Not Exactly Fair: Investigating the Relationship Between Symbolic Number Knowledge and Equitable Resource Distribution in Children

• In Event: How Much is Fair: Integrating the Development of Numerical Cognition with Children's Understanding of Fairness

Abstract

When evaluating the fairness of resource distribution, one salient diagnostic is numerical equality, which can be established by placing the distributions in one-to-one correspondence. One-to-one is used to establish equality in situations involving fairness cross-culturally, and some of the earliest human artifacts record one-to-one tallies for trading (Schmandt-Besserat, 1978). One possible explanation for the early emergence of one-to-one in the anthropological record is that it does not appear to require symbolic number. However, there is evidence that individuals without symbolic number systems do not deploy one-to-one to establish equality (Gordon, 2004), raising the question of why this might be. Here, we ask whether symbolic number could be a prerequisite to understanding the relationship between numerical equality and one-to-one, and whether fairness concerns might encourage deployment of one-to-one? We address this in children acquiring symbolic number. While recent work finds that children who have acquired symbolic number are more likely to make fair distributions numerically equal (Chernyak et al., 2016; Jara-Ettinger et al., 2016), several open questions remain: Do children care about exact, or approximate, equality? If children prefer exact equality, do fairness concerns precede symbolic number, prompting the development and deployment of methods which ensure exact equality (such as counting and one-to-one)? Or does symbolic number come first, unlocking both the relationship between one-to-one and equality and an ability to establish exactly equal distributions?

We tested 3- to 5-year-olds (N = 230, Mage = 4.03 years), with 122 “full counters” (i.e., children who understand how counting can be used to generate sets of specific cardinalities), and 108 “partial counters” (i.e., children who know only the meanings of a few number words). We adapted a “set-matching” paradigm used with non-numerate populations (Gordon, 2004); children received a blue board, 15 plastic fish, and completed either: (1) a “matching” game, where children made their “pond” look like the experimenter’s; or (2) a “sharing” game, where children helped the experimenter fairly distribute fish between two puppets. In both conditions, the experimenter generated sets above the child’s, allowing the use of one-to-one.

In both conditions, we found that full counters were significantly more likely to generate numerically equal sets than partial counters even when controlling for age (Figure 1; ps < .001). While full counters were more accurate than partial counters (M=29%), their performance was below ceiling (M=57%). We found no effect of framing the task as a sharing game for full counters (p = .17).

These results show that children who are otherwise competent counters do not yet understand the logical basis of numerical equality, suggesting that acquisition of symbolic number on its own may not be sufficient to guarantee such knowledge. Although multiple sources of evidence suggest that children care about numerical equality in establishing fair resource distributions, our findings additionally suggest that fairness concerns do not motivate children to use one-to-one to guarantee exact equality. Instead, we find that children’s ability to establish exactly equal distributions is driven primarily by their symbolic number knowledge, rather than a concern for fairness.

Authors

• Rose Schneider, University of California - San Diego
  Presenting Author

• Roman Feiman, Brown University
  Non-Presenting Author

• David A Barner, University of California - San Diego
  Non-Presenting Author