  Ranking is fundamental to many areas, such as search engine optimization,
human feedback for language models, as well as peer grading. Crowdsourcing,
which is often used for these tasks, requires proper incentivization to ensure
accurate inputs. In this work, we draw on the field of \emph{contract theory}
from Economics to propose a novel mechanism that enables a \emph{principal} to
accurately rank a set of items by incentivizing agents to provide pairwise
comparisons of the items. Our mechanism implements these incentives by
verifying a subset of each agent's comparisons, a task we assume to be costly.
The agent is compensated (for example, monetarily or with class credit) based
on the accuracy of these comparisons. Our mechanism achieves the following
guarantees: (1) it only requires the principal to verify $O(\log s)$
comparisons, where $s$ is the total number of agents, and (2) it provably
achieves higher total utility for the principal compared to ranking the items
herself with no crowdsourcing.
