You are speaking of perhaps Google's RAPPOR protocol specifically, in which answers are sent through a series of BSC-like channels. These channels introduce noi

You are speaking of perhaps Google's RAPPOR protocol specifically, in which answers are sent through a series of BSC-like channels. These channels introduce noise, meaning the input signal is degraded, but by no means is it gone -- otherwise no statistics could be collected. Multiple independent reads would be an obvious attack; actually it's a form of repetition coding; but there are many other coding strategies against noisy channels -- there is an entire field dedicated to that task alone. To contrast, encrypting with a one-time pad is information theoretically secure. Attacks aside, the point is really that in this age of statistical machine learning we should be vigilant against even this sort of data collection. A leak is a leak. Ideally people can opt into providing just enough information for the statistics they want to participate in and no more; realistically, more is always collected.