  We study the design and approximation of optimal crowdsourcing contests.
Crowdsourcing contests can be modeled as all-pay auctions because entrants must
exert effort up-front to enter. Unlike all-pay auctions where a usual design
objective would be to maximize revenue, in crowdsourcing contests, the
principal only benefits from the submission with the highest quality. We give a
theory for optimal crowdsourcing contests that mirrors the theory of optimal
auction design: the optimal crowdsourcing contest is a virtual valuation
optimizer (the virtual valuation function depends on the distribution of
contestant skills and the number of contestants). We also compare crowdsourcing
contests with more conventional means of procurement. In this comparison,
crowdsourcing contests are relatively disadvantaged because the effort of
losing contestants is wasted. Nonetheless, we show that crowdsourcing contests
are 2-approximations to conventional methods for a large family of "regular"
distributions, and 4-approximations, otherwise.
