  How does the number of collaborators affect individual productivity? Results
of prior research have been conflicting, with some studies reporting an
increase in individual productivity as the number of collaborators grows, while
other studies showing that the {free-rider effect} skews the effort invested by
individuals, making larger groups less productive. The difference between these
schools of thought is substantial: if a super-scaling effect exists, as
suggested by former studies, then as groups grow, their productivity will
increase even faster than their size, super-linearly improving their
efficiency. We address this question by studying two planetary-scale
collaborative systems: GitHub and Wikipedia. By analyzing the activity of over
2 million users on these platforms, we discover that the interplay between
group size and productivity exhibits complex, previously-unobserved dynamics:
the productivity of smaller groups scales super-linearly with group size, but
saturates at larger sizes. This effect is not an artifact of the heterogeneity
of productivity: the relation between group size and productivity holds at the
individual level. People tend to do more when collaborating with more people.
We propose a generative model of individual productivity that captures the
non-linearity in collaboration effort. The proposed model is able to explain
and predict group work dynamics in GitHub and Wikipedia by capturing their
maximally informative behavioral features, and it paves the way for a
principled, data-driven science of collaboration.
