I am in a complicated relationship on FB with my fish. Who has a lot more fish and human friends than me (~800 against 99). Never understood how he gets new friend requests everyday.
I did an experiment a few years ago where I set up a profile for someone who supposedly went to my university. His pictures were pulled from the profile of a male model, the rest was all made up. I went through every profile I could get and sent friend requests. I actually hit the 5000 friends limit. Usually I would send a message saying "hey we met at X party last night!" if I could find that information on their public profile. Many of the people "remembered" that. The account still gets people wishing him happy birthday.
The funny thing is that I NEVER asked anyone from my fish account and he now has friends from all over the world, while his name is "My fish Ploup" in French.
About your fake account and its birthday wishes, An experiment could be to put a erroneous birthday date. I guess that day you can get a lot of wishes, even from close friends. We are just lazy I guess.
I tried that experiment, and the first couple of years it was about 50/50, but most recently almost everyone who posted did so on the FB birthday date. I think theyv'e come to rely on the Facebook reminders.
It was also interesting to see the cognitive dissonance from some posts: "I'm pretty sure it was your birthday next week, but Facebook says its this week, so Happy Birthday".
Of my friends who are friends but not best friends, I only know one of their birthdays. I only know that because her Xbox Live gamertag has her birth month and day in it (and she was born one year and one month before me, kind of interesting I guess).
Birthdays are a thing that are hard to remember. People used to mark them down on a calendar or just wait for the person to remind them. Both of those functions have been replaced with Facebook now.
That's actually what got me to close my FB account. I was tired of getting emailed birthday spam because FB knew my birthday, so I changed it to April 1st and forgot about it. This April, I got about 10 or 20 'Happy Birthday!'s before I posted saying "It's not actually my birthday, April Fool's!" ... and then people kept posting happy birthday without noticing.
