Non-monotone social learning

We revisit the canonical binary-state model of social learning to investigate the possibility of non-monotone learning: ceteris paribus, with some predecessor(s) switching to actions that reveal greater confidence in one state of the world, agents nevertheless become more confident in the other. A necessary and sufficient condition for non-monotone learning is provided in an illustrative setting where agents are either uninformed or partially informed by binary private signals. In a general setting with continuous private signals, we obtain a sufficient condition for non-monotone learning that does not rely on the shape of the underlying information structures apart from a couple of simple boundary requirements. As a result, a social learning process that completes eventually can be well approximated in a way such that non-monotone learning and anti-imitation are bound to happen.