Subliminal anchoring: The effects of subliminally presented numbers on probability estimates

Previous research demonstrated that if attention is paid to a supraliminally presented number, a subsequent quantitative estimate assimilates towards this number (the anchor effect). One explanation states that this effect is merely caused by the heightened accessibility level of the anchor value itself. Based on this numeric priming account and generalizing from subliminal priming studies, we expected a short-lived subliminal anchor effect. We presented participants subliminally with a low or high anchor value (10 or 90) and next they had to estimate the probability of an epidemic. Half of them were pressed to do this quickly. Only under time pressure, a significant anchor effect emerged.     

The limits of anchoring

Anchoring and adjustment is a pervasive bias in which decision makers are influenced by random or uninformative numbers or starting points. As a means of understanding this effect, we explore two limits on anchoring. In Experiments 1 and 2, implausibly extreme anchors had a proportionally smaller effect than anchors close to the expected value of the lotteries evaluated. In Experiments 2 and 3, anchoring occurred only if the anchor and preference judgment were expressed on the same scale. Incompatible anchors and response modes resulted in no anchoring bias. A confirmatory search mechanism is proposed to account for these results.     

Subliminal anchoring: Judgmental consequences and underlying mechanisms

Judgmental anchoring—the assimilation of a numeric estimate towards a previously considered standard—is an exceptionally ubiquitous effect that influences human judgment in a variety of domains and paradigms. Three studies examined whether anchoring effects even occur, if anchor values are presented subliminally, outside of judges’ awareness. Studies 1 and 2 demonstrate such subliminal anchoring effects: judges assimilated target estimates towards the subliminally presented anchor values. Study 3 further demonstrates that subliminal anchors produced a selective increase in the accessibility of anchor-consistent target knowledge. The implications of these findings for the ubiquity of judgmental anchoring, its different underlying mechanisms, and comparative information processing are discussed.     

Anchors aweigh: a demonstration of cross-modality anchoring and magnitude priming

Research has shown that judgments tend to assimilate to irrelevant "anchors." We extend anchoring effects to show that anchors can even operate across modalities by, apparently, priming a general sense of magnitude that is not moored to any unit or scale. An initial study showed that participants drawing long "anchor" lines made higher numerical estimates of target lengths than did those drawing shorter lines. We then replicated this finding, showing that a similar pattern was obtained even when the target estimates were not in the dimension of length. A third study showed that an anchor's length relative to its context, and not its absolute length, is the key to predicting the anchor's impact on judgments. A final study demonstrated that magnitude priming (priming a sense of largeness or smallness) is a plausible mechanism underlying the reported effects. We conclude that the boundary conditions of anchoring effects may be much looser than previously thought, with anchors operating across modalities and dimensions to bias judgment.     

The development of geographic categories and biases

Children and university students (N=58) estimated the locations of major cities in North America. At age 9, a distinct home region was apparent, but no differentiation between northern US and Canadian cities. At 11, four developments were observed: Children divided North America into regions that were not based solely on national boundaries but were the same as university students' regions; psychological border zones between regions exaggerated distances between them; children used new location information to update their estimates for all cities in a seeded region and in adjacent and nonadjacent regions; children preserved the ordinal structure of their initial location estimates for cities in their home region but relied on regional prototype locations to adjust estimates in less familiar regions. The updating methods reflect fundamentally different mechanisms. Theoretical and educational implications are discussed.     

Language-guided visual processing affects reasoning: The role of referential and spatial anchoring

Language is more than a source of information for accessing higher-order conceptual knowledge. Indeed, language may determine how people perceive and interpret visual stimuli. Visual processing in linguistic contexts, for instance, mirrors language processing and happens incrementally, rather than through variously-oriented fixations over a particular scene. The consequences of this atypical visual processing are yet to be determined. Here, we investigated the integration of visual and linguistic input during a reasoning task. Participants listened to sentences containing conjunctions or disjunctions (Nancy examined an ant and/or a cloud) and looked at visual scenes containing two pictures that either matched or mismatched the nouns. Degree of match between nouns and pictures (referential anchoring) and between their expected and actual spatial positions (spatial anchoring) affected fixations as well as judgments. We conclude that language induces incremental processing of visual scenes, which in turn becomes susceptible to reasoning errors during the language-meaning verification process.     

Elaboration and consequences of anchored estimates: An attitudinal perspective on numerical anchoring

In the standard numerical anchoring paradigm, the influence of externally provided anchors on judgment is typically explained as a result of elaborate thinking (i.e., confirmatory hypothesis testing that selectively activates anchor-consistent information in memory). In contrast, theories of attitude change suggest that the same judgments can result from relatively thoughtful or non-thoughtful processes, with more thoughtful processes resulting in judgments that last longer over time and better resist future attempts at change. Guided by an attitudinal approach to anchoring, four studies manipulated participants’ level of cognitive load to produce relatively high versus low levels of thinking. These studies show that, although anchoring can occur under both high and low thought conditions, anchoring based on a higher level of thinking involves greater use of judgment-relevant background knowledge, persists longer over time, is more resistant to subsequent attempts at social influence, and is less likely to result from direct numeric priming.     

The malleability of anchoring effects

Anchoring effects--the assimilation of a numeric estimate to a previously considered standard--are typically described as very robust and persistent. Based on the assumption that judgmental anchoring involves a hypothesis-testing process in which judges actively seek and generate judgment-relevant target knowledge, it was assumed that anchoring effects might at the same time be fairly malleable. Specifically, subtle influences that change the nature of the tested hypothesis are likely to affect the magnitude of anchoring. Using a procedural priming task, judges were induced to focus on similarities versus differences during a series of anchoring tasks. The results demonstrate that the magnitude of the obtained effect critically depended on this manipulation. In particular, a more pronounced anchoring assimilation effect resulted for judges with a similarity rather than a difference focus. Implications of these findings for models of anchoring as well as for the nature of the anchoring phenomenon are discussed.     

The durability of anchoring effects

Recent research suggests that judgmental anchoring is mediated by a selective increase in the accessibility of knowledge about the judgmental target. Anchoring thus constitutes one instance of the judgmental effects of increased knowledge accessibility. Such knowledge accessibility effects have repeatedly been demonstrated to be fairly durable, which suggests that the effects of judgmental anchoring may also persist over time. Consistent with this assumption, three experiments demonstrate that judgmental anchors influence judgment even if they were present one week before the critical judgment is made. In fact, the magnitude of anchoring was found to remain undiminished over this period of time. Copyright © 2001 John Wiley & Sons, Ltd.     

A neuropsychological dimension for anchoring effects

Previous research has shown that strength of handedness predicts differences in sensory illusions, Stroop interference, episodic memory, and beliefs about body image and the origin of species. Recent evidence also suggests handedness differences in the susceptibility to information framing and persuasion. The present paper extends this line of work to decision anchoring effects. In Experiment 1, 131 introductory psychology students responded to 12 real‐world knowledge questions after being given random, uninformative high or low anchors. Results indicated that “strong‐handers” showed larger anchoring effects than “mixed‐handers.” In Experiment 2, 89 introductory psychology students responded to 6 real‐world knowledge questions in a modified, two‐step anchoring task in which participants were given a credible source for the anchored information and asked to give pre‐ and post‐anchor estimates. In contrast to Experiment 1, results revealed that mixed‐ and strong‐handers were affected similarly by anchoring. In Experiment 3, 158 students were asked to estimate the answer to one of two versions of 8! (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 or 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8)—a multiplication problem in which the high and low anchors are inherently informative. Here, mixed‐handers showed larger anchoring effects than strong‐handers. A theory centered around the notion of hemispheric specialization and the communication between the two halves of the brain as well as arguments about the informativeness of anchors, metacognition, and recent theorizing in the anchoring literature are used to account for these data. Copyright © 2005 John Wiley & Sons, Ltd.     

The long and short of it: physical anchoring effects

Attempts to reconstruct the magnitude of recently encountered physical stimuli were influenced by the provision of physical anchors. Whether estimating length, weight, or loudness, those increasing the magnitude of a relatively small (short, light, or quiet) physical anchor produced estimates that were reliably lower than did those decreasing the magnitude of a relatively large (long, heavy, or loud) anchor. Estimates produced without an anchor were also low, suggesting that when people physically adjust upwards from a self‐selected starting point, “no anchor” may, in fact, act as a very low anchor. Physical anchors appear to influence estimates of recently encountered physical stimuli, much as numerical anchors influence estimates of more abstract numerical quantities. Implications for processes underlying anchoring, adjustment, and related tasks are discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Path dependent preferences: The role of early experience and biased search in preference development

What is the role of early experiences in shaping preferences? What are the mechanisms by which such early encounters influence the way preferences are formed? In this research, we examine the impact of the entry position and favorability of initial (and ongoing) experiences on preference development. We predict that the starting point will heavily influence which particular region people select from initially, and favorableness of early experiences and myopic search will both limit their search to that particular region. Across four studies, we find that when the initial experiences are favorable, subjects engage in lower levels of search, experience only a narrow breadth of possible alternatives, demonstrate less ongoing experimentation, and have a reduction in the amount of preference development.     

A descriptive model for perception of optical illusions

The apparent curves of stable geometrical illusions of angle are modeled by a first-order differential equation depending on a single parameter, called the strength of the illusion. The model is based on Brentano's theory that the human visual system tends to overestimate acute angles. It is mathematically equivalent to Hoffman's Lie-theoretic model (SIAM Review, 13 (1971), pp. 169–184) except for some deficiencies of detail in Hoffman's approach which are noted and corrected. By reversing the sign of the strength parameter, “correction” curves may be plotted which cause the illusion to “disappear,” thereby demonstrating the effectiveness and accuracy of the model. The method is illustrated with the classical illusions of Poggendorff, Zöllner, Hering, Orbison, Ponzo, and Müller-Lyer.     

Thinking aloud during reading: A descriptive model and its application

The problem-solving aspect of reading was studied by a thinking-aloud procedure. A model was developed, describing the information attended to, the thought operation used, and the result derived. Four main operations were identified: Reading, Evoking, Interpreting , and Comparing. A coding system, based upon this model, was developed. Its interrater reliability was between 0.86 and 0.92. This system was used to study the effect of reading purpose. An experimental group was instructed to apply a text concerning creativity to the problem of inducing constructive learning at the university. A control group was assigned reading with no particular purpose in mind. The experimental group used the Interpreting operation more often. Also, the Comparing operation, applied to a comparison between the text and the subjects' own knowledge, less often resulted in disagreement. Thus, the coding system is detailed enough to reflect differences in thought processes.     

The dynamics of multimodal integration: The averaging diffusion model

We combine extant theories of evidence accumulation and multi-modal integration to develop an integrated framework for modeling multimodal integration as a process that unfolds in real time. Many studies have formulated sensory processing as a dynamic process where noisy samples of evidence are accumulated until a decision is made. However, these studies are often limited to a single sensory modality. Studies of multimodal stimulus integration have focused on how best to combine different sources of information to elicit a judgment. These studies are often limited to a single time point, typically after the integration process has occurred. We address these limitations by combining the two approaches. Experimentally, we present data that allow us to study the time course of evidence accumulation within each of the visual and auditory domains as well as in a bimodal condition. Theoretically, we develop a new Averaging Diffusion Model in which the decision variable is the mean rather than the sum of evidence samples and use it as a base for comparing three alternative models of multimodal integration, allowing us to assess the optimality of this integration. The outcome reveals rich individual differences in multimodal integration: while some subjects’ data are consistent with adaptive optimal integration, reweighting sources of evidence as their relative reliability changes during evidence integration, others exhibit patterns inconsistent with optimality.     

SARA: A cognitive process model to simulate the anchoring effect and hindsight bias

The cognitive process model "SARA" aims to explain the anchoring effect and hindsight bias by making detailed assumptions about the representation and alteration of item-specific knowledge. The model assumes that all processes, namely generating an estimate, encoding new information (i.e., the "anchor"), and reconstructing a previously generated estimate, are based on a probabilistic sampling process. Sampling probes long-term memory in order to retrieve information into working memory. Retrieval depends on the associative strength between this information and the currently active retrieval cues. Encoding the anchor may alter this associative pattern ("selective activation") or the anchor may serve as a retrieval cue, thus directing memory search ("biased reconstruction"). Both processes lead to systematically changed retrieval probabilities, thus causing the anchoring effect or hindsight bias. The model is completely formalised and implemented as a computer program. A series of simulations demonstrates the power of SARA to reproduce empirical findings and to predict new ones.