Evolution of transmission bias in cultural inheritance is investigated using simple models of cultural selection. Conventional models of cultural transmission describe cultural changes by incorporating transmission bias and non-vertical pathways into the ordinary population genetic framework. The methodology has been successful in understanding cultural changes in terms of natural selection, but it is difficult to see from the theoretical framework how biased transmission in favor of maladaptive traits might have evolved. To show that ordinary cultural processes lead at times to the evolution of a preference that favors a deleterious cultural variant, this study presents an alternative model of cultural transmission, where cultural elements are transmitted in a manner more like infections in epidemiological transmission. An ordinary equilibrium analysis indicates that, under certain conditions, runaway dynamics emerges and the coevolution of a maladaptive cultural variant and an associated preference in favor of the maladaptive variant is observed. If the preference of an individual does not change during its ontogeny (e.g., if it is transmitted genetically), however, then cultural selection alone does not produce such runaway dynamics, and only those preferences that favor adaptive variants should eventually evolve. Since cultural processes may at times result in a reduction in the fitness of individuals, simplistic adaptive interpretations of culture are unconvincing without detailed specification of the cultural processes involved. Moreover, cultural runaway of this kind may help to explain the existence of traits that are apparently maladaptive at the individual level but may be advantageous for the group. Inferences are also made regarding the observed differences between human and non-human social information transfer.