In response to the replication crisis in science, a group of prominent scholars has proposed redefining statistical significance by reducing the p-value significance threshold from 0.05 to 0.005. Rather than solving the replication problem, I show that lowering the significance threshold can increase the rate of false positives by creating a negative selection effect. Thus, redefining statistical significance may not be a silver bullet for solving the replication crisis.
Social learning and rational disagreement have been studied in environments in which agents are either homogeneous or the distribution of types is known. We study social learning under unobserved heterogeneity, where the distribution of types is unknown and is itself the subject of learning. This dual learning process unlocks a number of new results. Rational agents display confirmation bias. Learning is local: individuals place greater weight on opinions closer to their own and rationally discount more divergent views. Not only is there asymptotic disagreement, but social learning can polarize beliefs. Dual learning also provides a basis for social identification and group formation. We explore applications to political opinion formation, extremist behavior, and choice of news media.
Typically, public discussions of questions of social import exhibit two important properties: (1) they are inﬂuenced by conformity bias, and (2) the inﬂuence of conformity is expressed via social networks. We examine how social learning on net-works proceeds under the inﬂuence of conformity bias. In our model, heterogeneous agents express public opinions where those expressions are driven by the competing priorities of accuracy and of conformity to one’s peers. Agents learn, by Bayesian conditionalization, from private evidence from nature, and from the public declarations of other agents. Our key ﬁndings are that networks that produce conﬁgurations of social relationships that sustain a diversity of opinions empower honest communication and reliable acquisition of true beliefs, and that the networks that do this best turn out to be those which are both less centralized and less connected.
In this paper, I argue that people value playing a role in achieving outcomes they deem to have normative value. The achievement of a positive outcome (electing one’s preferred candidate in an election, helping those in need, etc.) operates as a club good, being consumed in accordance to the degree that one “plays a role” in its achievement. Applications suggest that large and small donors respond differently to government contributions to charity; one’s individual propensity to vote is non-monotonic in the proportion of the population supporting the same candidate as one’s self; and successful social movements experience a sudden burst in participation that is followed by a period of gradual decline.