The difference is there are actually formal guarantees wrt privacy - such as k anonymiy, l diversity, and differential privacy.

If you can PROVE anonymiy (to a certain extent), theres little privacy issue.

The problem is that, frankly, lots of people have no idea what they're doing (or are just lying about it) – claiming location data is anonymous (it doesn't take many data points over time to identify someone), or that datasets with names removed are anonymous (they're deidentified, and the remaining attributes might be enough to identify someone).

Of course people can claim that these dare "anonymous data" when there are not in fact so.

The poster seems to have privacy issues with anonymous data, so for the sake of the discussion we ought to consider actual anonymous data, and my question is therefore because to me the very definition of anonymous data means that there cannot be privacy issues. As such, the point the poster makes appears contradictory.

Where does the anonymous data come from? If anonymous data are considered as a disjoint and absolute point, then you're right. However, when considering the result of a set of transformations originating from an actual individual, we may have to question ourselves. Does the individual agree to be part of the process? Shouldn't we ask for his consent in the first place?

> If data collected are anonymous, what right to privacy is being infringed upon?

The data are collected. In their essence, they originate from the individual (in any way whatsoever). Doesn't the individual have an absolute right of the property upon these data?

> others are still free to e.g. count me if they want to make statistics on how busy a street is.

Is that something we are used to or something that should be questioned? Can I require not to be counted, to not exists in the statistics?

In a world (the web) where it is so easy to ask for consent, isn't that shameful not to do so? In contrast, within the street, one could argue that stopping pedestrians could be difficult.