Using a laboratory experiment with nested local and global public goods, we analyze the stability of global groups when individuals have the option to separate, according to the degree of decentralization of decision-making. We show that increasing the number of decisions made at the local level within a smaller group reduces the likelihood that individuals vote in favor of a configuration that includes no global good for interacting only within their local group. Voting for such a configuration is more likely when global group members are less cooperative and local group members are more cooperative. Reinforcing local group identity has no impact on votes.