Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
We characterize optimal honest and obedient (HO) mechanisms for the classic collective action problem with private information, where group success requires costly participation by some fraction of its members. For large n, a simple HO mechanism, the volunteer-based organization, is approximately optimal. Success is achieved in the limit with probability one or zero depending on the rate at which the required fraction declines with n. For finite n, optimal HO mechanisms provide substantial gains over unorganized groups when the success probability converges to zero, because the optimal HO success probability converges slowly and is always positive, while finite-sized unorganized groups have exactly zero probability of success.