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. (Science 2010) from a dyad (a pair) to a group of n interacting minds. We analyze a few models of the communication, the decision-making and the 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 the decisive 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 also varies: it is arithmetic mean, quadratic mean, or maximum of the individual slopes. We conclude that even suboptimal forms of communication can be almost as efficient as the optimal one, given the participants have similar individual performances.