Theoretical work on sequential choice and large-scale experiments in online ranking and voting systems has demonstrated that social influence can have a drastic impact on social and technological systems. Yet, the effect of social influence on online rating systems remains understudied and the few existing contributions suggest that online ratings would self-correct given enough users. Here, we propose a new framework for studying the effect of social influence on online ratings. We start from the assumption that people are influenced linearly by the observed average rating, but postulate that their propensity to be influenced varies. When the weight people assign to the observed average depends only on their own latent rating, the resulting system is linear, but the long-term rating may substantially deviate from the true mean rating. When the weight people put on the observed average depends on both their own latent rating and the observed average rating, the resulting system is non-linear, and may support multiple equilibria, suggesting that ratings might be path-dependent and deviations dramatic. Our results highlight potential limitations in crowdsourced information aggregation and can inform the design of more robust online rating systems.