Abstract
Voluntary participation is a central yet understudied aspect of collaboration. Here, we model collaboration as people's voluntary choices between joining an uncertain public goods provisioning in groups and pursuing a less profitable but certain individual option. First, we find that voluntariness in collaboration increases the likelihood of group success via two pathways, both contributing to form more optimistic groups: pessimistic defectors are filtered out from groups, and some individuals update their beliefs to become cooperative. Second, we reconcile these findings with existing literature that highlights the detrimental effects of an individual option. We argue that the impact of an outside individual option on collaboration depends on the "externality" of loners - the influence that those leaving the group still exert on group endeavors. Theoretically and experimentally, we show that if collaboration allows for flexible group formation, the negative externality of loners remains limited, and the presence of an individual option robustly aids collaborative success.