Processing of Numerical and Proportional Quantifiers

Quantifier expressions like “many” and “at least” are part of a rich repository of words in language representing magnitude information. The role of numerical processing in comprehending quantifiers was studied in a semantic truth value judgment task, asking adults to quickly verify sentences about visual displays using numerical (at least seven, at least thirteen, at most seven, at most thirteen) or proportional (many, few) quantifiers. The visual displays were composed of systematically varied proportions of yellow and blue circles. The results demonstrated that numerical estimation and numerical reference information are fundamental in encoding the meaning of quantifiers in terms of response times and acceptability judgments. However, a difference emerges in the comparison strategies when a fixed external reference numerosity (seven or thirteen) is used for numerical quantifiers, whereas an internal numerical criterion is invoked for proportional quantifiers. Moreover, for both quantifier types, quantifier semantics and its polarity (positive vs. negative) biased the response direction (accept/reject). Overall, our results indicate that quantifier comprehension involves core numerical and lexical semantic properties, demonstrating integrated processing of language and numbers.     

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 logic in language: How all quantifiers are alike,but each quantifier is different

Quantifier words like each, every, all and three are among the most abstract words in language. Unlike nouns, verbs and adjectives, the meanings of quantifiers are not related to a referent out in the world. Rather, quantifiers specify what relationships hold between the sets of entities, events and properties denoted by other words. When two quantifiers are in the same clause, they create a systematic ambiguity. “Every kid climbed a tree” could mean that there was only one tree, climbed by all, or many different trees, one per climbing kid. In the present study, participants chose a picture to indicate their preferred reading of different ambiguous sentences – those containing every, as well as the other three quantifiers. In Experiment 1, we found large systematic differences in preference, depending on the quantifier word. In Experiment 2, we then manipulated the choice of a particular reading of one sentence, and tested how this affected participants’ reading preference on a subsequent target sentence. We found a priming effect for all quantifiers, but only when the prime and target sentences contained the same quantifier. For example, all-a sentences prime other all-a sentences, while each-a primes each-a, but sentences with each do not prime sentences with all or vice versa. In Experiment 3, we ask whether the lack of priming across quantifiers could be due to the two sentences sharing one fewer word. We find that changing the verb between the prime and target sentence does not reduce the priming effect. In Experiment 4, we discover one case where there is priming across quantifiers – when one number (e.g. three) is in the prime, and a different one (e.g. four) is in the target. We discuss how these findings relate to linguistic theories of quantifier meaning and what they tell us about the division of labor between conceptual content and combinatorial semantics, as well as the mental representations of quantification and of the abstract logical structure of language.     

Prior expectation and the interpretation of natural language quantifiers

Abstract

The interpretation of natural language quantifiers depends, in part, on one's prior expectations about what the proportion being described might be. This hypothesis is tested empirically, by comparing the interpretation of 10 different quantifier expressions in three contexts which contained proportions about which subjects' expectations were reliably different (Experiment 1). It is further argued that quantifiers perform many functions which cannot be observed by considering only the proportion(s) denoted by a quantifier. The experimental evidence presented shows that quantifiers can provide information about what the user of the quantifier had expected before “knowing the facts” (Experiment 2). It is also clear that when writers produce a quantifier, they can reveal their assumptions about the prior expectations held by their readers (Experiment 2).     

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.     

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.     

锚定效应的研究范式、理论模型及应用启示

锚定效应是普遍存在的一种现象,它是指在不确定状态判断过程中,人们会以最初的信息作为参照点来调整对事件的估计,这往往会导致得出错误的判断。本文首先阐述了锚定效应的相关概念及经典研究范式,后者包括语意启动范式、数值启动范式、自发锚与外部锚启动范式等。然后对锚定效应的不充分调整启发模型、锚定调整模型、选择通达模型、双加工模型以及神经心理模型等进行了深入的探讨,并总结了锚定效应在经济管理等领域中的应用。最后指出了锚定效应的研究局限及未来的研究发展方向。     

Judgments of blame and forgiveness: A comparison of young adults,older adults,and older adults with dementia

IntroductionAlzheimer's disease may modify moral judgment.ObjectiveIn two studies, we assessed the impact of dementia on blame and forgiveness. Study 1 compared the ways in which young adults, older adults, and older adults with dementia cognitively integrated two factors. Study 2 assessed the number of different factors that older adults with dementia were able to integrate during these moral judgments.MethodThe participants recorded their moral judgements in a blame task and in a forgiveness task. In study 1, the two questionnaires contained scenarios built from the combination of two factors. In study 2, the participants were confronted with the same tasks under three different conditions with scenarios that combined three, four or five factors.ResultsThe data from study 1 showed that the older adults with dementia did not combine the two factors in the same way as young adults did: the combination depended on the type of moral judgment. Study 2 revealed differences in moral judgment between older adults with dementia and adults without dementia in all tasks (i.e. with three, four or five factors combined).ConclusionDementia has an impact on moral judgments. Moral judgment among people with dementia is both task- and condition-dependant.     

Anchoring,Activation, and the Construction of Values

Anchoring is a pervasive judgment bias in which decision makers are systematically influenced by random and uninformative starting points. While anchors have been shown to affect a broad range of judgments including answers to knowledge questions, monetary evaluations, and social judgments, the underlying causes of anchoring have been explored only recently. We suggest that anchors affect judgments by increasing the availability and construction of features that the anchor and target hold in common and reducing the availability of features of the target that differ from the anchor. We test this notion of anchoring as activation in five experiments that examine the effects of several experimental manipulations on judgments of value and belief as well as on measures of cognitive processes. Our results indicate that prompting subjects to consider features of the item that are different from the anchor reduces anchoring, while increasing consideration of similar features has no effect. The anchoring-as-activation approach provides a mechanism for debiasing anchoring and also points to a common mechanism underlying anchoring and a number of other judgment phenomena.     

The anchoring effect in metamemory monitoring

Judgments about future memory performance (metamemory judgments) are known to be susceptible to illusions and bias. Here we asked whether metamemory judgments are affected, like many other forms of judgment, by numerical anchors. Experiment 1 confirmed previous research showing an effect of informative anchors (e.g., past peer performance) on metamemory monitoring. In four further experiments, we then explored the effects of uninformative anchors. All of the experiments obtained significant anchoring effects on metamemory monitoring; in contrast, the anchors had no effect on recall itself. We also explored the anchoring effect on metamemory control (restudy choices) in Experiment 4. The results suggested that anchors can affect metamemory monitoring, which in turn affects metamemory control. The present research reveals that informative and, more importantly, uninformative numbers that have no influence on recall itself can bias metamemory judgments. On the basis of the current theoretical understanding of the anchoring effect and metamemory monitoring, these results offer insight into the processes that trigger metacognitive biases.     

Uninformative Anchors Have Persistent Effects on Valuation Judgments

Anchoring effects influence a wide range of numeric judgments, including valuation judgments, such as willingness‐to‐pay (WTP). However, prior research has not established whether anchoring only temporarily distorts responses or exerts persistent influence on preferences. This article presents three incentive compatible experiments examining the long‐term effects of random anchoring on WTP. Study 1 evaluated the persistence of anchoring effects over long durations, and showed that the strength of the effect decayed but did not disappear completely even 8 weeks later. In Study 2, a random anchor significantly influenced WTP after one week, regardless of whether WTP was also elicited immediately following the anchoring procedure, showing that consistency motivations do not account for persistence of anchoring effects. Study 3 showed relatively low anchors resulted in more stable valuations, compared with participants who reported WTP with no anchoring procedure. Together with the pattern of decay over time in Study 1, this suggests that anchoring facilitates the “imprinting” of valuation judgments for later retrieval. These studies show that anchoring effects can lead to lasting changes in valuation judgments, providing the first demonstration of long‐term persistence of constructed preferences as a result of an uninformative and arbitrary manipulation.     

Anchoring unbound

An attitudes and persuasion perspective can broaden our understanding of anchoring by highlighting sources of variability in anchoring effects that have been largely overlooked. As the target article suggests, research guided by this perspective can help identify (1) different types of anchors that exert their influence through different underlying mechanisms, 2) important social psychological moderators of anchoring effects, and 3) sources of variability in the consequences of anchoring for judgment and choice. In this commentary, we take an even broader perspective on the types of anchors that are likely to influence judgment, suggesting four potentially distinct types—intuitive approximations, best/worst case scenarios, environmental suggestions, and magnitude priming. We conclude by discussing how an attitudes and persuasion perspective on anchoring may provide novel insights into the moderators and consequences of anchoring effects in everyday life.     

Anchoring effects on performance judgments

Three studies were conducted investigating the effects of irrelevant anchors on performance judgments. Both a lab and field study demonstrated that an alternative anchoring manipulation that did not involve an explicit comparative question had effects on performance judgments similar to a traditional anchoring manipulation. The final study examined whether the anchoring effects were more likely when the anchor was highly applicable to the final judgment. The results indicated that both highly applicable and low applicable anchors produced an anchoring effect, but the highly applicable anchors had a larger effect on performance judgments. Evidence was also found for asymmetrical anchoring effects. In two of the three studies, high anchors increased performance judgments relative to the control group, whereas low anchors were not significantly different from the control group.     

When knowledge matters—differential effects of available knowledge in standard and basic anchoring tasks

The present research examines whether anchoring effects—the assimilation of a numeric estimate towards a previously considered standard—depend on judges' available knowledge in the target domain. Based on previous research, I distinguish two types of anchoring effects. Standard anchoring is obtained if judges are explicitly asked to compare the anchor to the target. Basic anchoring results if the accessibility of the anchor is increased prior to judgments about the target. I expected that only basic but not standard anchoring is reduced by providing judges with judgment‐relevant knowledge. Using a standard versus basic anchoring paradigm, 112 participants were confronted with a high versus low anchor before estimating the average price of a German midsize car. Prior to this task, participants were provided with information about prices of cars (relevant knowledge) versus kitchens (irrelevant knowledge). Results demonstrate that this knowledge only influenced the magnitude of basic but not standard anchoring effects. This finding demonstrates that knowledge has differential effects in different types of anchoring. Copyright © 2007 John Wiley & Sons, Ltd.     

Calibration processes in a serial talent test

ObjectivesIn the beginning of serial evaluations, raters assess performances without knowledge about following performances. We assume that judges must observe a certain number of performances to calibrate their judgment scale, leading to systematic biases (avoidance of extreme judgments) in the beginning of judgment series. The present experiment investigates how many performance observations are necessary to calibrate internal judgment scales, leading to consistent judgments.DesignA between-group design was used.MethodVideos of a talent-test were presented in different orders. Every performance was presented in early, medium, and late positions. Thirty participants rated these series and we assessed the effect of performance position on performance evaluations.ResultsWe found calibration biases within the first nine performances; after that, evaluations remained stable and consistent.ConclusionCalibration processes are completed after a specific number of judgments; this implies interesting interventions for consistent judgments independent of the position in a series.     

Affect Is Greater Than,Not Equal to,Condition: Condition and Person Effects in Affective Priming Paradigms

Affective primes may impact ensuing behavior through condition and person effects. However, previous research has not experimentally disentangled these two sources of influence in affective priming paradigms. In the current research, we simultaneously examine the influence of condition factors, in terms of prime valence, and person factors, in terms of affect reactivity and personality. In both studies, undergraduate participants (total N = 174) were primed with either positive or negative affective stimuli (words, Study 1; pictures, Study 2) prior to judging the likability of a neutral target (Arabic characters, Study 1; inkblots, Study 2). Although we did observe between‐condition differences for positive and negative primes, person‐level effects were more consistent predictors of target ratings. Affect reactivity (affect Time 2, controlling Time 1) to the primes predicted evaluative judgments, even in the absence of condition effects. In addition, the personality traits of Neuroticism (Study 1) and behavioral inhibition system sensitivity (Study 2) predicted evaluative judgments of neutral targets following negative affective primes. With effects for condition, affect reactivity, and personality, our results suggest that affective primes influence ensuing behaviors through both informational and affective means. Research using affective priming methodologies should take into account both condition and person‐level effects.     

Automatic Activation and Use of Gender Subgroups

Two experiments tested whether, similarly to global gender categories, gender subgroups are activated and applied on an automatic basis. In Experiment 1 (N?=?90) the female subgroup career woman was activated in a subliminal priming procedure. Experiment 2 (N?=?40) contrasted the subliminal priming of career woman with the activation of the global category woman. In both experiments the activated subgroup was applied to a target person in an ostensibly unrelated judgment task: Judgments of the target person were significantly higher on features typical for the subgroup than on untypical features. Activating the global category led to clearly different judgments than when the subgroup was activated. Results are discussed with respect to the use of global and subordinate gender categories in social categorization.     

Elaborating a simpler theory of anchoring

Within the classic anchoring paradigm, in which respondents are forced to consider provided numbers as possible responses to a target judgment, Wegener et al. (2008) proposed that cognitive load affects the psychological mechanism by which these anchors influence judgments. We propose, instead, that level of cognitive resources does not fundamentally affect how anchoring works, but only whether respondents can access other considerations that bear on the target judgment. Though we share the authors' view that environmental circumstances can influence the relative contribution of associative and deliberative inputs in judgments, we contend that cognitive load primarily affects the types of information that respondents consider, not the manner by which a focal element is processed.     

How to Precisify Quantifiers

I here argue that Ted Sider's indeterminacy argument against vagueness in quantifiers fails. Sider claims that vagueness entails precisifications, but holds that precisifications of quantifiers cannot be coherently described: they will either deliver the wrong logical form to quantified sentences, or involve a presupposition that contradicts the claim that the quantifier is vague. Assuming (as does Sider) that the “connectedness” of objects can be precisely defined, I present a counter-example to Sider's contention, consisting of a partial, implicit definition of the existential quantifier that in effect sets a given degree of connectedness among the putative parts of an object as a condition upon there being something (in the sense in question) with those parts. I then argue that such an implicit definition, taken together with an “auxiliary logic” (e.g., introduction and elimination rules), proves to function as a precisification in just the same way as paradigmatic precisifications of, e.g., “red”. I also argue that with a quantifier that is stipulated as maximally tolerant as to what mereological sums there are, precisifications can be given in the form of truth-conditions of quantified sentences, rather than by implicit definition.