that are often used in psychologic ..."
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Cited by 3 (2 self)
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Conditional probability and Bayesian reasoning are important to psychology students because they are involved in the understanding of classical and Bayesian inference, regression and correlation, linear models, multivariate analysis and other statistical procedures that are often used in psychological research. A study of previous literature showed that there is considerable research on this topic, but no comprehensive questionnaires have been developed to globally assess students ' understanding and misconceptions on these topics. At the University of Granada we started building a questionnaire, which takes into account the content of conditional probability taught in the Spanish universities to psychology students, as well as the biases and misconceptions described in the literature. In this work we will describe the process of developing the questionnaire and will report the results from a sample of 206 psychology students.
How to confuse with statistics. The use and misuse of conditional probabilities
 Statistical Science
, 2005
"... Abstract. This article shows by various examples how consumers of statistical information may be confused when this information is presented in terms of conditional probabilities. It also shows how this confusion helps others to lie with statistics, and it suggests both confusion and lies can be exp ..."
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Cited by 3 (3 self)
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Abstract. This article shows by various examples how consumers of statistical information may be confused when this information is presented in terms of conditional probabilities. It also shows how this confusion helps others to lie with statistics, and it suggests both confusion and lies can be exposed by using alternative modes of conveying statistical information. Key words and phrases: Conditional probabilities, natural frequencies, heuristical reasoning. 1.
The Monty Hall Dilemma Revisited: Understanding the Interaction of Problem Definition and Decision Making
, 1999
"... We examine a logical decision problem, the "Monty Hall Dilemma," in which a large portion of sophisticated subjects appear to insist on an apparently wrong solution. Although a substantial literature examines the structure of this problem, we argue that the extant analyses have not recognized the co ..."
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Cited by 1 (0 self)
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We examine a logical decision problem, the "Monty Hall Dilemma," in which a large portion of sophisticated subjects appear to insist on an apparently wrong solution. Although a substantial literature examines the structure of this problem, we argue that the extant analyses have not recognized the constellation of cues that guide respondents' answers. We show that insight into subjects' decisions may be obtained by considering problems with similar surface structure to the Monty Hall Dilemma but which are common in environments that they routinely face. In particular, we consider the problem modeled as a game in which actors have possibly opposing interests, and as an environment with information provided by an objective source. We present experimental evidence showing that these comparisons help to explain subject responses. Monty Hall Dilemma Revisited 3 Analyses of decision making behavior frequently focus on decision problems in which subjects violate normative standards. One of t...
A note on neglect defaulting
"... I introduce the notion of “neglect defaulting, ” which labels the propensity to neglect possibilities which are ordinarily sensibly neglected. In familiar contexts we are welltuned to recognize when to override the default. But outside the range of familiar experience — here in the artificial conte ..."
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Cited by 1 (0 self)
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I introduce the notion of “neglect defaulting, ” which labels the propensity to neglect possibilities which are ordinarily sensibly neglected. In familiar contexts we are welltuned to recognize when to override the default. But outside the range of familiar experience — here in the artificial context of puzzles — these ordinarily benign defaults can make it difficult for even sophisticated subjects, such as readers of this note, to avoid responses which on reflection will be seen as obviously mistaken. A detail of particular importance is that, although subjects are easily prompted to take one step in the direction of reaching a sound response, the tendency to then neglect to consider that another step may be needed is remarkably strong. In each of the five examples the needed but usually neglected second step is quite trivial. Concluding remarks point to consequences for larger questions outside the range of familiar experience, in politics and other contexts out of scale with everyday experience.
The Ellsberg ‘Problem ’ and Implicit Assumptions under Ambiguity
"... Empirical research has revealed that people try to avoid ambiguity in the Ellsberg problem and make choices inconsistent with the predictions of Expected Utility Theory. We hypothesized that people might be forming implicit assumptions to deal with the ambiguity resulting from the incomplete informa ..."
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Empirical research has revealed that people try to avoid ambiguity in the Ellsberg problem and make choices inconsistent with the predictions of Expected Utility Theory. We hypothesized that people might be forming implicit assumptions to deal with the ambiguity resulting from the incomplete information in the problem, and that some assumptions might lead them to deviate from normative predictions. We embedded the Ellsberg problem in various scenarios that made one source of ambiguity (i.e., the implied distribution of the unknown number of the colored balls) explicit. Results of an experiment showed that more people chose consistently (and hence rationally) when the scenario encouraged them to think that the probability distribution of the number of balls was normal. The results give insight into the implicit assumptions that might lead to choices congruent with normative models.