We introduce a model of preference diffusion in which agents in a social network update their preferences based on those of their influencers in the network, and we study the dynamics of this model. Preferences are modelled as ordinal rankings over a finite set of alternatives. At each time step, some of the agents update the relative ordering of two alternatives adjacent in their current ranking with the majority view of their influencers. We consider both a synchronous and an asynchronous variant of this model. Our results show how the graphtheoretic structure of the social network and the structure of the agents' preferences affect the termination of the diffusion process and the properties of the preference profile at the time of termination.