Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one specifies the information format in which it is designed to operate. The authors show that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Frequency formats correspond to the sequential way information is acquired in natural sampling, from animal foraging to neural networks. By analyzing several thousand solutions to Bayesian problems, the authors found that when information was presented in frequency formats, statistically naive participants derived up to 50 % of all inferences by Bayesian algorithms. Non-Bayesian algorithms included simple versions of Fisherian and Neyman-Pearsonian inference. Is the mind, by design, predisposed against performing Bayesian inference? The classical probabilists of the Enlightenment, including Condorcet, Poisson, and Laplace, equated probability theory with the common sense of educated people, who were known then as “hommes éclairés.” Laplace (1814/1951) declared that “the theory of probability is at bottom nothing more than good sense reduced to a calculus which evaluates that which good minds know by a sort of instinct,

Abstract not found

Research on people’s confidence in their general knowledge has to date produced two fairly stable effects, many inconsistent results, and no comprehensive theory. We propose such a comprehensive framework, the theory of probabilistic mental models (PMM theory). The theory (a) explains both the overconfidence effect (mean confidence is higher than percentage of answers correct) and the hard-easy effect (overconfidence increases with item difficulty) reported in the literature and (b) predicts conditions under which both effects appear, disappear, or invert. In addition, (c) it predicts a new phenomenon, the confidence-frequency effect, a systematic difference between a judgment of confidence in a single event (i.e., that any given answer is correct) and a judgment of the frequency of correct answers in the long run. Two experiments are reported that support PMM theory by confirming these predictions, and several apparent anomalies reported in the literature are explained and integrated into the present framework. Do people think they know more than they really do? In the last 15 years, cognitive psychologists have amassed a large and apparently damning body of experimental evidence on overconfidence in knowledge, evidence that is in turn part of an even larger and more damning literature on socalled cognitive biases. The cognitive bias research claims that people are naturally prone to making mistakes in reasoning and memory, including the mistake of overestimating their knowledge.

What counts as human rationality: reasoning processes that embody content-independent formal theories, such as propositional logic, or reasoning processes that are well designed for solving important adaptive problems? Most theories of human reasoning have been based on content-independent formal rationality, whereas adaptive reasoning, ecological or evolutionary, has been little explored. We elaborate and test an evolutionary approach, Cosmides’ (1989) social contract theory, using the Wason selection task. In the first part, we disentangle the theoretical concept of a “social contract” from that of a “cheater-detection algorithm.” We demonstrate that the fact that a rule is perceived as a social contract—or a conditional permission or obligation, as Cheng and Holyoak (1985) proposed—is not sufficient to elicit Cosmides’ striking results, which we replicated. The crucial issue is not semantic (the meaning of the rule), but pragmatic: whether a person is cued into the perspective of a party who can be cheated. In the second part, we distinguish between social contracts with bilateral and unilateral cheating options. Perspective change in contracts with bilateral cheating options turns P & not-Q responses into not-P & Q responses. The results strongly support social contract theory, contradict availability theory, and cannot be accounted for by pragmatic reasoning schema theory, which lacks the pragmatic concepts of perspectives and cheating detection.

The study of scientific discovery—where do new ideas come from?—has long been denigrated by philosophers as irrelevant to analyzing the growth of scientific knowledge. In particular, little is known about how cognitive theories are discovered, and neither the classical accounts of discovery as either probabilistic induction (e.g., Reichenbach, 1938) or lucky guesses (e.g., Popper, 1959), nor the stock anecdotes about sudden “eureka ” moments deepen the insight into discovery. A heuristics approach is taken in this review, where heuristics are understood as strategies of discovery less general than a supposed unique logic of discovery but more general than lucky guesses. This article deals with how scientists’ tools shape theories of mind, in particular with how methods of statistical inference have turned into metaphors of mind. The tools-to-theories heuristic explains the emergence of a broad range of cognitive theories, from the cognitive revolution of the 1960s up to the present, and it can be used to detect both limitations and new lines of development in current cognitive theories that investigate the mind as an “intuitive statistician.” Scientific inquiry can be viewed as “an ocean, continuous everywhere and without a break or division ” (Leibniz, 1690/1951, p. 73). Hans Reichenbach (1938) nonetheless divided this ocean into two great seas, the context of discovery and the context of justification. Philosophers, logicians,

Findings in recent research on the `conjunction fallacy ' have been taken as evidence that our minds are not designed to work by the rules of probability. This conclusion springs from the idea that norms should be content-blind Ð in the present case, the assumption that sound reasoning requires following the conjunction rule of probability theory. But content-blind norms overlook some of the intelligent ways in which humans deal with uncertainty, for instance, when drawing semantic and pragmatic inferences. In a series of studies, we ®rst show that people infer nonmathematical meanings of the polysemous term `probability' in the classic Linda conjunction problem. We then demonstrate that one can design contexts in which people infer mathematical meanings of the term and are therefore more likely to conform to the conjunction rule. Finally, we report evidence that the term `frequency ' narrows the spectrum of possible interpretations of `probability ' down to its mathematical meanings, and that this fact Ð rather than the presence or absence of `extensional cues ' Ð accounts for the low proportion of violations of the conjunction rule when people are asked for

s in the courtroom among the so-called `Bayesian enthusiasts' and the `Bayesio-skeptics'. Precursors of the first camp include: Bernoulli, D'Alembert, Condorcet, and Boole. Skeptics include: Voltaire, Montaigne, J.S. Mill. 1 Introduction The "legal science" school, one generation ago, yielded among the other things a vision in which aspects of legal scholarship could be approached scientifically, and for that matter, even quantitatively. It must be said from the start that quantification, in models for law, is not necessarily quantification of evidence; for example, consider the pervasiveness, in legal matters relating to actual (or expected) events, of the temporal dimension (see, e.g., Jackson 1998) and of spatial dimensions (which come in different grainsizes: see Nissan (1997)); even when reasoning about legal time qualitatively, quantitative considerations about absolute time or relative time are inescapably involved (see formal models in Martino and Nissan (1998a)). Lennart Aq

The term “nonrational” denotes a heterogeneous class of theories of decision making designed to overcome problems with traditional “rational ” theories. Nonrational theories have been denoted by various terms, including models of bounded rationality, procedural rationality, and satisficing. Although there is as yet no agreed-upon definition of “nonrational,” rational and nonrational theories typically differ on several dimensions, discussed below. The term “decision making” is used broadly here to include preference, inference, classification, and judgment, whether conscious or unconscious. Nonrational theories of decision making should not be confused with theories of irrational decision making. The label “nonrational” signifies a type of theory, not a type of outcome. In other words, the fact that nonrational theories postulate agents with emotions, limited knowledge, and little time—rather than postulating omniscient “rational” beings—need not imply that such agents fare badly in the real world.

What is the nature of moral behavior? According to the study of bounded rationality, it results not from character traits or rational deliberation alone, but from the interplay between mind and environment. In this view, moral behavior is based on pragmatic social heuristics rather than moral rules or maximization principles. These social heuristics are not good or bad per se, but solely in relation to the environments in which they are used. This has methodological implications for the study of morality: Behavior needs to be studied in social groups as well as in isolation, in natural environments as well as in labs. It also has implications for moral policy: Only by accepting the fact that behavior is a function of both mind and environmental structures can realistic prescriptive means of achieving moral goals be developed.

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20 th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality. 1 1.