On the Calibration of Crowdsourcing Aggregators

Calibration has been extensively studied for classifiers, but remains largely unexplored for crowdsourcing aggregation methods, which are increasingly used for making probabilistic decisions. To the best of our knowledge, we provide the first theoretical and empirical study of calibration in label aggregation. To our great surprise, we find that widely used aggregation methods can be severely miscalibrated, and in opposite directions: Majority Vote is underconfident while model-based aggregators are overconfident. We prove that the Bayesian aggregator is perfectly calibrated under its data-generating model. We also show that exact calibration of weighted majority votes requires highly restrictive conditions, which helps explain why Majority Vote is generally miscalibrated in realistic crowds. Empirically, we study calibration across 39 human crowdsourcing datasets and LLM-based crowds. In both cases, we observe systematic miscalibration for aggregation models such as Majority Vote, Dawid--Skene, GLAD, and CrowdFM. Finally, we propose a post-hoc calibration procedure that aggregates the aggregators: for any aggregation function ϕ, we introduce a transformation that first combines its predictive distribution with those of complementary aggregators, before applying temperature scaling. This simple and interpretable transformation makes temperature scaling more effective than when applied directly to ϕ. It improves calibration, especially in the high-redundancy regime where there are many annotations per item, while generally preserving or even improving accuracy.