Information-sharing and aggregation models for interacting minds

TL;DR

This paper develops mathematical models to analyze how groups of interacting minds perform in a two-choice discrimination task, extending previous dyad models to larger groups and exploring communication and decision-making strategies.

Contribution

It introduces a theoretical framework for group performance based on communication models, extending prior dyad work to groups of n, and characterizes performance scaling with group size.

Findings

Group performance scales as a power function of group size.

Voting can be nearly as effective as complex communication models.

Performance depends on the average of individual slopes and a size-dependent scaling factor.

Abstract

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.