  We study mathematical models of the collaborative solving of a two-choice
discrimination task. We estimate the difference between the shared performance
for a group of n observers over a single person performance. Our paper is a
theoretical extension of the recent work of Bahrami et al. (2010) from a dyad
(a pair) to a group of n interacting minds. We analyze several models of
communication, decision-making and hierarchical information-aggregation.
  The maximal slope of psychometric function (closely related to the percentage
of right answers vs. easiness of the task) is a convenient parameter
characterizing performance. For every model we investigated, the group
performance turns out to be a product of two numbers: a scaling factor
depending of the group size and an average performance. The scaling factor is a
power function of the group size (with the exponent ranging from 0 to 1),
whereas the average is arithmetic mean, quadratic mean, or maximum of the
individual slopes. Moreover, voting can be almost as efficient as more
elaborate communication models, given the participants have similar individual
performances.
