In such a situation the expected utility theorem states that in- dividuals make (and behave according to) estimates of their accident probabilities; if these estimates are unbiased in the sense that the average accident probability of those who estimate their accident probability to be p actually is p, then the analysis goes through as before. Unbiasedness seems a reasonable assumption (what is a more attractive alternative?). However, not even this low level of correctness of beliefs is required for our conclusions. Suppose, for example, that individuals differ both with respect to their accident probabilities and to their risk aversion, but they all assume that their own accident probabilities are p. If low-risk individuals are less risk-averse on av- erage, then there will not exist a pooling equilibrium; there may exist no equilibrium at all; and if there does exist an equilibrium, it will entail partial insurance for both groups. Figure IV shows that there