Overcoming illusory inferences in a probabilistic counterintuitive problem: The role of explicit representations

In the context of conditional probabilities, a good example of the marked discrepancy between intuition and formal reasoning is the Monty Hall dilemma (MHD). We used the MHD to study the effects of practicing the game, making explicit the underlying structure, or enhancing the representation of the different possibilities, on reaching and stating the correct answer. The results of the experiments showed that accumulated experience with the MHD increased the proportion of switching responses but did not change erroneous intuitions (Experiment 1). However, when the dilemma was presented in the form of an adversary game that made the underlying structure more explicit, more participants formed complete mental representations that enabled them to reason correctly (Experiment 2). This result was observed even without any practice with the game if the participants were encouraged to represent possibilities (Experiment 3). Therefore, in this context, correct reasoning seems to depend more on the ability to consider different possibilities than on extensive practice with the game.     

The influence of information redundancy on probabilistic inferences

Information redundancy affects the accuracy of inference strategies. A simulation study illustrates that under high-information redundancy simple heuristics that rely on only the most important information are as accurate as strategies that integrate all available information, whereas under low redundancy integrating information becomes advantageous. Assuming that people exercise adaptive strategy selection, it is predicted that their inferences will more often be captured by simple heuristics that focus on part of the available information insituations ofhigh-information redundancy, especially when information search is costly. This prediction is confirmed in two experiments. The participants' task was to repeatedly infer which of two alternatives, described by several cues, had a higher criterion value. In the first experiment, simple heuristics predicted the inference process better under high-information redundancy than under low-information redundancy. In the second experiment, this result could be generalized to an inference situation in which participants had no prior opportunity to learn about the strategies' accuracies through outcome feedback. The results demonstrate that people are able to respond adaptively to different decision environments under various learning opportunities.     

Representation of linear orders

Two binary classification tasks were used to explore the associative structure of linear orders. In Experiment 1, college students classified English letters as targets or nontargets, the targets being consecutive letters of the alphabet. The time to reject nontargets was a decreasing function of the distance from the target set, suggesting response interference mediated by automatic associations from the target to the nontarget letters. The way in which this interference effect depended on the placement of the boundaries between the target and nontarget sets revealed the relative strengths of individual interletter associations. In Experiment 2, students were assigned novel linear orders composed of letterlike symbols and asked to classify pairs of symbols as being adjacent or nonadjacent in the assigned sequence. Reaction time was found to be a joint function of the distance between any pair of symbols and the relative positions of those symbols within the sequence. The effects of both distance and position decreased systematically over 6 days of practice with a particular order, beginning at a level typical of unfamiliar orders and converging on a level characteristic of familiar orders such as letters and digits. These results provide an empirical unification of two previously disparate sets of findings in the literature on linear orders, those concerning familiar and unfamiliar orders, and the systematic transition between the two patterns of results suggests the gradual integration of a new associative structure.     

The role of familiarity in binary choice inferences

In research on the recognition heuristic (Goldstein & Gigerenzer, Psychological Review, 109, 75–90, 2002), knowledge of recognized objects has been categorized as “recognized” or “unrecognized” without regard to the degree of familiarity of the recognized object. In the present article, we propose a new inference model—familiarity-based inference. We hypothesize that when subjective knowledge levels (familiarity) of recognized objects differ, the degree of familiarity of recognized objects will influence inferences. Specifically, people are predicted to infer that the more familiar object in a pair of two objects has a higher criterion value on the to-be-judged dimension. In two experiments, using a binary choice task, we examined inferences about populations in a pair of two cities. Results support predictions of familiarity-based inference. Participants inferred that the more familiar city in a pair was more populous. Statistical modeling showed that individual differences in familiarity-based inference lie in the sensitivity to differences in familiarity. In addition, we found that familiarity-based inference can be generally regarded as an ecologically rational inference. Furthermore, when cue knowledge about the inference criterion was available, participants made inferences based on the cue knowledge about population instead of familiarity. Implications of the role of familiarity in psychological processes are discussed.     

Position effects in chunked linear orders

Summary When someone is asked which of two items from a linearly ordered set of items comes first in that order, reaction time decreases with increasing distance between the two items in the given order. This is known as thedistance effect, a very robust finding in studies on linear orders. Surprisingly, investigations onchunked linear orders show unexpected diverse results. For example, reaction times todifferent probes (i. e., probes with items from different chunks) are sometimes longer than those tosame probes (i. e., probes with items from the same chunk). But if subjects' latency depends on the discriminability of chunk labels vs. exact position information within a chunk,different probes should always yield faster order judgments thansame probes. Two experiments investigated whether position effects, including both end-of-list and end-ofchunk effects, can account for the unexpected finding that between-chunk probes are sometimes answered more slowly than within-chunk probes. Moreover, the linea-rorder paradigm was extended to complex action sequences with more than two chunks, using original cooking recipes as materials. The results showed thatchunk-position effects play a crucial role in comparative judgments. Probes from the first and the last chunk were answered faster than those from a middle chunk.Border items (i. e., items next to a chunk boundary) did not produce a significant effect. However, chunking affected subjects' reaction time, as was indicated by the absence of a distance effect fordifferent probes. Besides, action sequences that are ordered in time, as well as concept lists used previously, can be considered linear orders, thus supporting the view that linear orders reflect a basic representation schema of human memory.     

Finite condensations of recursive linear orders

The complexity of aII ₄ set of natural numbers is encoded into a linear order to show that the finite condensation of a recursive linear order can beII ₂–II ₁. A priority argument establishes the same result, and is extended to a complete classification of finite condensations iterated finitely many times.     

Colour associates to semantic linear orders

Summary People were asked whether they had strong colour associates (rather than associations) for different linear orders. Eighteen informants responded that they associated colours with numbers, and ten that they associated colours with the days of the week. The colours associated with both linear orders were consistent between subjects and correlated with each other. The order of the associates correlated with the order noted in the anthropological linguistic typology of Berlin and Kay (1969). Together, the patterns noted indicate that the association of colours with linear orders is an orderly cognitive phenomenon. While no causal explanation of the phenomenon is given, some implications are suggested.     

Correcting erroneous inferences in memory: The role of source credibility

People often continue to rely on erroneous information about people and events, even in the face of subsequent counter information. The current study examined whether this information could be effectively corrected by a credible source. We examined two aspects of credibility: trustworthiness and expertise. Experiment 1 showed that receiving a correction from a source high in trustworthiness and expertise reduced participants’ use of original information when making inferences. Experiment 2 showed that source expertise alone was not sufficient to reduce participants’ reliance on the original information. The results from Experiment 3 showed that source trustworthiness alone significantly decreased participants’ use of the original information when making inferences. The results suggest that people may be able to reduce their use of original information if they receive a correction from a person who is deemed to be highly trustworthy. These findings have implications for decision making in politics and other applied areas.     

The role of inferences in children's comprehension of pronouns

Several researchers have suggested that children have difficulty in drawing inferences to understand prose and, although inferences have been shown to be important in the reference decisions of adults there have been very few studies that have specifically investigated children's use of them in reference assignments. The results of the three sentence comprehension studies reported here suggest that some children are able to draw the relevant inferences to assign reference. But many children appear to use an order-of-mention strategy which biases them towards the first-mentioned noun phrase. This strategy seems to be adopted even when children are aware that the resulting pronoun assignment conflicts with their inferences. Children in the third study appear to be able to use local selectional information to reject a noun phrase chosen by their order-of-mention strategy but, at least at the youngest ages (4.5 years), children do not use the information provided by the whole sentence. These results are seen as yet another example of the lack of comprehension monitoring in young children.     

Perspectives of probabilistic inferences: Reinforcement learning and an adaptive network compared

The assumption that people possess a strategy repertoire for inferences has been raised repeatedly. The strategy selection learning theory specifies how people select strategies from this repertoire. The theory assumes that individuals select strategies proportional to their subjective expectations of how well the strategies solve particular problems; such expectations are assumed to be updated by reinforcement learning. The theory is compared with an adaptive network model that assumes people make inferences by integrating information according to a connectionist network. The network's weights are modified by error correction learning. The theories were tested against each other in 2 experimental studies. Study 1 showed that people substantially improved their inferences through feedback, which was appropriately predicted by the strategy selection learning theory. Study 2 examined a dynamic environment in which the strategies' performances changed. In this situation a quick adaptation to the new situation was not observed; rather, individuals got stuck on the strategy they had successfully applied previously. This "inertia effect" was most strongly predicted by the strategy selection learning theory.     

The role of subjective theories for leadership evaluation

This study reviews prior construct-related validity research in assessment centres. Special focus is placed on disentangling possible explanations for the construct-related validity findings. The conclusion is that we now have a much better picture of the reasons behind the construct-related validity findings. Careful assessment centre design and high interrater reliability among assessors seem necessary albeit insufficient conditions to establish assessment centre construct-related validity. The nature of candidate performances is another key factor. This study next discusses how these empirical findings have changed how assessment centres are conceptualized (theoretical advancements framed in the application of trait activation theory), analysed (methodological advancements), and designed (practical advancements).     

The role of cues to differential absolute size in children's transitive inferences

To investigate the role that "nonlogical" cues might play in transitive inference, 6- and 7-year-olds were given a three-term transitive task in which perceptual cues to differential absolute size were either present or absent. Relationships between the taught premises and the relational information that was physically present were manipulated using four basic conditions: "congruent," "inverse," "pretended," or "persuaded." Both age groups showed identical overall premise memory, but the younger group tended to reason more on the basis of the perceptual information rather than on the successfully encoded premise information. Contrasts between the various conditions showed that categorical effects can be circumvented in three-term problems with appropriate controls, that there may be qualitative as well as quantitative differences in transitive inference with age, and that transitive inference is not based solely on memory. The findings also indicate that, although 7-year-olds are competent in "logic-based" transitive inference, they experience great difficulty on tasks involving pretend information.     

The role of discontinuities in the perception of subjective figures

Recently we proposed a theory of visual interpolation (Kellman & Shipley, in press) that addresses a variety of unit formation phenomena, including the perception of partly occluded objects and subjective figures. A basic notion of the theory is that discontinuities in the first derivative of projected edges are the initiating conditions for interpolation of boundaries that are not physically specified. In this paper, we report four experiments in which this claim was tested in the domain of subjective figures. Experiments 1 and 2 demonstrate that discontinuities in the first derivative of the edges of inducing elements have a clear effect on the frequency of report and the perceived clarity of simple subjective figures. Similar effects are found when unfamiliar subjective figures and inducing elements are used (Experiment 3). Experiment 4 rules out the possibility that the discontinuities in the first derivative merely add to the clarity of subjective figures. These experiments suggest that first-order discontinuities play a central role in unit formation.     

The role of logical and nonlogical factors in making inferences about category membership

Three postulates are proposed concerning the manner in which persons infer the validity of propositions that do not necessarily follow logically from the information available. These postulates assume that subjects first attempt to identify the propositions that are most and least likely to follow from the information given. They then use their beliefs in these propositions as anchors, relative to which the validity of other propositions is evaluated on the basis of both logical and nonlogical criteria. Two experiments are reported in which these postulates are used successfully to diagnose the logical and nonlogical factors that underlie inferences based upon both single statements and sets of syllogistically related propositions. The implications of the proposed postulates for existing formulations of social inference and cognitive organization are discussed.     

The moderating role of objective and subjective numeracy in attribute framing

Previous research has found that objective numeracy moderates framing effects: People who are less numerate were found to be more susceptible to goal‐framing and attribute‐framing effects than people who are highly numerate. This study examined the possibility that subjective numeracy likewise moderates attribute framing in contexts where participants are presented with percentages of success or failure. The results show that compared with highly numerate participants, less numerate participants were more susceptible to the effect of attribute framing. Interestingly, this moderating effect was revealed only when using objective numeracy measures, and not when subjective numeracy measures were used. Future research is suggested to replicate these findings, to establish the generalizability of numeracy as a moderator of other cognitive biases, and to examine several possible theoretical explanations for the differential moderation of attribute‐framing bias.     

The role of inferences about referential intent in word learning: evidence from autism

Young children are readily able to use known labels to constrain hypotheses about the meanings of new words under conditions of referential ambiguity. At issue is the kind of information children use to constrain such hypotheses. According to one theory, children take into account the speaker's intention when solving a referential puzzle. In the present studies, children with autism were impaired in monitoring referential intent, but were equally successful as normally developing 24-month-old toddlers at mapping novel words to unnamed items under conditions of referential ambiguity. Therefore, constraints that lead the child to map a novel label to a previously unnamed object under these circumstances are not solely based on assessments of speakers' intentions.     

Effects of inflation on the subjective value of delayed and probabilistic rewards

In the years prior to 1994, there were very high rates of inflation in Poland, and the zloty depreciated relative to the U.S. dollar. However, the new zloty, introduced in 1995, was associated with greatly decreased rates of inflation and provided a more stable currency. We report a series of three experiments that take advantage of these changes to examine the effects of inflation on the subjective value of delayed and probabilistic rewards. Subjects were Polish citizens familiar with both zlotys and dollars. The first two experiments, conducted in 1994, used dollars and old zlotys, and the third experiment, conducted in 1996, used dollars and new zlotys. In all three experiments, the dollar and zloty rewards were of equivalent worth, according to the then current exchange rates. In Experiment 1, subjects chose between immediate and delayed rewards and, in Experiment 2, chose between certain and probabilistic rewards. The subjective value of a delayed reward was greater when its amount was specified in dollars than when it was specified in old zlotys. In contrast, the currency in which a reward was specified had no effect on the subjective value of probabilistic rewards. The results of these two experiments suggest a selective effect of inflation on decisions involving delayed rewards. This was verified in the third experiment, in which, using new zlotys, no differences in discounting were observed between the two currencies with either probabilistic or delayed rewards. Importantly, in all three experiments, the discounting of both delayed and probabilistic rewards was well described by the same simple mathematical model, suggesting that similar decision-making processes underlie both phenomena. However, the present results argue against a single-process theory in which the discounting of probabilistic rewards is derived from the discounting of delayed rewards.