High-Effort Crowds: Limited Liability via Tournaments

We consider the crowdsourcing setting where, in response to the assigned tasks, agents strategically decide both how much effort to exert (from a continuum) and whether to manipulate their reports. The goal is to design payment mechanisms that (1) satisfy limited liability (all payments are non-negative), (2) reduce the principal’s cost of budget, (3) incentivize effort and (4) incentivize truthful responses. In our framework, the payment mechanism composes a performance measurement, which noisily evaluates agents’ effort based on their reports, and a payment function, which converts the scores output by the performance measurement to payments. Previous literature suggests applying a peer prediction mechanism combined with a linear payment function. This method can achieve either (1), (3) and (4), or (2), (3) and (4) in the binary effort setting. In this paper, we suggest using a rank-order payment function (tournament). Assuming Gaussian noise, we analytically optimize the rank-order payment function, and identify a sufficient statistic, sensitivity, which serves as a metric for optimizing the performance measurements. This helps us obtain (1), (2) and (3) simultaneously. Additionally, we show that adding noise to agents’ scores can preserve the truthfulness of the performance measurements under the non-linear tournament, which gives us all four objectives. Our real-data estimated agent-based model experiments show that our method can greatly reduce the payment of effort elicitation while preserving the truthfulness of the performance measurement. In addition, we empirically evaluate several commonly used performance measurements in terms of their sensitivities and strategic robustness.