  We propose an agent-based model of collective opinion formation to study the
wisdom of crowds under social influence. The opinion of an agent is a
continuous positive value, denoting its subjective answer to a factual
question. The wisdom of crowds states that the average of all opinions is close
to the truth, i.e. the correct answer. But if agents have the chance to adjust
their opinion in response to the opinions of others, this effect can be
destroyed. Our model investigates this scenario by evaluating two competing
effects: (i) agents tend to keep their own opinion (individual conviction
$\beta$), (ii) they tend to adjust their opinion if they have information about
the opinions of others (social influence $\alpha$). For the latter, two
different regimes (full information vs. aggregated information) are compared.
Our simulations show that social influence only in rare cases enhances the
wisdom of crowds. Most often, we find that agents converge to a collective
opinion that is even farther away from the true answer. So, under social
influence the wisdom of crowds can be systematically wrong.
