Comparative judgments with numerical reference points

Holyoak, Keith J.

doi:10.1016/0010-0285(78)90014-2

Cited by 152 publications

(166 citation statements)

References 42 publications

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“…The modulation of precision will maximally impact discriminability between objects with relatively similar magnitudes, in accord with the general finding that congruity effects are larger when the objects being compared are closer in magnitude (Petrusic, 1992). The BARTlet model could easily be extended to account for the impact of explicit reference points (e.g., in a task requiring selection of which of two digits is closer in magnitude to 5; Holyoak, 1978), which can shift the favored attention band to an intermediate region on a continuum.…”

Section: Reference Points In Magnitude Comparisonsmentioning

confidence: 54%

“…Such discriminability effects might arise by a mechanism through which the form of the question modulates magnitude representations in working memory. A number of specific models have been proposed, which share the hypothesis that the polarity of the comparative serves to establish a reference point at or near the corresponding end of the continuum, and that magnitude differences between objects close to the reference point are discriminated more easily than otherwise comparable differences between objects far from the reference point (Holyoak, 1978;Holyoak & Mah, 1982;Jamieson & Petrusic, 1975;Marks, 1972). Holyoak (1978) argued that attending to a reference point at the congruent extreme of a dimension aids in coding the polarity of the question (i.e., distinguishing between ''choose greater'' versus ''choose lesser'' for a specific pair of comparatives).…”

Section: Reference-point Modelsmentioning

confidence: 99%

“…Jamieson and Petrusic (1975) and Holyoak (1978) suggested that observers assess the ratio of distances from each object to the reference point, rather than simply taking the difference. The distance ratio provides good quantitative fits to some data sets, including data from experiments in which an explicit reference point is specified at an intermediate point on the scale (e.g., judging which digit, 2 or 3, is closer to 5; Holyoak, 1978). However, other data sets are less well fit by the quantitative form specified by the distance ratio.…”

Section: Reference-point Modelsmentioning

confidence: 99%

“…To partially compensate, observers focus attention on a favored region, or magnitude band, along the relevant continuum (Luce et al, 1976;Nosofsky, 1983). When making comparisons based on relative concepts, such as ''choose larger'' or ''choose smaller'', attention is guided by a reference point located at or near the end of the continuum cued by the form of the question (Holyoak, 1978;Jamieson & Petrusic, 1975;Marks, 1972). More specifically, selective attention causes the precision of magnitudes in working memory to be greatest (i.e., associated with low variance) for values close to the reference point, decreasing with distance from the reference value (Marks, 1972).…”

Section: Relational Comparisons Without Explicit Relationsmentioning

confidence: 99%

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The discovery and comparison of symbolic magnitudes

Chen

Holyoak

2014

Cognitive Psychology

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a b s t r a c tHumans and other primates are able to make relative magnitude comparisons, both with perceptual stimuli and with symbolic inputs that convey magnitude information. Although numerous models of magnitude comparison have been proposed, the basic question of how symbolic magnitudes (e.g., size or intelligence of animals) are derived and represented in memory has received little attention. We argue that symbolic magnitudes often will not correspond directly to elementary features of individual concepts. Rather, magnitudes may be formed in working memory based on computations over more basic features stored in long-term memory. We present a model of how magnitudes can be acquired and compared based on BARTlet, a representationally simpler version of Bayesian Analogy with Relational Transformations (BART; Lu, Chen, & Holyoak, 2012). BARTlet operates on distributions of magnitude variables created by applying dimension-specific weights (learned with the aid of empirical priors derived from pre-categorical comparisons) to more primitive features of objects. The resulting magnitude distributions, formed and maintained in working memory, are sensitive to contextual influences such as the range of stimuli and polarity of the question. By incorporating psychological reference points that control the precision of magnitudes in working memory and applying the tools of signal detection theory, BARTlet is able to account for a wide range of empirical phenomena involving magnitude comparisons, including the symbolic distance effect and the semantic congruity effect. We discuss the role of reference points in cognitive and social decision-making, and implications for the evolution of relational representations.

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Section: Reference Points In Magnitude Comparisonsmentioning

confidence: 54%

Section: Reference-point Modelsmentioning

confidence: 99%

Section: Reference-point Modelsmentioning

confidence: 99%

Section: Relational Comparisons Without Explicit Relationsmentioning

confidence: 99%

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The discovery and comparison of symbolic magnitudes

Chen

Holyoak

2014

Cognitive Psychology

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“…This phenomenon is called the "semantic congruity effect." Semantic congruity effects have been replicated with a variety of continua, and considerable attention has been given to their explanation (Banks, 1977;Holyoak, 1978;Holyoak & Mah, 1982;Marks, 1972;Moyer & Dumais, 1978;Petrusic & Baranski, 1989;Potts et al, 1978). For example, when comparing digits, subjects are faster at deciding "9 is more than 8" than "2 is more than 1"; however, they are faster at deciding that "1 is less than 2" than "8 is less than 9.…”

Section: Semantic Congruity Effectmentioning

confidence: 99%

A theory of comparative response times and “difference” judgments

Birnbaum

Jou

1990

Cognitive Psychology

112

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In two experiments, subjects performed three tasks: First, they learned associations between names of hypothetical persons and adjectives that described them. Second, they judged "differences" in likeableness between pairs of names. Third, they pressed one of two keys to indicate which person of each pair was more (or less) likeable. Response times showed the traditional distance effect, end effect, and semantic congruity effect. A simple model was developed to describe response times and "difference" ratings, using a single scale of subjective magnitude. The second experiment applied this model to measure the likeableness of persons described by two or four adjectives. This experiment indicated that adjectives do not combine by a parallel-averaging model. Instead, "difference" ratings and comparative response times were consistent with Bimbaum's contigUral-weight theory, in which the weight that a stimulus receives depends on its relation to the other stimuli to be combined. In the case of impression formation, the less favorable information receives greater weight. Results are consistent with the hypothesis that ratings of "differences" and choice response times are mediated by the same scale of subjective value. Q 1990 Academic PESS, IK.The time required to compare two stimuli on a given dimension depends on the subjective difference between the stimuli on that dimension. The farther apart the stimuli are, the smaller the time required to decide which is greater. For example, as Dashiell (1937, p. 57) put it, "it should take a person less time to choose between something he likes very much and something he likes very little than for him to choose between two things he likes equally well." This phenomenon, sometimes called the "distance effect," has been observed in a large number of experiments involving a variety

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Distinguishing the Ratio Bias from Unsystematic Error: Situation and Individual‐difference Effects

Stone

Parker

Townsend

2018

Behavioral Decision Making

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People often perceive the occurrence of events to be less likely when the likelihood of the event is expressed in ratios consisting of smaller numbers versus larger numbers, an effect known as the ratio bias. This work presents a theoretical framework for the conditions that need to be met for the ratio bias to occur. In doing so, we contrast effects on the ratio bias to those on unsystematic error, which have often been confounded in previous research. We find that the ratio bias is weaker (1) when both sets of numbers are relatively large than when both sets of numbers are relatively small; (2) for scenarios involving lottery tickets than for scenarios involving drawing balls from a bin; and (3) when a physical display depicting the numbers is provided to participants. Each of these factors reduced the ratio bias without reducing unsystematic error. Additionally, we show that unsystematic error is lower among people who (1) reason on the basis of proportions rather than on the basis of the numerator and denominator individually; (2) score higher on the rational scale of the Rational-Experiential Inventory; and (3) are of higher numeracy. We use these results to distinguish causes of error generally from those on the ratio bias specifically and discuss the implications for our understanding of when the ratio bias occurs.

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Comparative judgments with numerical reference points

Cited by 152 publications

References 42 publications

The discovery and comparison of symbolic magnitudes

The discovery and comparison of symbolic magnitudes

A theory of comparative response times and “difference” judgments

Distinguishing the Ratio Bias from Unsystematic Error: Situation and Individual‐difference Effects

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