Earlier quoted context omitted.
> provably private citation?
http://research.microsoft.com/pubs/74339/dwork_tamc.pdf They define the mathematical guarantees on privacy, which are computational guarantees against a polynomial-time adversary trying to distinguish between the analyses of two databases that differ in a single record. I.e., nobody can reasonably tell whether your information is included in the analysis.
I still would prefer a choice in the matter - a required small check box that says "record my data" or "do not record my data" XOR "erase my data". The term 'reasonably' has a very different meaning to me (assuming many unknowns in the future) over the long term.
It is either that, or people should literally stop making such a hard line distinguishing person A from person B. If the data is going to be used to make an inference from the collective to the individual, and it doesn't matter whether my data is included or not, well, shrug and thumbs up. It really depends on the context of the application. Does it determine whether my imaginary future children get to go to college or not?
The problem with data and private organizations is that we do not know what the data analysis is being used for, and as private citizens we do not have any control over how that data is mathematically reasoned about and qualitatively assessed aside from forging the data itself it (garbage in, garbage out).