Theoretical Characteristics of δ-Margin 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 δ. We show a way to model such
“δ-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 δ 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.