I used "you" incorrectly, my bad. They can predict that people who listen to band A are likely to like band C, but their data for whether you listen to band A still has a significant chance of being wrong.
Yes, the data has a significant chance of being wrong. But it is useful only insofar as it supports a prediction with a probability of being right that is greater than 0.5.
That's what makes the data useful and that's what makes it a privacy issue at the same time.
It doesn't have to support that prediction in specific instances, just in a general trend, where random noise tends to average itself out in a lot of cases. There are lots of different distributions with the same averages, the same conditional probablities, etc. with wildly different data. If you have some mathematical proofs that say you can not reach one of these other distributions by injecting random noise to mask individual contributions, then please write a paper on it! But to my knowledge, Cynthia Dwork's work and others still stands. There is definitely no simple, common sense reason that it doesn't work.
How does sending the same list of conditional probabilities for liking pairs of bands to everyone's device and then having the device pick out the ones actually pertinent to your library compromise your privacy?
I don't doubt the validity of Dwork's work. I think we're talking past each other.
What I'm saying is that if Apple keeps data on its servers that is sufficient to predict some of my actions or likes with any accuracy greater than 50%, then that is a privacy concern.
But if you're saying that the data in Apple's database does not have any predictive power on its own, then I agree that it is not a privacy concern.
In that case, my device would have to download some of Apple's data and combine it with data that resides only on my device in order to make a prediction locally on my device.
They even limit the number of samples they get from a specific person so they can't filter out the noise for that person and get their individual response.
But, keep in mind that Apple will have records of all your iTunes rentals and purchases at least for billing purposes. However, at least in the US there's a law about keeping that data private (because of Robert Bork).
