Decentralized Information Elicitation Without Verification

Information Elicitation Without Verification (IEWV) refers to eliciting high-accuracy solutions from crowd members when the ground truth is unverifiable. While prior research on IEWV has focused on central entities providing incentives to motivate effort exertion, this work explores the less-studied decentralized setting, which is increasingly relevant in machine learning, crowd decision-making, and autonomous organization applications. We model members' strategic interactions as a two-stage game, where each member decides her incentive contribution strategy in Stage I and her effort exertion strategy in Stage II. We examine two types of incentive allocation mechanisms: Equal Allocation (EA), where each member receives an equal proportion of the total incentives, and Output Agreement (OA), where a member receives incentives if her solution matches a reference solution generated by other members. This paper first analyzes the two-member case and provides closed-form equilibrium results. For more than two members, we use a binomial approximation to simplify the combinatorial computation of the majority voting problem and characterize the symmetric Nash equilibrium under EA. For OA, we derive equilibrium results for effort exertion and propose an algorithm for the incentive contribution game due to discontinuous payoffs. Our results show that OA outperforms EA in the aggregated team solution accuracy at equilibrium. Furthermore, we reveal that higher member ability beyond a certain threshold may lead to reduced effort exertion under EA, and that smaller teams achieve better accuracy when the effort cost is high due to less free-riding behavior. Numerical and empirical simulations validate our theory.