Children’s imitation of causal action sequences is influenced by statistical and pedagogical evidence

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Daphna Buchsbaum^{a, ,} , Alison Gopnik^a, Thomas L. Griffiths^a and Patrick Shafto^b

^a Department of Psychology, University of California, Berkeley, United States
^b Department of Psychology, University of Louisville, United States

Abstract

Children are ubiquitous imitators, but how do they decide which actions to imitate? One possibility is that children rationally combine multiple sources of information about which actions are necessary to cause a particular outcome. For instance, children might learn from contingencies between action sequences and outcomes across repeated demonstrations, and they might also use information about the actor’s knowledge state and pedagogical intentions. We define a Bayesian model that predicts children will decide whether to imitate part or all of an action sequence based on both the pattern of statistical evidence and the demonstrator’s pedagogical stance. To test this prediction, we conducted an experiment in which preschool children watched an experimenter repeatedly perform sequences of varying actions followed by an outcome. Children’s imitation of sequences that produced the outcome increased, in some cases resulting in production of shorter sequences of actions that the children had never seen performed in isolation. A second experiment established that children interpret the same statistical evidence differently when it comes from a knowledgeable teacher versus a naïve demonstrator. In particular, in the pedagogical case children are more likely to “overimitate” by reproducing the entire demonstrated sequence. This behavior is consistent with our model’s predictions, and suggests that children attend to both statistical and pedagogical evidence in deciding which actions to imitate, rather than obligately imitating successful action sequences.

Article Outline

1.

Introduction

2.

Bayesian ideal observer model

2.1. Model details

2.2. A simple modeling example

2.3. Model predictions for children’s inferences

3.

Experiment 1

3.1. Method

3.1.1. Participants

3.1.2. Stimuli

3.1.3. Procedure

3.2. Results and discussion

3.2.1. Effect of statistical evidence on imitation

3.2.2. Effect of differing causal outcomes on imitation

3.2.3. Performance of “Other” actions

4.

Modeling Experiment 1

5.

Learning from knowledgeable pedagogical demonstrators

5.1. Modeling pedagogical learning

5.2. Model predictions

6.

Experiment 2: Effect of combined pedagogical and statistical evidence on imitation

6.1. Method

6.1.1. Participants

6.1.2. Stimuli

6.1.3. Procedure

6.2. Results and discussion

7.

General discussion

Acknowledgements

References

Fig. 1. Part of an example hypothesis space. Graphs (a)–(d) each represent a different hypothesis about which action sequences are causal.

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Fig. 2. Modeling the results of Experiment 1. (a) Children’s performance. (b) Predictions of our Bayesian model.

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Fig. 3. Predictions of our model given assumptions of pedagogical sampling (as in Experiment 2) or random sampling (as in Experiment 1).

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Fig. 4. Modeling the results of Experiment 2, using assumptions of Pedagogical sampling. (a) Children’s performance. (b) Our model’s predictions.

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Table 1. Example demonstrations, and the associated set of potential causal sequences.
Note: Letters represent unique observed actions (e.g. A = Knock, B = Roll, C = Squish) while a + indicates a causal outcome.

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Table 2. Example model results, p = 0.5 and β = 0.
Note: Values are the probability of choosing to perform this action sequence to bring about the effect given the observed data, p(ad), as described in Eq. (4).

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Table 3. Example model results, p = 0.1 and β = 1.4.
Note: Values are the probability of choosing to perform this action sequence to bring about the effect given the observed data, p(ad), as described in Eq. (4).

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Table 4. The demonstration sequences for “ABC”, “BC” and “C” conditions.

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Table 5. Number of children producing each sequence type in each condition of Experiment 1.

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Table 6. Number of children producing each sequence type in Experiment 1, median split by age.

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Table 7. Number of children producing each sequence type in Experiment 2.

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Corresponding author. Address: University of California, Department of Psychology, 3210 Tolman Hall # 1650, Berkeley, CA 94720-1650, United States. Tel.: +1 510 643 2172; fax: +1 510 642 5293.