The problem just outlined obtains a mathematically more sophisticated form in the problem that Bayesians expect to be well-calibrated.  This problem, as formulated in Dawid (1982), concerns a Bayesian forecaster, e.g., a weatherman who determines a daily probability for precipitation in the next day.  It is then shown that such a weatherman believes of himself that in the long run he will converge onto the correct probability with probability 1. Yet it seems reasonable to suppose that the weatherman realizes something could potentially be wrong with his meteorological model, and so sets his probability for correct prediction below 1. The weatherman is thus led to incoherent beliefs. It seems that Bayesian statistical analysis places unrealistic demands, even on an ideal agent.