Insight into the Law of Large Numbers: A Comparison of Piagetian and Judgement Theory

Abstract

Subjects were tested for their understanding of the law of large numbers in three ways: by means of a Piagetian task involving the distribution of balls between two compartments, by means of written tasks similar to those devised by Kahneman and Tversky (1972), and by means of a task involving comparisons of samples of counters drawn from a larger population. For the sample comparison task, subjects relied heavily on proportional information-ignoring sample size, thereby supporting the conclusions of Kahneman and Tversky (1972). However with regard to the other two tasks an order effect was found: subjects did significantly better with the Kahneman and Tversky tasks if they had first been tested on a Piagetian task. In Experiment II, the order effect was replicated, indicating that subjects may have a narrow insight into the law of large numbers which is not recruited in appropriate contexts unless primed by the task environment.