How does the process of information transmission affect the cultural or linguistic products that emerge? This question is often studied experimentally and computationally via iterated learning: a procedure in which participants learn from previous participants in a chain. Iterated learning is a powerful tool because, when all participants share the same priors, the stationary distributions of the iterated learning chains reveal those priors. In many situations, however, it is unreasonable to assume that all participants share the same prior beliefs. We present four simulation studies and one experiment demonstrating that when the population of learners is heterogeneous, the behavior of an iterated learning chain can be unpredictable, and is often systematically distorted by the learners with the most extreme biases. This results in group-level outcomes that reflect neither the behavior of any individuals within the population nor the overall population average. We discuss implications for the use of iterated learning as a methodological tool as well as for the processes that might have shaped cultural and linguistic evolution in the real world.