A Tunable Incentive Mechanism for Binary Aggregation Without Verification

2026-06-29

AI Summary

This work addresses binary crowdsourcing settings where ground-truth verification is unavailable and proposes an adjustable reward-penalty mechanism to incentivize participants to truthfully report their private signals. By establishing cost-adjusted bounds on the reward-penalty ratio, the study identifies a feasible region satisfying both incentive compatibility and individual rationality. To accommodate heterogeneous agents, the mechanism incorporates entropy scaling and stake-weighted redistribution. Theoretical analysis yields closed-form equilibrium conditions and proves the existence of a fully obedient Nash equilibrium under constrained strategies. Numerical experiments further validate the mechanism’s effectiveness and demonstrate its robustness to variations in threshold parameters.

Abstract

Binary aggregation without verifiable ground truth arises when agents' reports must be aggregated without access to gold-standard labels. This paper studies a tunable reward--penalty mechanism for binary aggregation without verification. Agents choose between a conforming strategy, which reports an informative private signal, and a non-conforming strategy, which follows a deterministic prior-informed report rule. For this mechanism, we derive cost-adjusted sufficient conditions for incentive compatibility and individual rationality as bounds on the reward--penalty ratio. The analysis identifies feasible ratio regions, cases in which ratio adjustment restores feasibility, and parameter regimes in which no ratio satisfies both constraints under the modeled construction. We also state a conditional all-conforming Nash equilibrium result within the restricted strategy set. Entropy-based scaling and stake-weighted redistribution are treated as extensions, with stake-weighted redistribution inducing agent-specific incentive constraints. Numerical checks support the closed-form Tier 1 quantities and illustrate threshold sensitivity.

Problem

• binary aggregation
• incentive mechanism
• without verification
• incentive compatibility
• individual rationality

Innovation

• tunable incentive mechanism
• binary aggregation without verification
• reward-penalty ratio
• incentive compatibility
• stake-weighted redistribution