  Collective intelligence is believed to underly the remarkable success of
human society. The formation of accurate shared beliefs is one of the key
components of human collective intelligence. How are accurate shared beliefs
formed in groups of fallible individuals? Answering this question requires a
multiscale analysis. We must understand both the individual decision mechanisms
people use, and the properties and dynamics of those mechanisms in the
aggregate. As of yet, mathematical tools for such an approach have been
lacking. To address this gap, we introduce a new analytical framework: We
propose that groups arrive at accurate shared beliefs via distributed Bayesian
inference. Distributed inference occurs through information processing at the
individual level, and yields rational belief formation at the group level. We
instantiate this framework in a new model of human social decision-making,
which we validate using a dataset we collected of over 50,000 users of an
online social trading platform where investors mimic each others' trades using
real money in foreign exchange and other asset markets. We find that in this
setting people use a decision mechanism in which popularity is treated as a
prior distribution for which decisions are best to make. This mechanism is
boundedly rational at the individual level, but we prove that in the aggregate
implements a type of approximate "Thompson sampling"---a well-known and highly
effective single-agent Bayesian machine learning algorithm for sequential
decision-making. The perspective of distributed Bayesian inference therefore
reveals how collective rationality emerges from the boundedly rational decision
mechanisms people use.
