Putting it to a non-scientific test, where I grew up is within the zip code of 98632. From the 2000 census there are 47,202 within that zip code. This is probably a good average city for America - not too big, not too small. Based on the fact that there are 366 possible (year excluded) birthdays (I'm including Feb. 29th) and only two genders, just about the best I can do for uniquely identifying people in that county is 1 in 64. Add in the year and what I would assume is an even population between the ages of 1 to 50 and that gets you closer to 1:1. Not bad.
A zip code with large populations probably are more around 50% than 87%, and obviously the reverse is true as well. I wonder what the population size for a zip code would have to be to be really close to 100%. Just throwing some numbers in a calculator I'd guess at 15-20k people would be damn close. So 10k is probably just about a unique identifier.
I didn't at first to show the 1:64, and then I added the year (well 50 of them) to show how I got closer to the 87% with my extremely un-scientific and fuzzy math.
Using the tools at USPS.com, I could find examples where ZIP+4 was unique down to just 6 apartments in a dense neighborhood. Just type in a street name with lots of apartment buildings on it.
Longview probably just has the one zip code. Seattle has 59, for just over 10000 average per zip code, so we up here are probably a bit worse in a big city.
Worse or better? With only 10k per zip you'd get very close to a 100% unique identifier.
I realized after looking at both Portland and Seattle zip codes that they seem to be distributed better than the less dense areas so you do have very few zip codes over 20k.
A zip code with large populations probably are more around 50% than 87%, and obviously the reverse is true as well. I wonder what the population size for a zip code would have to be to be really close to 100%. Just throwing some numbers in a calculator I'd guess at 15-20k people would be damn close. So 10k is probably just about a unique identifier.