We consider the problem of conducting a survey with the goal of obtaining an unbiased estimator of some population statistic when individuals have unknown costs (drawn from a known prior) for participating in the survey. Individuals must be compensated for their participation and are strategic agents, and so the payment scheme must incentivize truthful behavior. We derive optimal truthful mechanisms for this problem for the two goals of minimizing the variance of the estimator given a fixed budget, and minimizing the expected cost of the survey given a fixed variance goal.
Concurrently with this work, Roth and Schoenebeck REF consider the problem of deriving Bayesian optimal survey mechanisms for computing minimum variance unbiased estimators of a population statistic from individuals who have costs for participating in the survey.
Conducting truthful surveys, cheaply
EC '12
Computer Science Mathematics