  In this paper, we introduce the family of Anonymized Local Privacy
mechanisms. These mechanisms have an output space of three values "Yes", "No",
or "$\perp$" (not participating) and leverage the law of large numbers to
generate linear noise in the number of data owners to protect privacy both
before and after aggregation yet preserve accuracy.
  We describe the suitability in a distributed on-demand network and evaluate
over a real dataset as we scale the population.
