Thanks for this. I would have been happier if the authors had phrased their findings in term of differential privacy rather than the effectiveness of the algorithms they were able to achieve.

https://en.wikipedia.org/wiki/Differential_privacy

When setting policy, it is better to have theoretical mathematical results rather than empirical effectiveness, since you can bet the technological frontier of privacy violation is a moving one. As with cryptography, you want solid foundations in unbreakable maths -- not 'we can't break this cipher with what we know today'. Probably, someone can.