The power of diversity over large solution spaces

We consider a team of agents with limited problem-solving ability facing a disjunctive task over a large solution space. We provide sufficient conditions for the following four statements. First, two heads are better than one: a team of two agents will solve the problem even if neither agent alone would be able to. Second, teaming up does not guarantee success: if the agents are not sufficiently creative, even a team of arbitrary size may fail to solve the problem. Third, "defendit numerus": when the agent's problem-solving ability is adversely affected by the complexity of the solution space, the solution of the problem requires only a mild increase in the size of the team. Fourth, groupthink impairs the power of diversity: if agents' abilities are positively correlated, a larger team is necessary to solve the problem.