Full Characterization of Adaptively Strong Majority Voting in Crowdsourcing

A commonly used technique for quality control in crowdsourcing is to task the workers with examining an item and voting on whether the item is labeled correctly. To counteract possible noise in worker responses, one solution is to keep soliciting votes from more workers until the difference between the numbers of votes for the two possible outcomes exceeds a pre-specified threshold {\delta}. We show a way to model such {\delta}-margin voting consensus aggregation process using absorbing Markov chains. We provide closed-form equations for the key properties of this voting process -- namely, for the quality of the results, the expected number of votes to completion, the variance of the required number of votes, and other moments of the distribution. Using these results, we show further that one can adapt the value of the threshold {\delta} to achieve quality-equivalence across voting processes that employ workers of different accuracy levels. We then use this result to provide efficiency-equalizing payment rates for groups of workers characterized by different levels of response accuracy. Finally, we perform a set of simulated experiments using both fully synthetic data as well as real-life crowdsourced votes. We show that our theoretical model characterizes the outcomes of the consensus aggregation process well.