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Avoiding Imposters and Delinquents: Adversarial Crowdsourcing and Peer Prediction

We consider a crowdsourcing model in which $n$ workers are asked to rate the quality of $n$ items previously generated by other workers. An unknown set of $\alpha n$ workers generate reliable ratings, while the remaining workers may behave arbitrarily and possibly adversarially. The manager of the experiment can also manually evaluate the quality of a small number of items, and wishes to curate together almost all of the high-quality items with at most an $\epsilon$ fraction of low-quality items. Perhaps surprisingly, we show that this is possible with an amount of work required of the manager, and each worker, that does not scale with $n$: the dataset can be curated with $\tilde{O}\Big(\frac{1}{\beta\alpha^3\epsilon^4}\Big)$ ratings per worker, and $\tilde{O}\Big(\frac{1}{\beta\epsilon^2}\Big)$ ratings by the manager, where $\beta$ is the fraction of high-quality items. Our results extend to the more general setting of peer prediction, including peer grading in online classrooms.

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