The Hazards and Benefits of Condescension in Social Learning

TL;DR

The paper studies a misspecified sequential social-learning model in which agents underweight others' information (condescension) while correctly interpreting their own signals. It shows that when the tail-exponent difference ${\tilde{\alpha}-\alpha}$ is strictly between 0 and 1, asymptotic and efficient learning hold, meaning the expected number of incorrect actions is finite and correct consensus is eventually reached; anti-condensation or overly strong condescension destroy learning, while well-known well-specified results are overturned by mild misspecification. The authors derive a continuous-time approximation for the public log-likelihood and establish precise thresholds via tail regularity, showing that mild condescension accelerates information aggregation without sacrificing long-run accuracy. These results reveal a potential welfare role for bounded misperceptions in social learning and clarify how learning speed depends on the informativeness of private versus public signals.

Abstract

In a misspecified social learning setting, agents are condescending if they perceive their peers as having private information that is of lower quality than it is in reality. Applying this to a standard sequential model, we show that outcomes improve when agents are mildly condescending. In contrast, too much condescension leads to worse outcomes, as does anti-condescension.

Theorems & Definitions (42)

• Definition 1
• Theorem 1
• Proposition 1
• Proposition 2
• Lemma 1: Stationarity
• Lemma 2: Overturning principle
• proof
• Lemma 3
• Lemma 4
• proof