Sampling Assumptions in Inductive Generalization
Article first published online: 5 DEC 2011
Copyright © 2011 Cognitive Science Society, Inc.
Volume 36, Issue 2, pages 187–223, March 2012
How to Cite
Navarro, D. J., Dry, M. J. and Lee, M. D. (2012), Sampling Assumptions in Inductive Generalization. Cognitive Science, 36: 187–223. doi: 10.1111/j.1551-6709.2011.01212.x
- Issue published online: 5 MAR 2012
- Article first published online: 5 DEC 2011
- Received 9 February 2010; received in revised form 3 February 2011; accepted 19 April 2011
- Inductive inference;
- Bayesian modeling
Inductive generalization, where people go beyond the data provided, is a basic cognitive capability, and it underpins theoretical accounts of learning, categorization, and decision making. To complete the inductive leap needed for generalization, people must make a key ‘‘sampling’’ assumption about how the available data were generated. Previous models have considered two extreme possibilities, known as strong and weak sampling. In strong sampling, data are assumed to have been deliberately generated as positive examples of a concept, whereas in weak sampling, data are assumed to have been generated without any restrictions. We develop a more general account of sampling that allows for an intermediate mixture of these two extremes, and we test its usefulness. In two experiments, we show that most people complete simple one-dimensional generalization tasks in a way that is consistent with their believing in some mixture of strong and weak sampling, but that there are large individual differences in the relative emphasis different people give to each type of sampling. We also show experimentally that the relative emphasis of the mixture is influenced by the structure of the available information. We discuss the psychological meaning of mixing strong and weak sampling, and possible extensions of our modeling approach to richer problems of inductive generalization.