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Taking the High (or Low) Road: A Quantifier Priming Perspective on Basic Anchoring Effects David Sleeth-Keppler

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Humboldt State University Accepted author version posted online: 07 Jan 2013.Published online: 13 May 2013.

To cite this article: David Sleeth-Keppler (2013) Taking the High (or Low) Road: A Quantifier Priming Perspective on Basic Anchoring Effects, The Journal of Social Psychology, 153:4, 424-447, DOI: 10.1080/00224545.2012.757543 To link to this article: http://dx.doi.org/10.1080/00224545.2012.757543

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The Journal of Social Psychology, 2013, 153(4), 424–447 Copyright © Taylor & Francis Group, LLC

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Taking the High (or Low) Road: A Quantifier Priming Perspective on Basic Anchoring Effects DAVID SLEETH-KEPPLER Humboldt State University

ABSTRACT. Current explanations of basic anchoring effects, defined as the influence of an arbitrary number standard on an uncertain judgment, confound numerical values with vague quantifiers. I show that the consideration of numerical anchors may bias subsequent judgments primarily through the priming of quantifiers, rather than the numbers themselves. Study 1 varied the target of a numerical comparison judgment in a between– participants design, while holding the numerical anchor value constant. This design yielded an anchoring effect consistent with a quantifier priming hypothesis. Study 2 included a direct manipulation of vague quantifiers in the traditional anchoring paradigm. Finally, Study 3 examined the notion that specific associations between quantifiers, reflecting values on separate judgmental dimensions (i.e., the price and height of a target) can affect the direction of anchoring effects. Discussion focuses on the nature of vague quantifier priming in numerically anchored judgments. Keywords: construct accessibility, heuristics, judgmental anchoring, quantifiers

NUMERICAL INFORMATION CAN PLAY an important role in everyday judgments and decisions. In a marketing context, for example, the amount of profit a company promises to donate to a charity may influence a person to buy the company’s products (Pracejus, Olsen, & Brown, 2004). In the domain of legal judgments, the amount of monetary injury compensation requested by the prosecution may profoundly influence a jury’s perception of a defendant’s legal culpability (Chapman & Bornstein, 1996). In the domain of price negotiations, the first offer on the table may prove to be a critical determinant of the final negotiated agreement (Galinsky & Mussweiler, 2001), to name just a few examples. The work on judgmental anchoring represents one of the most fruitful streams of research concerning the effects of numerical information on judgment (e.g.,

Address correspondence to David Sleeth-Keppler, Humboldt State University, School of Business, 1 Harpst St., Arcata, CA 95521, USA; [email protected] (e-mail). 424

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Epley & Gilovich, 2006; Strack & Mussweiler, 1997; Tversky & Kahneman, 1974; Wilson, Houston, Etling, & Brekke, 1996). Researchers typically employ a paradigm consisting of a staged set of questions to demonstrate judgmental anchoring effects. The first question prompts research participants to compare a judgmental target with an ostensibly random numerical anchor. Participants then provide an absolute estimate of the target quantity in response to a second question. For example, in a well-known demonstration of judgmental anchoring (Tversky & Kahneman, 1974), participants first considered whether the percentage of African nations in the United Nations was higher or lower than a set of values randomly generated by a wheel-of-fortune. Following this comparative question, participants then provided an absolute estimate of the percentage. Results revealed a robust anchoring effect: Participants provided larger estimates after considering larger anchors (e.g., 65%), compared to conditions in which the wheel-of-fortune generated lower percentages (e.g., 10%). As these results show, comparisons between judgmental targets and numerical anchors generally result in absolute judgments that are assimilated to anchors (see Strack & Mussweiler, 1997 for a demonstration of a contrast effect). Why do anchoring effects obtain? An important precondition of anchoring effects is the presence of uncertainty about a target quantity in question. Put differently, when a person possesses absolute knowledge of a given target quantity, such as the percentage of African nations in the United Nations, comparing the target to a numerical anchor exerts no influence on final judgments, because the person simply retrieves and states the quantity from memory. In everyday situations, many numerical judgments are accompanied by considerable lack of direct knowledge and, therefore, uncertainty. Under conditions of judgmental uncertainty people often rely on accessible, but non-diagnostic, information to arrive at a judgment a basic finding consistent with numerical anchoring (Nisbett, Zukier, & Lemley, 1981). For example, many judgments involving prices, such as those involving the price of real estate (Northcraft & Neale, 1987), have seen robust influence by arbitrary listing values (see Mussweiler, 2003 for a review). Judgmental uncertainty may be a necessary condition for anchoring effects to obtain, but uncertainty alone does not explain why people are influenced by ostensibly random number standards to begin with. Over the years, several major explanations of judgmental anchoring effects have emerged in the judgment literature. These explanations vary in a number of important ways. For example, a classic explanation of anchoring effects represents Tversky and Kahneman’s (1974) view, who argued that judges consider the anchor value as an initial starting point for an insufficient adjustment process. Judges incrementally adjust answers up or down from the anchor value, until they obtain an acceptable value. Differences in absolute estimates, as a function of different anchor values, obtain because adjustments often terminate prematurely. Epley and Gilovich (2001, 2006) developed the adjustment view more fully by showing that the amount of adjustment judges engage in varies as a function of the amount

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of available cognitive resources and processing motivation (Epley & Gilovich, 2006). Work by Wilson, Houston, Etling, and Brekke (1996), on the other hand, has shown that numerical anchors can directly influence judgments, without the inclusion of an intervening adjustment process. Wilson and colleagues’ (1996) perspective represents a pure numeric priming perspective on anchoring and will be considered in more detail below. The most popular explanation of anchoring effects, Strack and Mussweiler’s (1997) selective accessibility model (SAM), presents a view that anchors exert their influence primarily on a semantic level, rather than a purely numeric level of processing. According to this perspective, when judges compare a target to a numerical anchor, they recruit anchor-consistent semantic knowledge about the target from memory. Anchors influence final judgments about the target because people tend to selectively recruit knowledge confirming the anchor, rather than knowledge disconfirming the anchor. The underlying process is often referred to as confirmatory search or positive hypothesis testing (e.g., Klayman & Ha, 1987). Subsequent absolute judgments about a target are biased in favor of the anchor, according to the SAM, because people arrive at numerical estimates based on biased semantic knowledge confirming the anchor values (see Mussweiler, 2003 for a review). Insufficient adjustment (Epley & Gilovich, 2006), numeric (Wilson et al., 1996) and semantic (Strack & Mussweiler, 1997) anchoring effects appear to obtain under different experimental situations, suggesting that judgmental anchoring ought to be thought of as a collection of effects, rather than a unitary phenomenon. The purpose of the present work is to take another look at Wilson et al.’s (1996) numeric priming perspective of anchoring. Specifically, I explore the possibility that many instances of numerical anchoring may involve the activation of nonspecific (vague) semantic information about the general magnitude of the numerical anchor. According to this perspective, general semantic information about quantities may bias estimates in the anchoring paradigm, with or without the activation of specific semantic information about the target of the judgment (the SAM perspective). If the above account is veridical, the strict line of demarcation drawn in the current literature between numeric and semantic anchoring effects may be overstated, given that all anchoring effects involve at least the activation of vague quantifiers. This conceptualization offers some parsimony among anchoring explanations and allows for the testing of novel implications. The details of this research are described below. The Distinction Between Numeric and Semantic Anchoring In much of the existing anchoring research, participants’ comparison judgments (in which they encountered the anchor) and absolute judgments (in which they had to make a final estimation about the target quantity in question) involved the same target (for example, the % of African Nations in the United Nations for

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both questions; Tversky & Kahneman, 1974). Since the initial demonstration of anchoring, Wilson and colleagues (1996) have shown that anchoring effects may obtain even when the target of the comparison is unrelated to the target of the absolute judgment, and when only numbers are made accessibly, without the inclusion of specific comparisons. For example, in one study, Wilson and colleagues (1996) first asked participants to compare the number of physicians in the local phonebook to a random standard, or not, depending on condition. Surprisingly, the introduction of the anchor in the context of physicians influenced subsequent estimates of the number of African Nations in the United Nations, even though there was no discernible relationship between physicians and African Nations in the participants’ minds. Based on this research, it appears that any accessible number, fleetingly represented in short-term memory, holds the potential to bias a subsequent numerical estimate, even across unrelated contexts. In further support of a pure numeric anchoring hypothesis, Wilson and colleagues (1996) obtained anchoring effects even when participants did not make any explicit comparisons between a target and an anchor value, but merely engaged in tasks that increased the accessibility of differentially valued numbers in short-term memory. For example, participants in one study were asked to copy a series of numbers (4,421 . . . 4,579) under the guise of a graphology experiment, thereby increasing the accessibility of those numbers. Results showed an anchoring effect on a subsequent estimation task (involving the projected incidence of a campus health issue) as a function of how often participants copied the numbers, with higher estimates under conditions of high (vs. low) numeric accessibility. Due to the virtually limitless applicability of de-contextualized numbers on judgment, the boundary conditions of anchoring, according to Wilson and colleagues’ (1996) numeric perspective, appear to be quite flexible. Interestingly, however, work by Strack and Mussweiler’s (1997) has shown significant limits regarding the influence of number standards on judgment, but only in situations in which the target context in which the anchor is first encountered—the comparison question—matches the target of the final estimate (in other words, in the traditional anchoring paradigm). As described earlier, Strack and Mussweiler’s (1997) SAM proposes that people selectively recruit anchor-consistent semantic knowledge about the target from memory, knowledge that would only bias subsequent estimates about the same judgmental target, and not indiscriminately about unrelated targets. In order to test this notion, Strack and Mussweiler (1997, Study 1) asked participants to compare the height of the Brandenburg Gate in Berlin to either a high or low anchor, depending on condition. Subsequently, in a standard anchoring condition, half the participants performed an absolute estimation task involving the gate’s height. For the other half of the participants, this task pertained to estimating the gate’s width, representing a change in dimension between the comparative and absolute judgments. Consistent with the notion that activation of specific target knowledge mediates anchoring, an anchoring effect was obtained in the standard anchoring condition, whereas no anchoring effect was

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obtained in the condition involving a dimension change between the comparative and absolute judgments, supporting the knowledge relevance constraint of the SAM. To address the obvious inconsistency between Wilson and colleagues’ (1996) flexible numeric priming account of anchoring, and Strack and Mussweiler’s (1997) more restrictive semantic account of anchoring, Mussweiler and Strack (2001b) conducted a series of experiments, which showed that numeric effects primarily obtain when target knowledge, generated during the comparative judgment, is rendered irrelevant for a subsequent absolute judgment (that is, due to a target or dimension change). Put differently, numeric anchoring appears to be due to the residual effect of numbers that carry judgmental weight between unrelated contexts. Semantic effects primarily obtain within the classic anchoring paradigm, in which the target of the absolute judgment is identical to that of the comparative judgment, and therefore, anchor-consistent target knowledge can exert its judgmental impact. In the present article, I revisit Mussweiler and Strack’s (2001b) conclusion to investigate the notion that the distinction between semantic (Strack & Mussweiler, 1997) and numeric (Wilson et al., 1996) effects may be profitably understood as involving different types of semantic information, namely vague quantifiers in the numeric case, and target-specific knowledge in the semantic case. Considerable research provides evidence for the activation of target-specific semantic knowledge in traditional anchoring situations (see Mussweiler, 2003 for a review), but relatively little systematic work has been conducted to explore the possible role of vague quantifiers in judgments that saw previous classification as “pure” numeric anchoring effects. To close this gap, I will present several challenges to the notion that numeric anchoring effects, such as those reported by Wilson and colleagues (1996), are simply numeric effects devoid of semantic contents, followed by three experiments designed to test the veracity of a quantifier priming account of numerical anchoring. The Semantics of Numbers Wilson and colleagues’ (1996) numeric priming account of anchoring essentially predicts that simply processing numbers of different magnitudes may produce anchoring effects. For example, processing the number 7,300 would result in a larger subsequent estimate of some target quantity, compared to processing the number 7.3, because 7,300 is larger than 7.3 on a number line (see also Wong & Kwong, 2000). Although this notion appears non-controversial, it lacks specificity as to what exactly the impact of a “pure” number on judgment is. Specifically, it is possible that simply representing the actual sequence of numbers (e.g., 7-(,)3-0-0) in short-term memory influences judgments (see Wilson et al., 1996). Alternatively, judgments could be based on a semantic representation of the quantity the number represents (e.g., “a lot”).

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The distinction between “pure” numbers and the vague quantifiers they may invoke is not trivial. For example, the relative location of a number on a line, and the quantifier it may invoke, could sometimes be contradictory. This point is perhaps best illustrated by Birnbaum (1999), who showed that people may generate contexts other than an infinite number line to interpret numerical values, especially in the absence of any meaningful external context. Specifically, Birnbaum (1999) found that, in a between-participants design, participants judged the number 9 to be greater than the number 221. According to Birnbaum (1999), this counterintuitive effect obtains because people spontaneously invoke different internal scales as an interpretive context for the number. In the case of judging the size of the number 9, participants may have invoked a 10-point scale, resulting in a judgment that the number 9 is fairly large. However, when judging the size of the number 221 people may have invoked a 1,000-point scale, resulting in a judgment that the number 221 is fairly small. This finding illustrates that the meaning and judgmental impact of a number may change dramatically as a function of context, with the predominant judgmental impact of a number occurring on a semantic level. Put differently, numbers ought to be distinguished from the quantities they invoke, because the impact of a number on judgment may involve vague quantifiers, rather than its relative location on a number line. Also relevant to the current discussion, Brewer and Chapman (2002) have demonstrated that pure numbers appear to generally lose their judgmental impact when they are difficult to quantify. Specifically, Brewer and Chapman (2002) were only able to replicate Wilson and colleagues’ (1996) graphology experiment described earlier under conditions of exact replication, and not with any other set of numbers. Brewer and Chapman (2002) hypothesized that the numbers employed by Wilson and colleagues (1996) may have spontaneously invoked vague quantifiers, as many of them resembled numbers in ranges participants may have been more familiar with (e.g., numbers representing years). Brewer and Chapman (2002) concluded that the basic anchoring effect in its purest form (not involving explicit comparisons with judgmental targets) appears to be rather fragile. The above analysis suggests that numbers may primarily exert their impact when they become quantifiable, allowing for the semantic representation of the number in terms of nonspecific quantifiers (e.g., “many,” “few”). Stated in the reverse, pure numbers considered in isolation do not appear to represent particularly meaningful guides for judgments. On the basis of the above discussion, I propose that the influence of numerical anchors may best be understood against the backdrop of findings that people prefer to represent and communicate numerical values semantically (e.g., Zimmer, 1984). This preference for words over numbers appears to arise from a number of factors, including, for example, the easier understanding and communication of words, relative to numbers, under everyday rules of conversation (e.g., Wallsten, Budescu, Rapoport, Zwick, & Forsyth, 1986). Based on the above literature alone, it seems reasonable to assume that general semantic representations of the magnitude of numbers may be

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primarily responsible for influencing subsequent judgments in certain anchoring paradigms, and not merely the numbers themselves.

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Assimilation Versus Contrast Effects One of the classic issues in the literature on social judgments concerns the concepts of assimilation versus contrast (Sherif & Hovland, 1961). Originating from the work on psychophysics, assimilation occurs when a stimulus is judged as similar to a standard on some dimension (e.g., height), whereas contrast occurs when a stimulus is judged as dissimilar on some dimension (see Mussweiler, 2003). Applied to the current discussion, an important question regarding the effects of numerical anchors on judgment concerns their perception as plausible (close) versus implausible (distant) comparison standards, given a certain target judgment. For example, the anchor 240 may be plausible in connection with the ages of art objects, but implausible in connection with the age of a human. Would consideration of implausibly high standards result in contrast effects in the anchoring paradigm, compared to standards that are plausible, which would result in assimilation? Research by Mussweiler and Strack (2001a) has shown that implausible anchors exert even stronger assimilation effects than plausible anchors do. Specifically, as Mussweiler and Strack (2001a) have argued, people may consider different types of information when the anchor is implausible versus plausible. Relevant to the current discussion, answering a comparative question involving implausible anchors may prompt a person to first adjust to a value plausible for the target category (e.g., 105 for human age) before testing the hypothesis that the target in question is identical to the anchor. Because the initial adjustment process terminates at the upper (or lower) boundary of plausible values for a target category, effects based on implausible anchors tend to be larger, relative to anchors that fall closer to the middle of the distribution for a given category (see Mussweiler & Strack, 2001a). Although there is nothing inherently wrong with this explanation, the present quantifier priming account of anchoring makes a more straightforward prediction. Specifically, implausible anchors, relative to plausible ones, may simply increase the accessibility of vague quantifiers, which may result in larger anchoring effects in implausible, compared to plausible anchoring conditions. While testing the implication of differential quantifier activation as a function of anchor-extremity is beyond the scope of this paper, Study 2 in the present research tested for the presence of assimilation versus contrast in vague quantifier priming, involving implausible anchors. Overview of the Present Research A basic implication of my model is that identical numerical values embedded in different contexts ought to prime different vague quantifiers, and hence, exert different effects on judgment. This implication was tested in Study 1.

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Another way to tap more directly into the proposed quantifier-priming mechanism would be to manipulate semantic representations of quantity directly, within the more traditional anchoring paradigm. Specifically, if my account is valid, priming words inconsistent with the magnitude of an anchor should result in the reduction or reversal of anchoring effects. Similarly, priming anchor-consistent quantifiers should produce anchoring effects similar to those obtained in traditional anchoring studies. Study 2 was designed to test these notions. A secondary aim of Study 2 was to test whether the results of Study 1 were due to assimilative or contrastive judgments. According to research by Strack and Mussweiler (1997) changing the dimension of a target estimate between comparative and absolute judgments in the anchoring paradigm should eliminate anchoring effects (e.g., as exemplified by their Brandenburg Gate study). One way to explain this finding is that certain questions, such as those involving the height of an object, may prime very specific quantifiers (e.g., “high”), which may not readily transfer to estimates concerning another feature or dimension of the same object. This pattern might be particularly likely to obtain when the translation of the quantifier from one dimension to another requires additional mental computation. For example, the width of the Brandenburg Gate is roughly 1.5 times its height. Participants in Strack and Mussweiler’s (1997) study would have had to multiply an estimate based on an ostensibly random height anchor by a factor of 1.5 to arrive at an absolute estimate concerning the width of the gate. The presence of this additional burden may explain the observed null effect under conditions of changed target dimensions in Strack and Mussweiler’s (1997) study. However, it should generally be possible to obtain anchoring effects across judgmental dimensions. For example, subjectively perceiving a link between two dimensions involved in a judgment ought to facilitate a conditional carryover of the magnitude implication of the anchor to a judgment on another dimension. For example, persons with different occupations might learn to conditionally link concepts that reflect separate judgmental dimensions, based on their interactions with vocationally relevant stimuli. An antique dealer may, due to her professional involvement with “old” and “expensive” objects, chronically associate the quantifiers “old” and “expensive.” Following this logic, a comparative question concerning a person’s age could associatively influence a subsequent absolute judgment concerning the price of an unrelated target. A used car dealer may on the other hand acquire the rule “if old then inexpensive”. Hence, the antiques dealer who processed a high comparison standard for a given target’s age is likely to give a high estimate of the price (an “assimilation effect”) of an unrelated target, whereas a used car dealer is likely to give a low estimate of its price (a “contrast effect”). This novel mechanism for obtaining anchoring effects involving separate dimensions was tested in Study 3.

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Study 1 The first experiment tested the central implication of my quantifier-priming model that numerical anchors can influence numerical judgments purely on a semantic level of representation. To that end, I chose to vary the typical anchoring paradigm—in which the same target sees comparison with either a high or low numerical anchor, depending on experimental condition—by holding the numerical anchor value constant, while varying the target of the comparison judgment. The primary goal behind utilizing this design was to separate out the potential direct influence of the numerical value on absolute numerical judgments and the hypothesized influence of the semantic quantifier, activated within the context of the comparative question. Depending on condition, participants in Study 1 either received a comparative question involving a well-known older target person or a well-known younger target person. Participants in both conditions received the same anchor value, which fell roughly in the middle of a range of values considered plausible for human age. When the “young” target was compared to the anchor, I predicted the priming of the concept “old,” because the value constituted a high anchor for the target person’s age. Following the same logic, I expected participants comparing the “old” target person to the identical value to be primed with the concept “young,” because the value would be considered a low anchor for the target’s age. Following the comparative judgment phase, all participants estimated the age of a third, unrelated target. This judgment constituted the main dependent variable. Method Participants and Design Forty (male and female) students enrolled at a large university located in the eastern part of the United States participated in exchange for course credit in an introductory psychology course. They were randomly assigned to the two cells of a modified anchoring design. Procedure and Materials The participants were recruited under the pretext of a study designed to develop different wordings for general knowledge questions. The study, participants were told, included a comparison of novel and traditional methods to assess general knowledge to ultimately improve the wording of general knowledge questions. Moreover, participants were informed that some of the questions required a comparison with a given number standard and that these standards had been randomly selected by using a mechanism similar to that of a wheel of fortune. It was pointed out that the random selection of numbers was necessary to minimize the

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potential influence the standards may have on the answers and to identify the impact of different question formats. The particular emphasis on the random selection procedure was designed to reduce the potential conversational relevance of the anchors—the notion that the experimenter might be giving participants a clue as to the real value of target quantity in question (Grice, 1975). Next, all participants responded to 8 filler questions, namely absolute estimation tasks regarding a number of different targets. Afterwards, the independent variable was presented. Depending on condition, participants were asked to indicate whether pop singer Britney Spears was older or younger than 45 years, or whether Hollywood actor Clint Eastwood was older or younger than 45 years. These targets were chosen to reflect well-known exemplars of the categories “old” and “young.” Pre-testing (N = 26) prior to this study had revealed that students generally knew (a) who Britney Spears and Clint Eastwood were, and (b) that Britney Spears was perceived to be relatively young (her age was 21 at the time of the study) and Clint Eastwood to be relatively old (his age was 72 at the time of the study). The anchor value was chosen to reflect the midpoint of a range of plausible values for human age, which therefore constituted a high standard for Spears’ age and a low standard for Eastwood’s age. Following this manipulation, all participants were asked to estimate the ideal age (in years) of a bottle of French red wine, before it should be consumed. This question constituted the main dependent variable. I expected participants to show considerable amounts of uncertainty regarding this question. As described earlier, judgmental uncertainty is a pre-condition for anchoring effects to occur. Interestingly, even experts have been shown to fall victim to anchoring biases (e.g., Northcraft & Neale, 1987), and I would expect similar effects if a group of wine connoisseurs had been selected as participants, rather than undergraduate psychology students. The main difference between expert and lay judges in the anchoring paradigm appears to be the range of anchors judges consider to be plausible candidates for a judgment, and the range of answers provided as final judgments, with expert judges providing judgments around a more narrow range of options. Even though expertise reduces the variability of judgments in the anchoring paradigm, the overall effect would likely be robust among experts. Finally, all participants responded to a number of filler questions, before they were debriefed, thanked and dismissed. Results and Discussion The anchoring effect, using the modified anchoring design, was replicated. The results of a one-way analysis of variance (ANOVA) showed that participants gave higher estimates (in years) of the ideal age of a bottle of French red wine in the Britney Spears comparison condition (M = 21.95, SE = 2.685, N = 20), relative to the Clint Eastwood comparison condition (M = 13.5, SE = 2.685, N = 20), F(1, 38) = 4.951, p < .05, Cohen’s d = .7. The magnitude of the effect is moderate, in line with previous effects obtained in the anchoring literature (Wilson et al., 1996).

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These results provide initial support to the conclusion that absolute estimates in anchoring tasks may be solely based on semantic concepts associated with the anchor. Specifically, when the anchor value (45 years) saw presentation as a comparison standard for the age of a young person (Britney Spears), participants gave higher estimates of the age of an unrelated target (French wine), presumably due to the activation of the concept “old” after processing the comparative question. That is, because of the generality of the quantifier “old,” compared to target-specific semantic knowledge about Spears or Eastwood, this primed construct appeared to have influenced a subsequent estimate of the age of a bottle of wine, even though the concept was activated in a different initial context (of celebrity ages). Similarly, when the same anchor value served as a standard of comparison for an older person (Clint Eastwood), participants appeared to have been primed with the quantifier “young” (45 years constituted a low standard for the his age), resulting in lower estimates of the age of a bottle of wine. Because the anchor values themselves were specifically not varied in this study, an interpretation of these results based on a pure numerical priming perspective (Wilson et al., 1996) can be ruled out. With pure numerical priming ruled out, could Strack and Mussweiler’s (1997) model account for this finding? The answer appears to be negative. Under their model, participants in the Britney Spears condition would test the hypothesis that Britney Spears was 45 years old, thereby activating anchor-consistent semantic knowledge about her (that is, biased knowledge that she is relatively old). Similarly, participants testing the hypothesis that Clint Eastwood was relatively young (that is, 45 years of age) presumably activated knowledge about the actor that would be consistent with the notion that he is young. Based on the selective accessibility model’s (Strack & Mussweiler, 1997) applicability constraint of activated knowledge, no anchoring effect (or one reflecting contrast) should have obtained, because semantic knowledge generated in response to the respective comparative judgment would not be applicable to the target in the absolute judgment (a bottle of French wine). In sum, the presence of a significant anchoring effect in this study appears explicable only in terms of a general quantifier priming analysis. One weakness of the first study is that it does not rule out an alternative interpretation of the obtained pattern of results. Specifically, while thinking about Britney Spears, participants may have been primed with the concept “young,” after providing an answer to the comparative question. Because every participant in this study indicated that Britney Spears was younger than 45 years, they may consequently have been primed with the concept young, rather than the concept old, after processing the comparative question. Similarly, because every participant indicated that Clint Eastwood was older than 45 years, participants in this condition may have been primed with the concept old, rather than the anchorbased concept of young. Within the context of this alternative priming mechanism, the obtained results may have been due to a contrast effect. That is, the higher estimates of the age of the bottle of wine in the Britney Spears condition (compared to

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the Clint Eastwood condition) may have been the result of an over-correction process: Participants may have perceived a change in targets between the comparative question, and corrected for the potential influence of the alternative “young” prime in the Spears condition and the “old” prime in the Eastwood condition on their estimates of wine age. Even though this alternative explanation does not invalidate the operation of semantic quantifiers in the anchoring paradigm, it involves the complicating factor of a correction process, potentially triggered when participants notice a change in targets between judgments in one context (i.e., the comparison question) and another context (i.e., the absolute judgment). Because correction may limit or reverse the operation of general quantifiers—a process not observed in previous, “purely numerical” anchoring questions (that is, in Wilson et al.’s, 1996 experiments)—I designed a second study to directly address the question of contrasting versus assimilative judgments. Study 2 The aims of the present study were twofold: To provide further evidence for the operation of semantic quantifiers in numerical anchoring situations, and to address the question of whether the result of Study 1 were due to a contrast or assimilation effect. Similarly to the first study, Study 2 featured an easy-to-answer comparison question, followed by an absolute numerical judgment task, featuring a target unrelated to the initial comparison question. In order to create conditions similar to those in the previous study, in which all the participants knew that Clint Eastwood was older than the numerical anchor 45 and Britney Spears younger, Study 2 featured implausible anchor values as comparison standards, values that fall outside the range of values most people would consider to be acceptable candidates for the target quantity in question (Mussweiler & Strack, 2001a). Similarly to the results obtained in Study 1, implausible anchor values are expected to result in uniform answers to the comparative question (for example, all participants indicating that a target quantity is lower than an implausibly high anchor), because the question is easy to answer (c.f. Mussweiler & Strack, 2001a). Study 2 combined a standard anchoring paradigm—varying anchor values while holding the comparison target constant—with a separate semantic priming manipulation, designed to increase the accessibility of general quantifiers. Depending on experimental conditions some participants saw exposure to a priming task designed to increase the accessibility of anchor-consistent quantifiers. Specifically, participants in this condition saw exposure to words consistent with the general high or low magnitudes of the anchors. The priming of anchor-consistent quantifiers was predicted to have no specific effect on absolute estimates, because the primed quantifiers would be semantically redundant with the quantifiers hypothetically activated naturally in response to considering the anchors during the comparison question. On the other hand, if the alternative explanation of a contrast effect holds priming anchor-consistent quantifiers

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should interfere with the contrast judgment and result in null effect. Participants in a second priming condition were exposed to anchor-inconsistent quantifiers. In this condition, participants were exposed to words that opposed the semantic magnitude implications of the anchors, which were predicted to interfere with the expected impact of the numerical anchors, resulting in a reduction of the anchoring effect. Under the alternative explanation of a contrast effect, anchorinconsistent quantifiers would reinforce the contrast, resulting in a significant contrast effect. Thus, the present design allows for a direct test of the quantifier priming hypothesis, while shedding further light on the direction of the anchoring effect (assimilation versus contrast). Finally, participants in a control priming condition were only exposed to a neutral priming manipulation, which was predicted to result in absolute estimates similar to those obtained in a traditional anchoring paradigm. This condition was included to rule out any effect of the priming manipulation on absolute estimates (the final dependent variable). Method Participants One hundred and nine participants from an online participant pool managed by a large university located in the western United States participated in exchange for an opportunity to win a monetary prize in a random drawing. Participants were randomly assigned to the 6 cells of a 2 (high versus low anchor) × 3 (consistent prime, inconsistent prime, neutral prime) between-participants factorial design. Procedure and Materials Participants were recruited via an online research website, which notified them of an experiment that provided them with a chance to win a $20 gift certificate to a major online retailer. After logging on to the study, an instruction screen informed participants that they would be responding to two separate pre-tests designed to calibrate stimulus materials for larger, future studies. Specifically, it was explained that a first task was designed to test the impact of different question formats to study people’s responses to general knowledge questions. It was pointed out that some of the questions required participants to compare a given target to a number that was randomly generated by a computer program. Again, instructions emphasized that the numbers were randomly generated in order to minimize the influence of those numbers on actual responses. Participants then received five comparative questions, asking them to indicate whether a number of targets were higher or lower than a given numerical anchor. The fifth question included the critical independent variable. Specifically, participants were asked to indicate whether the height of the Eiffel Tower in Paris, France was

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(implausibly) more or less than 8 feet in the low anchor condition and more or less than 84,634 feet in the high anchor condition. Following the manipulation of the anchoring independent variable, participants were exposed to the priming independent variable, which consisted of a sentence unscrambling task (e.g., Bargh, Chen, & Burrows, 1996) designed to increase the accessibility of words related to high and low quantities. The priming task was framed as a test of language comprehension that was under development for future assessments, which required participants to form a grammatical fourword sentence using sets of five stimulus words. Participants received each set of words on a separate screen and they were instructed to type the sentence into a form field. In each priming condition, participants received 14 sets of words. In the “high” quantifier priming condition, the stimulus set included the words abundant, ample, more, sizeable, substantial, plentiful, [a] lot, many, expensive, high, huge, full, and long. In the “low” quantifier priming condition, participants were exposed to the words few, low, tiny, minimal, scarce, little, cheap, small, empty, short, puny, and dwarfed. Finally, in the control priming condition, participants received words unrelated to notions of quantity (e.g., cow, pencil). Following this phase, all participants responded to five absolute questions, with the first question designed to represent the critical dependent variable (the subsequent questions were included as filler questions). Specifically, participants were asked to estimate the average annual temperature in Hawaii (in degrees Fahrenheit). Suspicion Check To assess whether participants in the two priming conditions were aware of the connection between the priming task and the absolute estimates they provided, I used a funneled debriefing procedure suggested by Bargh and Chartrand (2000). None of the participants reported any suspicion of how the priming task may have influenced their responses to the subsequent questionnaire. Finally, all participants were debriefed, thanked and dismissed. Results and Discussion As the inspection of Table 1 reveals, participants’ estimates of the average annual temperature in Hawaii clearly depended on the anchors and the type of prime used. Specifically, participants in the neutral priming condition generally gave higher temperature estimates after receiving a high (versus low) anchor, replicating the standard anchoring effect, F(1,103) = 6.56, p < .05, Cohen’s d = .86. Furthermore, participants’ estimates appeared unaffected by the priming of anchor-consistent quantifiers, again, resulting in higher estimates in the high (versus) low anchoring condition, F(1,103) = 5.98, p < .05, Cohen’s d = .65. However, participants’ estimates in the anchor-inconsistent priming condition

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TABLE 1. Absolute Estimates of the Average Annual Temperature in Hawaii (in Degrees Fahrenheit) by Anchor and Priming Condition (Study 2) Priming condition

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Anchor High Low

Consistent M (SE)

Inconsistent M (SE)

Neutral M (SE)

83.05 (2.16) 75.67 (2.22)

76.94 (2.36) 82 (2.29)

83.75 (2.11) 76.21 (2.16)

reflected a contrast pattern, with higher estimates provided in the low (versus high) anchor condition. The difference between the estimates in this condition failed to reach conventional levels of significance, F(1,103) = 2.5, p = .117. The overall interaction between the anchoring and priming conditions was statistically significant, F(1,103) = 5.34, p < .05, whereas the main effect of anchor was marginally significant, F(1,103) = 3.47, p = .06. Finally, the main effect of prime was not significant, F < 1. The effect in the neutral priming condition is relatively large, and the effect in the anchor-consistent priming condition is moderate, consistent with the magnitudes of effects obtained in previous studies. The results obtained in Study 2 provide significant insight into the operation of vague quantifiers in the anchoring paradigm. Specifically, results appear to provide support for the notion that anchor-based quantifying concepts may influence absolute estimation tasks directly in judgmental anchoring paradigms. Particularly noteworthy are the findings obtained in the anchor-inconsistent condition, which showed that primed quantifiers may interfere with traditional anchoring effects. Similarly, priming anchor-consistent quantifiers, or no quantifiers at all, produces effects similar to those obtained using traditional comparison tasks and numerical anchors. In combination, these results rule out the contrast explanation put forth as part of the analysis of Study 1, while providing further convergent evidence for a quantifier priming hypothesis. Study 3 The purpose of Study 3 was to extend the exploration of the hypothesized quantifier priming mechanism to situations in which subjective associations between two (or more) quantifiers may operate on numerical judgments. Specifically, the present investigation shows that quantifiers primed in response to considering an anchor value during a comparative question may influence a seemingly unrelated absolute estimation, because numerically-based quantifiers are often of a general nature, allowing them to function as higher-order judgmental bridges between superficially incompatible judgment contexts. For example, in

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Study 2, consideration of the height of an object (the Eiffel Tower) influenced subsequent judgments of the temperature in a certain geographic location (Hawaii). In addition to general quantifier activation patterns, numerical judgments may be based on specific associations between quantifiers, involving quantities on separate judgmental dimensions and opposing relative magnitudes. Such associations may be formed based on any number of subjective experiences in the minds of lay judges (see Kruglanski & Sleeth-Keppler, 2007). Study 3 consisted of a priming task, followed by an anchoring task. The target of the judgment changed between the comparative and absolute questions. In one priming condition of the experiment, I first primed participants with a rule that “if expensive, then heavy” and “if inexpensive, then light,” using a questionnairebased manipulation. Since both “heavy” and “expensive” (inexpensive, light) semantically represent “high” (or “low”) values along these two dimensions, this condition was designed to result in an assimilation effect during a subsequent anchoring task. In the second condition, I primed the opposite rule: “if expensive, then light” and “if inexpensive, then heavy.” These two conditions linked a “high” quantifier to a “low” quantifier (and vice versa), which was predicted to result in a contrast effect. Subsequently, participants received a comparative question involving either a high or a low anchor of the price of an object, presumably priming either the concepts “expensive” or “inexpensive.” After answering the comparative question, participants were asked to provide an absolute estimate of the weight of an object (the dependent variable). The direction of the anchoring effect, with respect to the weight of the target, was predicted to vary as a function of the associations primed during the first part of the study. Method Participants and Design Forty-three (male and female) students enrolled at a large university located in the eastern part of the United States participated in exchange for course credit in an introductory psychology course. Participants were randomly assigned to the four cells of a 2 (high vs. low anchor) × 2 (“expensive = heavy”/“inexpensive = light” rules vs. “expensive = light”/“inexpensive = heavy” rules) factorial design. Procedure and Materials Participants were run in groups of 2–4. Each participant received a packet of surveys, including general instructions similar to those provided in Study 1. The first questionnaire contained an adapted version of a task, designed by Erb, Fishbach, and Kruglanski (2002) to manipulate associations between semantic terms presumed to activate a general rule (e.g., “small is likable” or “big is likable”). Using this specific methodology, for half the participants in Study 3, an “expensive = heavy” and “inexpensive = light” association was created, whereas

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for the other half, the opposite association-pair was created (“expensive = light”; “inexpensive = heavy”). Afterwards, participants received a comparative question, on a separate questionnaire, asking them to indicate whether the average price of a wristwatch was higher or lower than $10,000 in the high anchor condition and $2 in the low anchor condition. A group of participants (N = 26) who participated in a pretest, and only provided absolute estimates related to a number of targets, spontaneously thought the average price of a wristwatch was $79.03 (SD = 40.8, MIN = 15, MAX = 150). Based on this information, I specifically chose anchor values falling outside the range of values provided by this pretest group to minimize variability in the interpretation of the numerical values as “high” or “low.” That is, the choice to again present implausible anchor values was made to increase the probability that the concept “expensive” or “inexpensive” would be activated, resulting in the subsequent activation of the associated concepts of “heavy” or “light.” Immediately after responding to the comparative question, participants were asked to estimate the weight of the textbook (in lbs) they were currently using in their introduction to psychology course, which constituted the main dependent variable. Following this question, participants responded to 25 filler questions, to make the cover story of a questionnaire pretest more convincing. Results and Discussion As Figure 1 illustrates, the anchoring effect clearly depended on the type of association participants were primed with, and on the anchor values presented during the comparative question. Specifically, in the “assimilation” condition

Textbook Weight (in lbs.)

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10 9 8 7 6 5 4 3 2 1 0

High Anchor Low Anchor

Assimilation

Contrast

Association-Type

FIGURE 1. Textbook weight (in lbs.) by type of rule (contrast vs. assimilation) and anchor condition (high vs. low) (Study 3).

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(“expensive = heavy,” “inexpensive = light”), participants gave higher estimates of the weight (in lbs) of their current introduction to psychology textbook (M = 8.7, SE = 1.274), after considering a high anchor ($10,000) of the price of a wristwatch, compared to participants who considered a low ($2) anchor (M = 5.19, SE = 1.6). This pattern of results was reversed in the “contrast” rule condition. Specifically, when participants were primed with an “expensive = light” (“inexpensive = heavy”) association, estimates of the textbook weight were lower in the high anchor condition (M = 2.94, SE = 1.531), compared to the low anchor condition (M = 5.77, SE = 1.274). This pattern of results produced a significant interaction effect in a 2 (high vs. low anchor) × 2 (assimilation vs. contrast association) analysis of variance (ANOVA), F(1, 39) = 4.932, p < .05, Cohen’s d = .86. Neither the main effect of anchor nor the main effect of rule-prime reached conventional levels of significance. The magnitude of the interaction effect is relatively large and in line with effect sizes obtained in previous anchoring studies (Wilson et al., 1996). These results demonstrate that the subjective interpretation of the anchor value itself along a specific semantic dimension, activated via rule-like associations, can yield contrast or assimilation effects in anchoring. It is worth noting that there may exist a virtually limitless number of subjective associations, linking together judgmental dimensions such as “expensive” and “heavy” or “expensive” and “light”, depending on a person’s subjective experience. Thus, the concept “expensive” might associatively influence a judgment of weight if a person thinks of an expensive cell phone (expensive cell phones tend to be lighter and smaller than inexpensive ones). This association could yield contrast effects in a variety of weight related estimates, irrespective of specific targets. Similarly, the concept “expensive” might associatively prime the concept “heavy” if the person thinks (situationally) of diamond rings. Intriguingly, chronic associations may develop between judgmental dimensions frequently encountered by persons of different occupations, ages, backgrounds, and so forth, producing either contrast or assimilation effects on estimation tasks, depending on the exact concept that saw activation prior to the estimation. The above results also show that anchoring effects may be obtained across dimensions, if people perceive a connection between values on those dimensions. These results provide support for an additional mechanism whereby anchoring effects may be obtained in situations involving incompatible targets and dimensions. That is, on the level of the present quantifier priming analysis, anchoring effects may be obtained when dimensions change between the comparative and absolute questions through subjective associations that may create a relevant link between values on two or more dimensions. Of course, in the absence of such a connection, anchoring effects may fail to obtain if other specific semantic contents fail to apply to a judgment (Strack & Mussweiler, 1997). Finally, it should be noted that a simple numeric priming perspective (Wilson et al., 1996) cannot account for these findings, because it would simply predict assimilation effects

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in both conditions (e.g., higher estimates after considering a high anchor vs. low anchor), irrespective of association priming.

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General Discussion The present article explored the notion that anchoring effects may be obtained as a function of general semantic constructs (quantifiers) associated with anchor values. Specifically, I proposed that vague information about quantity, activated in response to processing an anchor value, can bias numerical estimation tasks in anchoring paradigms. I tested several novel implications of my perspective for understanding anchoring effects. Study 1 demonstrated that the same anchor value, placed in different contexts, can take on different semantic meanings, which can directly bias subsequent estimates. Study 2 was designed to tap more directly into the potential influence of vague quantifiers in the standard anchoring paradigm. Specifically, priming words inconsistent with the magnitude implications of an anchor eliminated the traditional anchoring effect, whereas priming words consistent with the anchor values did not affect the traditional effect. The third study demonstrated that anchoring effects may be obtained across two separate dimensions, when semantic representations of quantities reflecting values on the two dimensions in question are linked in a person’s mind. In combination, these findings suggest that anchoring effects may be flexibly determined by nonspecific semantic guides to judgment that can be spontaneously provided by numbers. Interestingly, numbers may non-consciously prime quantifiers when they were randomly generated, as is often the case in anchoring research, or when they clearly fall outside the range of values plausible for a judgment (e.g., Wegener, Petty, Detweiler-Bedell, & Jarvis, 2001). My perspective, thus, provides an explanation of anchoring that is consistent with the predominant view that the anchoring bias occurs on a non-conscious level (see Wilson et al., 1996) and is difficult to overcome without significant effort and specific instruction (e.g., Mussweiler, Strack, & Pfeiffer, 2000). The Semantic-Numeric Distinction One important theoretical question, raised by the present work, concerns the validity of the semantic-numeric distinction in explaining anchoring effects (see Mussweiler & Strack, 2001b). The current consensus in the literature appears to be that anchoring effects, obtained when the target of the initial comparison is identical to the target of the absolute estimate, represent semantic effects that are mediated by anchor-consistent knowledge about the target (e.g., Strack & Mussweiler, 1997). However, effects obtained when targets (or dimensions) change between the comparative and absolute judgments, or when simply numbers have been primed, have been classified as numeric effects, because target knowledge is generally rendered irrelevant by target or dimension changes

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(Wilson et al., 1996). The present set of studies raise the intriguing possibility that the above distinction may actually involve different types of semantic information, rather than reflecting qualitative differences between semantic and numeric modes of judgment. Specifically, my data are consistent with the notion that effects previously classified as numeric effects may actually be semantic in nature, because they appear to be driven by vague semantic information about quantity. This perspective also sheds light on the relative puzzle of the fragility of the basic anchoring effect, tested in its purest form (i.e. without comparison targets). Why do pure numbers, isolated from any specific context, generally lack robustness in their influence on numerical estimates (Brewer & Chapman, 2002)? The answer may simply be that, unless a given set of numbers spontaneously invoke semantic magnitude representations (see Birnbaum, 1999), they appear largely irrelevant for subsequent judgments and are therefore unlikely to have any impact.

On the Judgmental Impact of Numerical Anchors One of the most common ways in which anchors may become quantifiable, and hence, judgmentally relevant, is through the embedment of anchors in comparison tasks. These tasks typically include specific judgmental dimensions (e.g., height, weight, amount, and so forth) and target categories (e.g., historical gates, nations, people) as judgmental context, allowing for the representation of anchors in terms of a number of vague quantifiers (e.g., “high,” “few,” etc.), depending on their value. In addition to embedding numerical anchors in comparison questions, anchors may become quantifiable through the generation of some internal context that allows for the interpretation of an otherwise de-contextualized numerical value, as demonstrated by Birnbaum (1999) for example. In addition to the quantification mechanisms described above numbers may come to spontaneously serve as anchors, and invoke notions related to quantities, when they become associated with a target category of a given estimate. For example, Becker and Stephan (1994) showed that accessible, but initially meaningless, numbers can spontaneously come to serve as anchors for a judgment when they are later connected to a target of an estimate. However, spontaneous anchoring on random numbers only appears to occur when the numbers fall within a range of values appropriate for the target dimension in question (e.g., points on the German Stock exchange, in Becker & Stephan’s work). One interpretation of Becker and Stephan’s (1994) findings in terms of the current analysis is that the target dimension encountered in a question may provide a context for the interpretation of a random, accessible numerical value, which may spontaneously (backward) prime quantifiers relevant to the judgment at hand. Perhaps ironically, the quantifiers that may be activated by the target in question, can subsequently bias estimates pertaining to that same target. The important point here is that, according to my hypothesis, the judgmentally critical information need not consist

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of target-specific knowledge (Strack & Mussweiler, 1997) and can actually be quite vague. The question, thus, arises as to the nature of the impact of anchor-based quantifiers within the anchoring paradigm. I propose that, upon activation, a given quantifier, such as “high,” “expensive,” “much,” or “many,” may influence the subjective expected value of an estimate, relative to people’s baseline estimates of the same target. For example, in connection with a specific target scale, such as the age of a person, an activated quantifier such as “high,” “much,” or “old” may shift the baseline subjective expected value of a target’s age toward the upper bound of the distribution of values a person finds subjectively plausible. Conversely, the priming of quantifiers in response to low anchors, such as “few,” “little,” or “young” may shift the baseline subjective expected value toward the lower bound of the distribution. Numerical estimates in response to anchoring tasks, thus, represent translations of semantic constructs into subjectively predicted quantities (see also Wallsten et al., 1986; Wyer, 1973), appropriate for the target category of the absolute question. In contrast to these notions, simple numeric priming would predict absolute estimates much more similar in range to the actual anchor values considered during the comparative judgment, with little room for variability across different target categories. Clearly, however, such variability has been observed numerous times in studies that varied the target of the comparative and absolute judgments. For example, in addition to Wilson and colleagues’ (1996) demonstrations, participants in one study were apparently influenced in their estimate of the price of a bus by a previously considered comparison question involving the length of an airport runway (Wong & Kwong, 2000). In sum, it appears that the proposed mechanism of quantifier priming and the associated translation of general quantifiers into numerical estimates provide a viable explanation of judgmental anchoring effects. Limitations and Future Directions The present research is limited by its reliance on research participants residing in a western, developed nation. The results obtained in the present set of studies may vary across cultures, particularly among East Asian participants (e.g., Miyamoto & Kitayama, 2002). The present work also does not address several additional lines of inquiry concerning vague quantifiers in numerical estimates. The present perspective, although capable of explaining traditional anchoring effects, probably is limited to situations where participants do not engage in much additional thought about the target. This mechanism is not incompatible with the possibility that in other situations, anchors may prime quantifiers which then serve as guides to the activation of target-specific knowledge, which can then serve as the primary basis for subsequent estimates, as was argued by Strack and Mussweiler (1997).

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What factors may distinguish between these levels of processing? Similarly to the arguments involving elaboration likelihood in the persuasion literature (e.g., Petty & Wegener, 1999), people low in motivation or resources may simply base their estimates on vague quantifiers, whereas persons high in motivation and cognitive resources may engage in more elaborate knowledge activation through hypothesis testing. Similarly, as expertise about a given target increases, persons may be more willing and able to recruit information about the target from memory, which may be biased by the consideration of an anchor value. Consistent with this view are findings that have demonstrated anchoring effects among expert appraisers of real-estate (Northcraft & Neale, 1987), who often have to justify their decisions and are likely to think extensively about a given target. However, in the absence of any significant amount of knowledge about a given target, or among persons low in the need for cognition (Cacioppo & Petty, 1982), anchoring effects may merely obtain as a function of nonspecific quantifiers. These and similar questions could be fruitfully explored in future studies. AUTHOR NOTE David Sleeth-Keppler is affiliated with the School of Business, Humboldt State University.

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Received November 22, 2011 Accepted December 6, 2012

Taking the high (or low) road: a quantifier priming perspective on basic anchoring effects.

Current explanations of basic anchoring effects, defined as the influence of an arbitrary number standard on an uncertain judgment, confound numerical...
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