Blume and Easley (1992) show that if agents' have the same savings rule, those who maximize the expected logarithm of next period's outcomes will eventually hold all wealth (i.e. are ‘most prosperous’). However, if no agent adopts this rule then the most prosperous are not necessarily those who make the most accurate predictions. Thus, agents who make inaccurate predictions need not be driven out of the market. In this paper, it is shown that, among agents who have the same intertemporal discount factor (and who choose savings endogenously), the most prosperous are those who make accurate predictions. Hence, convergence to rational expectations obtains because agents who make inaccurate predictions are driven out of the market.