Democracy under uncertainty: the wisdom of crowds and the free-rider problem in group decision making.

We introduce a game theory model of individual decisions to cooperate by contributing personal resources to group decisions versus by free riding on the contributions of other members. In contrast to most public-goods games that assume group returns are linear in individual contributions, the present model assumes decreasing marginal group production as a function of aggregate individual contributions. This diminishing marginal returns assumption is more realistic and generates starkly different predictions compared to the linear model. One important implication is that, under most conditions, there exist equilibria where some, but not all, members of a group contribute, even with completely self-interested motives. An agent-based simulation confirmed the individual and group advantages of the equilibria in which behavioral asymmetry emerges from a game structure that is a priori perfectly symmetric for all agents (all agents have the same payoff function and action space but take different actions in equilibria). A behavioral experiment demonstrated that cooperators and free riders coexist in a stable manner in groups performing with the nonlinear production function. A collateral result demonstrated that, compared to a dictatorial decision scheme guided by the best member in a group, the majority/plurality decision rules can pool information effectively and produce greater individual net welfare at equilibrium, even if free riding is not sanctioned. This is an original proof that cooperation in ad hoc decision-making groups can be understood in terms of self-interested motivations and that, despite the free-rider problem, majority/plurality decision rules can function robustly as simple, efficient social decision heuristics.