Calibrating coupling for collaboration with Kuramoto.

Abstract

We calibrate a Kuramoto-model-inspired representation of peer-to-peer collaboration using data on the maximum team size where coordination breaks down. The Kuramoto model is modified, normalizing the coupling by the degree of input and output nodes, reflecting dispersion of cognitive resources in both absorbing incoming- and tracking outgoing-information. We find a critical point, with loss of synchronization as the number of nodes grows and analytically determine this point and calibrate the coupling with the known maximum team size. We test that against the known "span of control" for a leader/supervisor organization. Our results suggest larger maximum team sizes than early management science proposes, but are consistent with studies that focus only the relationship between supervisor and subordinates, excluding other internal interactions in the team.