Bartlett (1932) explored the consequences of "serial reproduction" of information, in which one participant's reconstruction of a stimulus from memory becomes the stimulus seen by the next participant. These experiments were done using relatively uncontrolled stimuli such as pictures and stories, but suggested that serial reproduction could reveal the biases inherent in memory. We analyze serial reproduction for simple one-dimensional stimuli assumed to be drawn from a category. When people reconstruct these stimuli, they are influenced by the structure of the category. Huttenlocher, Hedges, and Vevea (2000) proposed that this effect can be modeled as a Bayesian inference, in which people combine the inexact fine-grained stimulus information with category information to achieve higher accuracy. We show that if this is the case, serial reproduction can be modeled as a autoregressive time-series, with a predictable trajectory and stationary distribution. Within the same theoretical framework, we also formally analyze how the convergence rate and stationary distribution of this process are influenced by different category distributions, perceptual noise, and different types of response behavior. Our analyses provide a formal justification for the idea that serial reproduction reflects memory biases. |