Impact statement: LLP has been discussed as a model for summarizing a fully labeled dataset for public dissemination. The idea is that individual labels are not disclosed, so some degree of privacy is retained. As we show, consistent classification is still possible in this setting. If the two class-conditional distributions are nonoverlapping, labels of training instances can be recovered with no uncertainty by an optimal classifier. If the class-conditional distributions have some overlap, training instances in the nonoverlapping region can still be labeled with no uncertainty, while training instances in the overlapping regions can have their labels guessed with some uncertainty, depending on the degree of overlap.