Partition dependence in development: Are children's decisions shaped by the arbitrary grouping of options?

The grouping of options into arbitrary categories influences adults' decisions about allocating choices or resources among those options; this is called "partition dependence." Partition dependence has been demonstrated in a wide range of contexts in adults and is often presented as a technique for designing choice architectures that nudge people towards better decisions. Whether children also make partition dependent decisions is unknown, as are potential patterns of developmental change. In this experiment ( N = 159), we examined whether children exhibit partition dependence using a novel resource allocation task. This novel task, distributing food tokens to zoo animals, did elicit partition dependence in our developmental sample. Both older children (ages 7-10 years) and younger children (ages 3-6 years) made partition dependent allocations, and younger children exhibited a larger partition dependence effect than did older children. This work provides the first evidence that children's decisions, like adults', are influenced by the arbitrary grouping of the options, and suggests that younger children may be more susceptible to this influence, at least in the context explored here.

Partition dependence in consumer choice: Perceptual groupings do not reliably shape decisions.

The partitioning of options into arbitrary categories has been shown to influence decisions about allocating choices or resources among those options; this phenomenon is called partition dependence. While we do not call into question the validity of the partition dependence phenomenon in the present work, we do examine the robustness of one of the experimental paradigms reported by Fox, Ratner, and Lieb (Journal of Experimental Psychology: General, 134, 538-551, 2005, Study 4). In three experiments (N = 300) conducted here, participants chose from a menu of perceptually partitioned options (varieties of candy distributed across bowls). We found no clear evidence of partition dependent choice in children (Experiment 1) and no evidence at all of partition dependence in adults' choices (Experiments 1-3). This was true even when methods were closely matched to those of Fox et al.'s Study 4 (Experiment 3). We conclude that the candy-bowl choice task does not reliably elicit partition dependence and propose possible explanations for the discrepancy between these findings and prior reports. Future work will explore the conditions under which partition dependence in consumer choice does reliably arise.

Suboptimality in perceptual decision making and beyond.

We concur with the authors' overall approach and suggest that their analysis should be taken even further. First, the same points apply to areas beyond perceptual decision making. Second, the same points apply beyond issues of optimality versus suboptimality.

Developmental change in numerical estimation.

Mental representations of numerical magnitude are commonly thought to undergo discontinuous change over development in the form of a "representational shift." This idea stems from an apparent categorical shift from logarithmic to linear patterns of numerical estimation on tasks that involve translating between numerical magnitudes and spatial positions (such as number-line estimation). However, the observed patterns of performance are broadly consistent with a fundamentally different view, based on psychophysical modeling of proportion estimation, that explains the data without appealing to discontinuous change in mental representations of numerical magnitude. The present study assessed these 2 theories' abilities to account for the development of numerical estimation in 5- through 10-year-olds. The proportional account explained estimation patterns better than the logarithmic-to-linear-shift account for all age groups, at both group and individual levels. These findings contribute to our understanding of the nature and development of the mental representation of number and have more general implications for theories of cognitive developmental change.

Active (not passive) spatial imagery primes temporal judgements.

Previous research has shown that primes that induce particular spatial perspectives can influence temporal judgements. However, most studies have used priming stimuli that involve both spatial and motor language and imagery. Here we ask whether the motor content of these stimuli plays an important role in their ability to serve as effective primes. A total of 198 adult participants made temporal judgements after exposure to spatial primes involving varying levels of imagined effort. Spatial primes involving imagined motor actions, but not those involving equivalent passive motions through space, successfully primed decisions about time. This suggests that motor content, rather than spatial content alone, contributes to the priming effects that arise when people make temporal judgements after exposure to particular spatial perspectives.

Adults' number-line estimation strategies: evidence from eye movements.

Although the development of number-line estimation ability is well documented, little is known of the processes underlying successful estimators' mappings of numerical information onto spatial representations during these tasks. We tracked adults' eye movements during a number-line estimation task to investigate the processes underlying number-to-space translation, with three main results. First, eye movements were strongly related to the target number's location, and early processing measures directly predicted later estimation performance. Second, fixations and estimates were influenced by the size of the first number presented, indicating that adults calibrate their estimates online. Third, adults' number-line estimates demonstrated patterns of error consistent with the predictions of psychophysical models of proportion estimation, and eye movement data predicted the specific error patterns we observed. These results support proportion-based accounts of number-line estimation and suggest that adults' translation of numerical information into spatial representations is a rapid, online process.

The development of numerical estimation: evidence against a representational shift.

How do our mental representations of number change over development? The dominant view holds that children (and adults) possess multiple representations of number, and that age and experience lead to a shift from greater reliance upon logarithmically organized number representations to greater reliance upon more accurate, linear representations. Here we present a new theoretically motivated and empirically supported account of the development of numerical estimation, based on the idea that number-line estimation tasks entail judgments of proportion. We extend existing models of perceptual proportion judgment to the case of abstract numerical magnitude. Two experiments provide support for these models; three likely sources of developmental change in children's estimation performance are identified and discussed. This work demonstrates that proportion-judgment models provide a unified account of estimation patterns that have previously been explained in terms of a developmental shift from logarithmic to linear representations of number.

Judgments of discrete and continuous quantity: an illusory Stroop effect.

Evidence from human cognitive neuroscience, animal neurophysiology, and behavioral research demonstrates that human adults, infants, and children share a common nonverbal quantity processing system with nonhuman animals. This system appears to represent both discrete and continuous quantity, but the proper characterization of the relationship between judgments of discrete and continuous quantity remains controversial. Some researchers have suggested that both continuous and discrete quantity may be automatically extracted from a scene and represented internally, and that competition between these representations leads to Stroop interference. Here, four experiments provide evidence for a different explanation of adults' performance on the types of tasks that have been said to demonstrate Stroop interference between representations of discrete and continuous quantity. Our well-established tendency to underestimate individual two-dimensional areas can provide an alternative explanation (introduced here as the "illusory-Stroop" hypothesis). Though these experiments were constructed like Stroop tasks, and they produce patterns of performance that initially appear consistent with Stroop interference, Stroop interference effects are not involved. Implications for models of the construction of cumulative area representations and for theories of discrete and continuous quantity processing in large sets are discussed.