Full Characterization of Adaptively Strong Majority Voting in Crowdsourcing

In crowdsourcing, quality control is commonly achieved by having workers examine items and vote on their correctness. To minimize the impact of unreliable worker responses, a $\delta$-margin voting process is utilized, where additional votes are solicited until a predetermined threshold $\delta$ for agreement between workers is exceeded. The process is widely adopted but only as a heuristic. Our research presents a modeling approach using absorbing Markov chains to analyze the characteristics of this voting process that matter in crowdsourced processes. We provide closed-form equations for the quality of resulting consensus vote, the expected number of votes required for consensus, the variance of vote requirements, and other distribution moments. Our findings demonstrate how the threshold $\delta$ can be adjusted to achieve quality equivalence across voting processes that employ workers with varying accuracy levels. We also provide efficiency-equalizing payment rates for voting processes with different expected response accuracy levels. Additionally, our model considers items with varying degrees of difficulty and uncertainty about the difficulty of each example. Our simulations, using real-world crowdsourced vote data, validate the effectiveness of our theoretical model in characterizing the consensus aggregation process. The results of our study can be effectively employed in practical crowdsourcing applications.