  Online discussion threads are important means for individual decision-making
and for aggregating collective judgments, e.g. the `wisdom of crowds'.
Empirical investigations of the wisdom of crowds are currently ambivalent about
the role played by social information. While some findings suggest that social
information undermines crowd accuracy due to correlated judgment errors, others
show that accuracy improves. We investigate experimentally the accuracy of
threads in which participants make magnitude estimates of varying difficulty
while seeing a varying number of previous estimates. We demonstrate that, for
difficult tasks, seeing preceding estimates aids the wisdom of crowds. If,
however, participants only see extreme estimates, wisdom quickly turns into
folly. Using a Gaussian Mixture Model, we assign a persuadability score to each
participant and show that persuadability increases with task difficulty and
with the amount of social information provided. In filtered threads, we see an
increasing gap between highly persuadable participants and skeptics.
