Flipping and ex post aggregation

We show that Bayesian ex post aggregation is unstable with respect to refinements. Suppose a group of Bayesians use ex post aggregation. Since it is a joint problem, each agent’s problem is captured by the same model, but probabilities and utilities may vary. If they analyze the same situation in more detail, their refined analysis should preserve their preferences among acts. However, ex post aggregation could bring about a preference reversal on the group level. Ex post aggregation thus depends on how much information is used and may keep oscillating (‘‘flipping’’) as one keeps adding more information.