Many human interactions involve pieces of information being passed from one person to another, raising the question of how this process of information transmission is affected by the cognitive capacities of the agents involved. Bartlett (1932) explored the influence of memory biases on the "serial reproduction" of information, in which one person's reconstruction of a stimulus from memory becomes the stimulus seen by the next person. These experiments were done using relatively uncontrolled stimuli, but suggested that serial reproduction could transform information in a way that reflected the biases inherent in memory. We formally analyze serial reproduction using a Bayesian model of reconstruction from memory, giving a general result characterizing the effect of memory biases on information transmission. We then test the predictions of this account in four experiments using simple one-dimensional stimuli. Our results provide theoretical and empirical justification for the idea that serial reproduction reflects memory biases. (Contains 8 figures.)