Information-sharing and aggregation models for interacting minds

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 nn observers over a single person performance. Our paper is a theoretical extension of the recent work of Bahrami, Olsen, Latham, Roepstorff, and Frith (2010) from a dyad (a pair) to a group of nn interacting minds. We analyze several models of communication, decision-making and hierarchical information-aggregation. The maximal slope of psychometric function 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.

► How does the group performance depend on the individual ones of its participants?
► How do the ways in which they communicate impact the quality of shared information?
► We list mathematical models of the collaborative solving of a two-choice discrimination task.
► We analyze the decision-making and the hierarchical information-aggregation models.
► Even sub-optimal forms of communication can be almost as efficient as the optimal one.