First Impressions Matter: a Model of Confirmatory Bias

Psychological research indicates that people have a cognitive bias that leads them to misinterpret new information as supporting previously held hypotheses. We model such confirmatory bias in a symmetric model in which exactly one of two hypotheses is true. We show that the confirmatory bias induces overconfidence: Given any probabilistic assessment by an agent that one of the hypotheses is probably true, the appropriate beliefs should deem it less likely to be true. When the agent believes relatively weakly in a hypothesis after receiving extensive information, the hypothesis he believes in may be more likely to be wrong than right. If the confirmatory bias is strong enough, with positive probability the agent may eventually come to believe with near certainty in a false hypothesis even after receiving an infinite amount of information.