Can Agents Add and Subtract When Forming Beliefs?

Bayes' Theorem has an implicit, fundamental rule of how subjects should incorporate informationally equivalent signals of opposite direction: two opposite-directional signals should cancel out such that prior beliefs remain constant. In this study, we test whether agents always follow this simple counting heuristic. We find that this is not the case. Whenever a sequence of signals that go in the same direction is interrupted by a signal of opposite direction, agents violate the simple counting heuristic and strongly overreact to the signal of opposite direction. In contrast to that, subjects correctly follow the counting heuristic whenever opposite-directional signals alternate