Allocation strategies improve the efficiency of crowdsourcing by decreasing the work needed to complete individual tasks accurately. However, these algorithms introduce bias by preferentially allocating workers onto easy tasks, leading to sets of completed tasks that are no longer representative of all tasks. This bias challenges inference of problem-wide properties such as typical task difficulty or crowd properties such as worker completion times, important information that goes beyond the crowd responses themselves. Here we study inference about problem properties when using an allocation algorithm to improve crowd efficiency. We introduce Decision-Explicit Probability Sampling (DEPS), a method to perform inference of problem properties while accounting for the potential bias introduced by an allocation strategy. Experiments on real and synthetic crowdsourcing data show that DEPS outperforms baseline inference methods while still leveraging the efficiency gains of the allocation method. The ability to perform accurate inference of general properties when using non-representative data allows crowdsourcers to extract more knowledge out of a given crowdsourced dataset.
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