The probability heuristics model of syllogistic reasoning

A probability heuristic model (PHM) for syllogistic reasoning is proposed. An informational ordering over quantified statements suggests simple probability based heuristics for syllogistic reasoning. The most important is the "min-heuristic": choose the type of the least informative premise as the type of the conclusion. The rationality of this heuristic is confirmed by an analysis of the probabilistic validity of syllogistic reasoning which treats logical inference as a limiting case of probabilistic inference. A meta-analysis of past experiments reveals close fits with PHM. PHM also compares favorably with alternative accounts, including mental logics, mental models, and deduction as verbal reasoning. Crucially, PHM extends naturally to generalized quantifiers, such as Most and Few, which have not been characterized logically and are, consequently, beyond the scope of current mental logic and mental model theories. Two experiments confirm the novel predictions of PHM when generalized quantifiers are used in syllogistic arguments. PHM suggests that syllogistic reasoning performance may be determined by simple but rational informational strategies justified by probability theory rather than by logic.     

Participant recruitment methods and statistical reasoning performance

Optimal Bayesian reasoning performance has reportedly been elusive, and a variety of explanations have been suggested for this situation. In a series of experiments, it is demonstrated that these difficulties with replication can be accounted for by differences in participant-sampling methodologies. Specifically, the best performances are obtained with students from top-tier, national universities who were paid for their participation. Performance drops significantly as these conditions are altered regarding inducements (e.g., using unpaid participants) or participant source (e.g., using participants from a second-tier, regional university). Honours-programme undergraduates do better than regular undergraduates within the same university, paid participation creates superior performance, and top-tier university students do better than students from lower ranked universities. Pictorial representations (supplementing problem text) usually have a slight facilitative effect across these participant manipulations. These results indicate that studies should take account of these methodological details and focus more on relative levels of performance rather than absolute performance.     

Context-sensitive elemental theory

My theories of associative learning, like those of N. J. Mackintosh and almost all learning theorists, have employed elemental representations of the stimuli involved. We must take notice when two important contributors to elemental theory, J. M. Pearce and W. K. Estes, find sufficient problems with the theory type to cause them to defect from it. I will describe some of the essential problems, concerning the substantial influence of context on learning and retrieval, characterize the different responses of Pearce and Estes, and, then, propose a variation on a recently developed elemental model that was similarly inspired. The resulting elemental theory has a close quantitative relationship to the “product-rule” of Estes and D. L. Medin, and may help us to rationalize how the same formal experimental design can sometimes produce results that favour the configural interpretation of Pearce and at other times the elemental interpretation of R. A. Rescorla and A. R. Wagner, as these have often been pitted against each other.     

The effects of statistical training on choice heuristics in choice under uncertainty

Kahneman and Tversky (1984) proposed that decision makers perceive choice uncertainty in two ways: (1) as a distribution of possible outcomes or (2) as a single uncertain outcome. Using statistical training as a factor that influences these perceptions, and thus the type of decision approach individuals use, we found that individuals with different levels of experience displayed differences in the decisions they made and in the choice heuristics used to make those decisions. Statistically naive individuals were more likely to prefer loss-minimizing alternatives, use a more non-compensatory heuristic, and spend more time on loss-related information than their statistically experienced counterparts. When a distributional cue, indicating the distributional nature of choice outcomes, was presented to both experience groups, the naive group was found to use a decision approach similar to the experienced group and to make similar decisions. The results are discussed in terms of the need to include factors that alter individuals' approaches to uncertainty in future behavioral models of uncertain choice.     

Immediate and delayed transfer of training effects in statistical reasoning

Ss were trained on the law of large numbers in a given domain through the use of example problems. They were then tested either on that domain or on another domain either immediately or after a 2-week delay. Strong domain independence was found when testing was immediate. This transfer of training was not due simply to Ss' ability to draw direct analogies between problems in the trained domain and in the untrained domain. After the 2-week delay, it was found that (a) there was no decline in performance in the trained domain and (b) although there was a significant decline in performance in the untrained domain, performance was still better than for control Ss. Memory measures suggest that the retention of training effects is due to memory for the rule system rather than to memory for the specific details of the example problems, contrary to what would be expected if Ss were using direct analogies to solve the test problems.     

Ducking the collection of costly evidence: Motivated use of statistical heuristics

We examined whether motivation affects people's use of statistical heuristics. In two studies, subjects had to decide how many instances to observe before making predictions. Half the subjects were led to believe that the observation of each instance would be relatively high in cost, and half were led to believe that it would be relatively low in cost. In both studies, only subjects for whom evidence collection was relatively high in cost accessed the aggregation principle and came to believe that aggregates afforded greater predictability than did single instances. Their belief that predictability increases sharply with sample size may have allowed these subjects to conclude what they wanted to conclude, namely that smaller samples would suffice for their predictions.     

Frequency interpretation of ambiguous statistical information facilitates Bayesian reasoning

The idea that naturally sampled frequencies facilitate performance in statistical reasoning tasks because they are a cognitively privileged representational format has been challenged by findings that similarly structured numbers presented as chances similarly facilitate performance, on the basis of the claim that these are technically single-event probabilities. A crucial opinion, however, is that of the research participants, who possibly interpret chances as de facto frequencies. A series of experiments here indicate that not only is performance improved by clearly presented natural frequencies, rather than chances phrasing, but also that participants who interpreted chances as frequencies, rather than as probabilities, were consistently better at statistical reasoning. This result was found across different variations of information presentation and across different populations.     

Difference to Inference: Teaching logical and statistical reasoning through on-line interactivity

Difference to Inference is an on-line JAVA program that simulates theory testing and falsification through research design and data collection in a game format. The program, based on cognitive and epistemological principles, is designed to support learning of the thinking skills underlying deductive and inductive logic and statisticalreasoning. Difference to Inference has database connectivity so that game scores can be counted as part of course grades.     

Moral heuristics

With respect to questions of fact, people use heuristics--mental short-cuts, or rules of thumb, that generally work well, but that also lead to systematic errors. People use moral heuristics too--moral short-cuts, or rules of thumb, that lead to mistaken and even absurd moral judgments. These judgments are highly relevant not only to morality, but to law and politics as well. examples are given from a number of domains, including risk regulation, punishment, reproduction and sexuality, and the act/omission distinction. in all of these contexts, rapid, intuitive judgments make a great deal of sense, but sometimes produce moral mistakes that are replicated in law and policy. One implication is that moral assessments ought not to be made by appealing to intuitions about exotic cases and problems; those intuitions are particularly unlikely to be reliable. Another implication is that some deeply held moral judgments are unsound if they are products of moral heuristics. The idea of error-prone heuristics is especially controversial in the moral domain, where agreement on the correct answer may be hard to elicit; but in many contexts, heuristics are at work and they do real damage. Moral framing effects, including those in the context of obligations to future generations, are also discussed.     

Comparing associative, statistical, and inferential reasoning accounts of human contingency learning

For more than two decades, researchers have contrasted the relative merits of associative and statistical theories as accounts of human contingency learning. This debate, still far from resolution, has led to further refinement of models within each family of theories. More recently, a third theoretical view has joined the debate: the inferential reasoning account. The explanations of these three accounts differ critically in many aspects, such as level of analysis and their emphasis on different steps within the information-processing sequence. Also, each account has important advantages (as well as critical flaws) and emphasizes experimental evidence that poses problems to the others. Some hybrid models of human contingency learning have attempted to reconcile certain features of these accounts, thereby benefiting from some of the unique advantages of different families of accounts. A comparison of these families of accounts will help us appreciate the challenges that research on human contingency learning will face over the coming years.     

The effect of emotion on statistical reasoning: Findings from a base rates task

In this paper we explore the effect of emotion on statistical reasoning. We employed a base rates task to examine reliance on statistical information in the presence of congruent or incongruent anecdotal information. The impact of emotional content on statistical reasoning was investigated in controls and victims of sexual abuse. Two types of emotional contents were used, one generally emotional, and one related to sexual abuse. The latter category was included to investigate the effect of semantically identical stimuli that could potentially produce different levels of emotion in the victim and control groups. For control participants, emotional contents were associated with decreased use of statistical information and increased use of anecdotal information compared to neutral contents. Results from the victims group showed this effect to be increased for contents related to sexual abuse, suggesting that the effect is linked to the emotional connotation rather than semantic content. Victims perceived contents relating to their experience as more emotional and this was associated with specific reasoning impairments for these topics.     

The effect of iconicity of visual displays on statistical reasoning: evidence in favor of the null hypothesis

Knowing which properties of visual displays facilitate statistical reasoning bears practical and theoretical implications. Therefore, we studied the effect of one property of visual diplays?– iconicity (i.e., the resemblance of a visual sign to its referent)?– on Bayesian reasoning. Two main accounts of statistical reasoning predict different effect of iconicity on Bayesian reasoning. The ecological-rationality account predicts a positive iconicity effect, because more highly iconic signs resemble more individuated objects, which tap better into an evolutionary-designed frequency-coding mechanism that, in turn, facilitates Bayesian reasoning. The nested-sets account predicts a null iconicity effect, because iconicity does not affect the salience of a nested-sets structure—the factor facilitating Bayesian reasoning processed by a general reasoning mechanism. In two well-powered experiments (N = 577), we found no support for a positive iconicity effect across different iconicity levels that were manipulated in different visual displays (meta-analytical overall effect: log OR = ?0.13, 95 % CI [?0.53, 0.28]). A Bayes factor analysis provided strong evidence in favor of the null hypothesis—the null iconicity effect. Thus, these findings corroborate the nested-sets rather than the ecological-rationality account of statistical reasoning.     

Approximation error analysis in bicriteria heuristics

A value structure based on the Tchebycheff measure is proposed to assess the worst-case and average errors in bicriteria heuristics. This analysis builds on earlier results for additive value structures (Daniels, R. L., Manag. Sci., 38 , 501–513 (1992)). The significance of the Tchebycheff measure is that it is representative of a class of quasi-concave functions, and analysis based on this measure is indicative of the performance of the heuristic over a broad range of preference value structures. © 1998 John Wiley & Sons, Ltd.     

Bayes nets and babies: infants' developing statistical reasoning abilities and their representation of causal knowledge

A fundamental assumption of the causal graphical model framework is the Markov assumption, which posits that learners can discriminate between two events that are dependent because of a direct causal relation between them and two events that are independent conditional on the value of another event(s). Sobel and Kirkham (2006) demonstrated that 8-month-old infants registered conditional independence information among a sequence of events; infants responded according to the Markov assumption in such a way that was inconsistent with models that rely on simple calculations of associative strength. The present experiment extends these findings to younger infants, and demonstrates that such responses potentially develop during the second half of the first year of life. These data are discussed in terms of a developmental trajectory between associative mechanisms and causal graphical models as representations of infants' causal and statistical learning.     

Conditionals in reasoning

The paper presents a non-monotonic inference relation on a language containing a conditional that satisfies the Ramsey Test. The logic is a weakening of classical logic and preserves many of the ‘paradoxes of implication’ associated with the material implication. It is argued, however, that once one makes the proper distinction between supposing that something is the case and accepting that it is the case, these ‘paradoxes’ cease to be counterintuitive. A representation theorem is provided where conditionals are given a non-bivalent semantics and epistemic states are represented via preferential models.     

Event-learning and robust policy heuristics

In this paper we introduce a novel reinforcement learning algorithm called event-learning. The algorithm uses events, ordered pairs of two consecutive states. We define event-value function and we derive learning rules. Combining our method with a well-known robust control method, the SDS algorithm, we introduce Robust Policy Heuristics (RPH). It is shown that RPH, a fast-adapting non-Markovian policy, is particularly useful for coarse models of the environment and could be useful for some partially observed systems. RPH may be of help in alleviating the ‘curse of dimensionality’ problem. Event-learning and RPH can be used to separate time scales of learning of value functions and adaptation. We argue that the definition of modules is straightforward for event-learning and event-learning makes planning feasible in the RL framework. Computer simulations of a rotational inverted pendulum with coarse discretization are shown to demonstrate the principle.     

Problem structuring heuristics in strategic decision making

In a laboratory experiment using 73 undergraduate students as subjects, comparisons were made between the use of a convergent, divergent, and limited heuristic for problem structuring under different stress levels. It was found that subjects using either the convergent or the divergent heuristic had lower satisfaction with the process and lower confidence in their results than those using the limited heuristic. There were no differences in the time used or the quality of results between subjects using the convergent and divergent heuristic. Stress reduced the quantity of results when using either the convergent or divergent heuristic. The subjects may have preferred the limited heuristic because the use of the convergent or divergent heuristic used more time, thus more energy, and resulted in more alternatives, thus increased uncertainty. It is also possible that the subjects preferred their future career plans to be more ambiguous than the use of either the convergent or divergent heuristic allowed.     

Influences of credibility of testimony and strength of statistical evidence on children’s and adolescents’ reasoning

According to dual-process models that include analytic and heuristic modes of processing, analytic processing is often expected to become more common with development. Consistent with this view, on reasoning problems, adolescents are more likely than children to select alternatives that are backed by statistical evidence. It is shown here that this pattern depends on the quality of the statistical evidence and the quality of the testimonial that is the typical alternative to statistical evidence. In Experiment 1, 9- and 13-year-olds (N = 64) were presented with scenarios in which solid statistical evidence was contrasted with casual or expert testimonial evidence. When testimony was casual, children relied on it but adolescents did not; when testimony was expert, both children and adolescents relied on it. In Experiment 2, 9- and 13-year-olds (N = 83) were presented with scenarios in which casual testimonial evidence was contrasted with weak or strong statistical evidence. When statistical evidence was weak, children and adolescents relied on both testimonial and statistical evidence; when statistical evidence was strong, most children and adolescents relied on it. Results are discussed in terms of their implications for dual-process accounts of cognitive development.     

Illusions in modal reasoning

According to the mental model theory, models represent what is true, but not what is false. One unexpected consequence is that certain inferences should have compelling, but invalid, conclusions. Three experiments corroborated the occurrence of such illusions in reasoning about possibilities. When problems had the heading "Only one of the premises is true," the participants considered the truth of each premise in turn, but neglected the fact that when one premise is true, the others are false. When two-premise problems had the heading "One of the premises is true and one is false," the participants still neglected the falsity of one of the premises. As predicted, however, the illusions were reduced when reasoners were told to check their conclusions against the constraint that only one of the premises was true. We discuss alternative explanations for illusory inferences and their implications for current theories of reasoning.