Error Rate Bounds and Iterative Weighted Majority Voting for Crowdsourcing

Crowdsourcing has become an effective and popular tool for human-powered computation to label large datasets. Since the workers can be unreliable, it is common in crowdsourcing to assign multiple workers to one task, and to aggregate the labels in order to obtain results of high quality. In this paper, we provide finite-sample exponential bounds on the error rate (in probability and in expectation) of general aggregation rules under the Dawid-Skene crowdsourcing model. The bounds are derived for multi-class labeling, and can be used to analyze many aggregation methods, including majority voting, weighted majority voting and the oracle Maximum A Posteriori (MAP) rule. We show that the oracle MAP rule approximately optimizes our upper bound on the mean error rate of weighted majority voting in certain setting. We propose an iterative weighted majority voting (IWMV) method that optimizes the error rate bound and approximates the oracle MAP rule. Its one step version has a provable theoretical guarantee on the error rate. The IWMV method is intuitive and computationally simple. Experimental results on simulated and real data show that IWMV performs at least on par with the state-of-the-art methods, and it has a much lower computational cost (around one hundred times faster) than the state-of-the-art methods.