The Bayesian sampler : generic Bayesian inference causes incoherence in human probability

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; Costello & Watts, 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 distributions of probability estimates. We show in 2 new experiments that this model better captures these mean judgments both qualitatively and quantitatively; which model best fits individual distributions of responses depends on the assumed size of the cognitive sample

A quantum theoretical explanation for probability judgment errors

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning

Security Analysis: A Critical Thinking Approach

Security Analysis: A Critical-Thinking Approach is for anyone desiring to learn techniques for generating the best answers to complex questions and best solutions to complex problems. It furnishes current and future analysts in national security, homeland security, law enforcement, and corporate security an alternative, comprehensive process for conducting both intelligence analysis and policy analysis. The target audience is upper-division undergraduate students and new graduate students, along with entry-level practitioner trainees. The book centers on a Security Analysis Critical-Thinking Framework that synthesizes critical-thinking and existing analytic techniques. Ample examples are provided to assist readers in comprehending the material. Newly created material includes techniques for analyzing beliefs and political cultures. The book also functions as an introduction to Foreign Policy and Security Studies.https://encompass.eku.edu/ekuopen/1005/thumbnail.jp

Rationality and the experimental study of reasoning

A survey of the results obtained during the past three decades in some of the most widely used tasks and paradigms in the experimental study of reasoning is presented. It is shown that, at first sight, human performance suffers from serious shortcomings. However, after the problems of communication between experimenter and subject are taken into account, which leads to clarify the subject's representation of the tasks, one observes a better performance, although still far from perfect. Current theories of reasoning, of which the two most prominent are very briefly outlined, agree in identifying the load in working memory as the main source of limitation in performance. Finally, a recent view on human rationality prompted by the foregoing results is described

Overconfidence bias and conjunction fallacy in predicting outcomes of football matches

The aim of this study was to explore the occurrence of the overconfidence bias and the conjunction fallacy in betting behavior among frequent and sporadic bettors and to test whether it was influenced by the task format (probability vs. frequencies). Frequent bettors (N = 67) and sporadic bettors (N = 63) estimated whether the bets on football games presented to them via an on-line questionnaire would be successful. The bets consisted of singles (one match outcomes) and conjunctions (two matches outcomes), and were presented either in probability or frequency terms. Both frequent and sporadic bettors showed similar levels of the overconfidence bias. However, the frequent bettors made the conjunction fallacy more often than the sporadic bettors. The presentation of the task in the frequency terms significantly reduced the overconfidence bias in comparison to the evaluations in probability terms, but left the conjunction fallacy unaffected

The Impact of Motivation, Processing Difficulty and Cognitive Resources on the Use of Base-Rates in Social Judgment

This study explores the impact of motivation, cognitive resources and difficulty of processing on social judgment. We hypothesized and found all three variables influence the type of information used to render judgment. Only when the information was easy to process, cognitive resources were ample and motivation was high were subjects able to use difficult information as a basis for their judgment. Furthermore, contrary to the common notion that statistical information tends to be utilized when resources are high, we were able to show that subjects relied on statistical information when their motivation was low, the information was difficult to process and/or cognitive resources were limited. These results add to the growing body of evidence attesting that the contents of information as such do not affect the likelihood of their being made use of in judgment. Both base-rates and representativeness ("heuristic") information seem to be used in accordance with their subjective relevance - when such relevance is discerned given that the individuals' resources are sufficient to cope with the difficult posed by the cognitive task at hand

Logical intuitions and heuristic reflections : rethinking the role of intuition in probability judgements

This thesis aims to further our understanding of the role that intuition plays in human reasoning when making probability judgements. It attempts to: a) gain a better understanding of the cognitive processes underlying these judgements, b) determine how individual differences impacts the logicality of these judgements, and c) test original and theoretically-driven ways to increase logical intuitions in probability judgements. Classically, it is assumed that people make biased judgements because they rely on an intuitive thinking system (System 1) and apply the representativeness heuristic to make conjunctive probability judgements. In contrast, logical judgements are assumed to arise from the use of deliberation (System 2) to overrule the prepotent heuristic response and replace it with a logical one. Recent research; however, has challenged this claim and instead proposes that our intuitions do not always lead us astray. In fact, they can reflect a sensitivity to logic that is implicit, and potentially happens automatically and outside of awareness. This thesis takes this notion one step further and asks whether it is the slower, more deliberative, thinking system which may be vulnerable to prior beliefs and biases. A series of five experiments examined the relative impact of heuristic and logical considerations on probability judgements. The results indicated that people are readily able to detect the conflict underlying intuitive and deliberative assessments, and that people effortlessly engage in deliberative processing, which suggests they are not simply cognitive misers who fail to reason in line with the principles of logic because they either lack the cognitive ability or the motivation to do so. The results also supported the idea that people can intuit logical judgements (i.e., judgements in accordance with the laws of probability) when they rely on System 1 thinking; however, when they deliberate or use System 2 thinking, that is when the heuristic biases their judgements