Although research on open collaboration for innovation has generally focused on the voluntary participation of individuals who are not strictly governed by formal authority concentrated at higher levels of organizational hierarchy, more recent studies highlight the importance of exploring how their tasks should be organized in order to enhance performance outcomes. This study extends this line of work by conceptualizing polyarchy as a decentralized decision-making structure that directs how core members of a project team screen a large collection of novel ideas generated by team members, and empirically examining whether and how polyarchy affects task completion time. In the context of online projects for open source software development at GitHub, we find that a polyarchical decision-making structure reduces task completion time. Closer examination also shows that this positive effect on decision-making speed becomes stronger when tasks are explorative rather than exploitative in nature. Implications for open, distributed models of innovation and non-traditional forms of decision-making structures are discussed.