Numbers, not value, motivate cooperation in humans and orangutans

Cooperation among competitors-whether sharing the burden of wind resistance in the Tour de France, forming price-fixing cartels in economic markets, or adhering to arms-control agreements in international treaties-seldom spreads in proportion to the potential benefits. To gain insight into the minds of uncooperative agents, economists and social psychologists have used the prisoner's dilemma task to examine factors leading to cooperation among competitors. Two types of factors have emerged in these studies: the relative rewards of defecting versus cooperating and breakdowns in trust, forgiveness and communication. The generalizability of economic and social psychological factors, however, relies on the assumption that agents' comparisons of gains and losses (whether for themselves, others, or both) preserves ratio information over arbitrary units, such as dollars and cents, and real rewards, such as food. This assumption is inconsistent with psychophysical studies on how the brain represents quantitative information, which suggests that mental magnitudes increase logarithmically with actual value. Thus, discrimination of two numerical magnitudes improves as the numerical distance between them increases and decreases as the magnitudes increase. Here we show an important consequence of this representational system for economic decision making: in the prisoner's dilemma game, purely nominal increases in the numerical magnitude of payoffs (such as, converting dollar values to cents or whole grapes into grape-parts) has a large effect on cooperative behaviour. Moreover, a logarithmic scaling of the ratio of rewards for cooperation versus defection predicted 97% of variability in observed cooperation, whereas the objective ratio predicted 0% of variability. By linking the brain's system of representing the magnitude of rewards to motivations for cooperative behaviour, these findings suggest that the nature of numerical representations may also account for the subjective value function described by Bernoulli, in which the apparent value of monetary incentives increases logarithmically with actual value

The nature of the association between number line and mathematical performance: An international twin study

Background: The number line task assesses the ability to estimatenumerical magnitudes. People vary greatly in this abilityand this variability has been previously associated with mathematical skills. However, the sources of individual differences in number line estimation and its association with mathematics are not fully understood. Aims: This large scale genetically sensitive studyuses a twin design to estimate the magnitude of the effects of genes and environments on: (1) individualvariation in number line estimation and (2) the co-variation of number line estimation with mathematics. Samples: We used over3,0008-16 years-old twins from US, Canada,UK, and Russia, and a sample of 1,456 8-18 years-old singleton Russian students. Methods: Twins were assessed on: (1)estimation of numerical magnitudes using a numberline task and (2) two mathematics components: fluency and problemsolving. Results: Results suggest that environments largelydrive individual differences in numberline estimation.Both genes and environments contribute to different extents to the number line estimationandmathematics correlation, depending on the sample and mathematics component. Conclusions: Taken together, the results suggest that in more heterogeneous school settings, environments may be more important in driving variation in number line estimation and its associationwith mathematics, whereas in more homogeneous school settings, genetic effects drive the covariation between number line estimationand mathematics. These results are discussed in light of development and educational settings

Children's and Adults' Models for Predicting Teleological Action: The Development of a Biology-Based Model

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66309/1/1467-8624.00353.pd

Even Early Representations of Numerical Magnitude are Spatially Organized: Evidence for a Directional Magnitude Bias in Pre-Reading Preschoolers

Previous work has suggested that an important tool of adult numeric competence is a “mental number line ” that codes increasing numeric magnitudes spatially and with a directional bias. Partly because the direction of this bias (left-to-right versus right-to-left) is culture-specific, it has been assumed that a directionally-biased mental number line is a late development. Our results, in contrast, suggest that nearly half of all preschoolers possess a directional magnitude bias and that those who possess this bias demonstrate competence in representing large numbers, a competence that is otherwise lacking in same-aged peers. Further, this directional bias does not appear to be related to pre-reading abilities, but instead seems to build on already existing preferences in counting direction

Development of Quantitative Thinking

<p>For understanding development of quantitative thinking, the distinction between nonsymbolic and symbolic thinking is fundamental. Nonsymbolic quantitative thinking is present in early infancy, culturally universal, and similar across species. These similarities include the ability to represent and compare numerosities, the representations being noisy and increasing logarithmically with actual quantity, and the neural correlates of number representation being distributed in homologous regions of frontoparietal cortex. Symbolic quantitative thinking, in contrast, emerged recently in human history, differs dramatically across cultural groups, and develops over many years. As young children gain experience with symbols in a given numeric range and associate them with nonverbal quantities in that range, they initially map them to a logarithmically-compressed mental number line and later to a linear form. This logarithmic-to-linear shift expands children's quantitative skills profoundly, including their ability to estimate positions of numbers on number lines, to estimate measurements of continuous and discrete quantities, to categorize numbers by size, to remember numbers, and to estimate and learn answers to arithmetic problems. Thus, while nonsymbolic quantitative thinking is important and foundational for symbolic numerical capabilities, the capacity to represent symbolic quantities offers crucial cognitive advantages.</p