  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.
