  Human groups can perform extraordinary accurate estimations compared to
individuals by simply using the mean, median or geometric mean of the
individual estimations [Galton 1907, Surowiecki 2005, Page 2008]. However, this
is true only for some tasks and in general these collective estimations show
strong biases. The method fails also when allowing for social interactions,
which makes the collective estimation worse as individuals tend to converge to
the biased result [Lorenz et al. 2011]. Here we show that there is a bright
side of this apparently negative impact of social interactions into collective
intelligence. We found that some individuals resist the social influence and,
when using the median of this subgroup, we can eliminate the bias of the wisdom
of the full crowd. To find this subgroup of individuals more confident in their
private estimations than in the social influence, we model individuals as
estimators that combine private and social information with different relative
weights [Perez-Escudero & de Polavieja 2011, Arganda et al. 2012]. We then
computed the geometric mean for increasingly smaller groups by eliminating
those using in their estimations higher values of the social influence weight.
The trend obtained in this procedure gives unbiased results, in contrast to the
simpler method of computing the median of the complete group. Our results show
that, while a simple operation like the mean, median or geometric mean of a
group may not allow groups to make good estimations, a more complex operation
taking into account individuality in the social dynamics can lead to a better
collective intelligence.
