Eliciting private information with noise: The case of randomized response

Theory suggests that garbling may improve the transmission of private information. A simple garbling procedure, randomized response, has shown promise in the field. We provide the first complete analysis of randomized response as a game and implement it as an experiment. We find in our experiment that randomized response increases truth-telling and, importantly, does so in instances where being truthful adversely affects posterior beliefs. Our theoretical analysis also reveals, however, that randomized response has a plethora of equilibria in addition to truth-telling equilibria. Lab behavior is most consistent with those informative but not truth-telling equilibria.