After reporting on the NYT article Facebook Gave Device Makers Deep Access to Data on Users and Friends, a journalist asked me if this data leak affected more or less Facebook users than the Cambridge Analytica scandal (which was reported to affect 87 million users).
When trying to come up with an estimate, I realized that I do not know enough about stochastics. I just know that it would be wrong to multiply all the numbers because that would count many people several times.
Some facts from the NYT: Since 2007, more than 60 hardware manufacturers got access to an API that allowed them to retrieve profile information not only for the device's user but also for his or her friends and their friends (i.e. friends of friends).
Some more numbers to get you started:
- a Facebook user has 338 “friends” on average (arithmetic mean)
- Facebook currently has 2 bn monthly active users
- In 2016, an estimated 62.9 percent of the population worldwide already owned a mobile phone.
My gut feeling is that through the network effect, major hardware manufacturers had access to Facebook data of pretty much each and every Facebook user (even without sharing among manufacturers). Can this be corroborated mathematically? I guess this question is similar to the Coupon collector's problem, but I still need help.
If there is not enough data, I think it would be fair to make some simplifying assumptions here, namely that Facebook had a data sharing contract with all hardware manufacturers, and that every Facebook user has a mobile phone.