Abstract. Analyses of the Sleeping Beauty Problem are polarised between those advocating the “1/2 view” (“halfers”) and those endorsing the “1/3 view” (“thirders”). The disagreement concerns the evidential relevance of self-locating information. Unlike halfers, thirders regard self-locating information as evidentially relevant in the Sleeping Beauty Problem. In the present study, we systematically manipulate the kind of information available in different formulations of the Sleeping Beauty Problem. Our findings indicate that patterns of judgment on different formulations of the Sleeping Beauty Problem do not fit either the “1/2 view” or the “1/3 view”. Human reasoners tend to acknowledge self-locating evidence as relevant, but discount its weight significantly. Accordingly, self-locating information may trigger more cautious judgments of confirmation than familiar kinds of statistical evidence. We also discuss how these results can advance the debate by providing a more nuanced and empirically grounded account or explication of the evidential impact of self-locating information.

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Abstract. We report the first empirical data showing a significant amount of double conjunction fallacies in physicians’ probability judgments concerning prognosis and diagnosis. Our results support the hypothesis that physicians’ probability judgments are guided by assessments of evidential impact between diagnostic conditions and clinical signs. Moreover, we show that, contrary to some influential views, double conjunction fallacies represent an experimentally replicable reasoning bias. We discuss how the phenomenon eludes major current accounts of uncertain reasoning in medicine and beyond and how it relates to clinical practice.

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Abstract. Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people’s goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty and the reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma–Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information‐theoretic formalism.

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Crupi V., Nelson J.D., Meder B., Cevolani G., and Tentori K. (2018), Generalized information theory meets human cognition: Introducing a unified framework to model uncertainty and information search, Cognitive Science (in press).

Abstract. Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people’s goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty and the reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma-Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information-theoretic formalism.

Abstract. Although error is an integral part of the world of medicine, physicians have always been little inclined to take into account their own mistakes and the extraordinary technological progress observed in the last decades does not seem to have resulted in a significant reduction in the percentage of diagnostic errors. The failure in the reduction in diagnostic errors, notwithstanding the considerable investment in human and economic resources, has paved the way to new strategies which were made available by the development of cognitive psychology, the branch of psychology that aims at understanding the mechanisms of human reasoning. This new approach led us to realize that we are not fully rational agents able to take decisions on the basis of logical and probabilistically appropriate evaluations. In us, two different and mostly independent modes of reasoning coexist: a fast or non-analytical reasoning, which tends to be largely automatic and fast-reactive, and a slow or analytical reasoning, which permits to give rationally founded answers. One of the features of the fast mode of reasoning is the employment of standardized rules, termed ‘‘heuristics.’’ Heuristics lead physicians to correct choices in a large percentage of cases. Unfortu- nately, cases exist wherein the heuristic triggered fails to fit the target problem, so that the fast mode of reasoning can lead us to unreflectively perform actions exposing us and others to variable degrees of risk. Cognitive errors arise as a result of these cases. Our review illustrates how cognitive errors can cause diagnostic problems in clinical practice.

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Abstract. Inductive reasoning requires exploiting links between evidence and hypotheses. This can be done focusing either on the posterior probability of the hypothesis when updated on the new evidence or on the impact of the new evidence on the credibility of the hypothesis. But are these two cognitive representations equally reliable? This study investigates this question by comparing probability and impact judgments on the same experimental materials. The results indicate that impact judgments are more consistent in time and more accurate than probability judgments. Impact judgments also predict the direction of errors in probability judgments. These findings sug- gest that human inductive reasoning relies more on estimating evidential impact than on posterior probability.

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Abstract. According to Costello and Watts (2014), probability theory can account for key findings in human judgment research provided that random noise is embedded in the model. We concur with a number of Costello and Watts’s remarks, but challenge the empirical adequacy of their model in one of their key illustrations (the conjunction fallacy) on the basis of recent experimental findings. We also discuss how our argument bears on heuristic and rational thinking.

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Abstract. The aim of this paper is to survey and discuss some key connections between information and confirmation within a broadly Bayesian framework. We mean to show that treating information and confirmation in a unified fashion is an intuitive and fruitful approach, fostering insights and prospects in the analysis of a variety of related notions such as belief change, partial entailment, entropy, the value of experiments, and more besides. To this end, we recapitulate established theoretical achievements, disclose a number of underlying links, and provide a few novel results.

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