Theory-based Bayesian models of inductive reasoning 2 Theory-based Bayesian models of inductive reasoning

In many situations human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and that predicted by Bayesian inference: people often appear to make judgments based on a few samples from a probability distribution, rather than the full distribution. Although sample-based approximations are a common implementation of Bayesian inference, the very limited number of samples used by humans seems to be insufficient to approximate the required probability distributions. Here we consider this discrepancy in the broader framework of statistical decision theory, and ask: if people were making decisions based on samples, but samples were costly, how many samples should people use? We find that under reasonable assumptions about how long it takes to produce a sample, locally suboptimal decisions based on few samples are globally optimal. These results reconcile a large body of work showing sampling, or probability-matching, behavior with the hypothesis that human cognition is well described as Bayesian inference, and suggest promising future directions for studies of resource-constrained cognition.

When participants assess the relationship between two variables, each with levels of presence and absence, the two most robust phenomena are that: (a) observing the joint presence of the variables has the largest impact on judgment and observing joint absence has the smallest impact, and (b) participants’ prior beliefs about the variables ’ relationship influence judgment. Both phenomena represent departures from the traditional normative model (the phi coefficient or related measures) and have therefore been interpreted as systematic errors. However, both phenomena are consistent with a Bayesian approach to the task. From a Bayesian perspective: (a) joint presence is normatively more informative than joint absence if the presence of variables is rarer than their absence, and (b) failing to incorporate prior beliefs is a normative error. Empirical evidence is reported showing that joint absence is seen as more informative than joint presence when it is clear that absence of the variables, rather than their presence, is rare.

A basic issue in social influence is how best to change one’s judgment in response to learning the opinions of others. This article examines the strategies that people use to revise their quantitative estimates on the basis of the estimates of another person. The authors note that people tend to use 2 basic strategies when revising estimates: choosing between the 2 estimates and averaging them. The authors developed the probability, accuracy, redundancy (PAR) model to examine the relative effectiveness of these two strategies across judgment environments. A surprising result was that averaging was the more effective strategy across a wide range of commonly encountered environments. The authors observed that despite this finding, people tend to favor the choosing strategy. Most participants in these studies would have achieved greater accuracy had they always averaged. The identification of intuitive strategies, along with a formal analysis of when they are accurate, provides a basis for examining how effectively people use the judgments of others. Although a portfolio of strategies that includes averaging and choosing can be highly effective, the authors argue that people are not generally well adapted to the environment in terms of strategy selection.

implicit knowledge about motion

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A central proposition of demographic transition theory is that declines in infant and child mortality can encourage subsequent declines in fertility. Even the earliest formulations of the theory recognized that fertility decline would occur only with a lag, but neither theory nor empirical work has explored the length of such lags. This paper urges that individual perceptions and beliefs about mortality risks, conspicuously absent from the demographic research agenda, be studied directly. It proceeds to link mortality perceptions to health care decisionmaking and investments in children. The paper concludes by calling for a new agenda on mortality decline. This agenda would focus on three main themes: individual perceptions of health levels and trends, including mortality risks, with the concept of social learning being prominent; the overlap of modern and traditional health care systems and the associated beliefs, with an emphasis on the

of normative complexity, This research aims instead to test the.'rational choice ' models (Shafir & models, as well as their undeniable prominence in the social80 I FRAMING EFFECTS AND RATIONALITY seems, at first blush, a strange brew of the remarkably crude and the exquisitely subtle. For example, in studies of (explicit) visual recognition, people can be oblivious to changes even in gross details of the visual scene (Rensink et al., 1997); while in studies of (implicit) visual priming, people can be higWy sensitive to subtle unattended features of the visual stimulus, sometimes for weeks after a single viewing (Treisman & DeSchepper, 1996). For this reason, the ramifications of subtle information seeping unintended through an experimental design are usually difficult to prejudge. In empirical tests of all kinds-whether of rational actor models or explicitly cognitive models-the researcher must take pains to ensure that all of the information available to the subject has been accounted for. The second class of problems is more specific to the empirical study of normative models. This research requires, not just accounting for all the information that is

Framing experiments seek to rigorously separate out the effects of relevant and irrelevant information on human judgment and choice processes. Because they appear to elegantly streamline the normative analysis of human cognition, these experiments have assumed a central place in the so-called “Rationality Debate ” – the controversy, within and between the various

Framing effects occur when logically equivalent redescriptions of objects or outcomes lead to different behavior, and such effects have traditionally been seen as irrational. However, recent evidence has shown that a speaker’s choice among logically equivalent attribute frames can implicitly convey (or “leak”) normatively relevant information about, among other things, the speaker’s reference point. Reinterpreting data published elsewhere, this article shows that some common effects in inference tasks (covariation assessment and hypothesis testing) can also be seen as framing effects, thereby expanding the domain of framing. It is also shown that these framing effects are normatively defensible because normatively relevant information about event rarity is leaked through the description of data and through the phrasing of hypotheses, thereby broadening the information leakage approach to explaining framing effects. Information leakage can also explain why framing effects in these inference tasks disappear under certain conditions. Framing Effects in Inference Tasks-- 3 Framing Effects in Inference Tasks – And Why They’re Normatively Defensible A trend in research on reasoning is to explain, in rational terms, behavior that has