Simulating identification by zip code, sex, and birthdate

While the principal is broadly correct, in real life you've got to worry about a host of other things.

Firstly, while you can come up with a theoretical number of persons who are uniquely identified, its harder to establish who IS uniquely identified. This might seem like splitting hairs but its quite fundamental: imagine you knew you could identify 50% of the population uniquely, unless you know which 50% of the population, have you really identified anyone? Clearly knowing someone's sex, age and location gives me analytical information about them I can use to make predictions (a 5 year old female in california is going to be fundamentally different from a 85 year old male in alabama) but is it really identification yet and do we even need identification to make useful predictions?

Secondly, what you presumably care about in 'identification' is not 'single source' probability issues per se. In the real world what most people care about is multiple-source identifiability: not the odds of one piece of data uniquely identifying someone (just by collecting gender I might eventually uniquely identify someone in some remote geography for example), but the odds of uniquely identifying someone in TWO (or more) data sources that were previously 'unlinked', because that's what's required to expand your current information set (you didn't know this person was identifiable on two data sources, and now you do, so you can bring together more information than what you already held originally).

This second point is extremely important, because in the real world, you have to worry about transcription errors, recording formats, corruption, temporal changes and time, and scope of the two data sources. Most people do not get to work with total accurate census' of the population at two points in time in a population that doesn't change.

From my own practical experience, something like the zip code, sex and birthdate combination is powerful, and yes, you'll be able to uniquely identify some people with such information (especially in smaller geographical areas), but the practical rate will be far far less than 87%. But for many modelling purposes, it doesn't need to be spectacularly accurate to be useful anyway.

https://dataprivacylab.org/projects/identifiability/paper1.p...

I'll add that there are far fewer live births, per day, in the US than there are zip codes. I agree that some highly populated areas that are problematic, but this may be the only reason that 87.1% number isn't 100%!

But in other settings they are usually conflated.

The real distribution of birth days within a neighborhood is almost always far less spread than an assumption of uniformity across the entire probability distribution (because schools, dinks, retirees, students, workers, etc all trend to cluster in real life).

This tendency of demographics to cluster makes de-identification harder than the theoretical models, and in some ways even protects it aa bit, because researchers who don't test their models assume greater accuracy than they actually achieve.

Of course, this might not be as protecting as one might assume, because for a lot of activities, even if people do casually link you to someone else, odds are pretty good you have similar modelled outcomes as someone very close to you in properties anyway...