In a complete markets economy with heterogeneous consumers whether consumers vanish or survive is determined entirely by discount factors and beliefs. All else equal, the (complete) market selects for consumers who use Bayesian learning with truth in support of their prior and selects among Bayesians according to the size of their parameter space. Even though some consumers vanish the resulting complete markets allocations are Pareto optimal. This suggests that for an economy in which consumers have heterogeneous beliefs, Pareto optimality is an inappropriate welfare criterion as those who are wrong are making decisions that they would regard as incorrect if only they had correct beliefs. We propose a new welfare criterion that allows us to rank alternative market structures in the presence of belief heterogeneity. We describe circumstances under which various forms of incomplete markets are desirable according to our welfare criterion. Based on joint work with Lawrence Blume, Timothy Cogley, Thomas Sargent and Viktor Tsyrennikov.