A Theory of the Critical Mass. I. Interdependence, Group Heterogeneity, and the Production of Collective Action

Collective action usually depends on a "critical mass" that behaves differently from typical group members. Sometimes the critical mass provides some level of the good for others who do nothing, while at other times the critical mass pays the start-up costs and induces widespread collective action. Formal analysis supplemented by simulations shows that the first scenario is most likely when the production function relating inputs of resource contributions to outputs of a collective good is decelerating (characterized by diminishing marginal returns), whereas the second scenario is most likely when the production function is accelerating (characterized by increasing marginal returns). Decelerating production functions yield either surpluses of contributors or order effects in which contributions are maximized if the least interested contribute first, thus generating strategic gaming and competition among potential contributors. The start-up costs in accelerating production functions create severe feasibility problems for collective action, and contractual or conventional resolutions to collective dilemmas are most appropriate when the production function is accelerating.