When a person has systematically biased beliefs about how an other thinks, understanding how she thinks about the bias in the way the other thinks she think is essential since these two are directly linked. We find that while people fail to engage in sufficient informational perspective taking and naively project their information onto differentially-informed others, they also anticipate that these differentially-informed others mistakenly project their differential information onto them. In particular, we test the hypothesis of Madarasz (2016) that social beliefs arise from a coherent, but fully-egocentric belief hierarchy with a partial probabilistic adjustment to the truth. This idea predicts a tight one-to-one relationship between the partial extent to which the typical person projects onto others, ρ, and the partial extent to which she anticipates, but underestimates the projection of others onto her, ρ-square. We find not only that most people are partially biased and partially anticipate the biases of others, but that the structure of biased beliefs, even at the level of individual heterogeneity, is remarkably consistent with the idea proposed. Furthermore, we find that it is informational differences per se, rather than the way private information is acquired that seems to matter. Applications to organizations and law and economics are discussed.