EdgeRank
Facebook uses EdgeRank to calculate the connection between two people, determined by the amount of mutual friends, interactions, tagged photos, attended events and other parameters in a time period. Besides other things, the EdgeRank influences which posts get displayed in your news feed. It seems Facebook is saying that a similar algorithm is used for the friends on your profile, but is it really?
The exploit
Some time ago, someone managed to find a way inside the EdgeRank results. This guy noticed that Facebook caches the list of your friends, together with the level of proximity you have with each one. This stored part of the social graph helps search and other lists on Facebook to work faster and be sorted better. He was nice enough to write a script and made it public, so everybody can see who their Facebook BFFs are. The results looks like the real deal, and it's actually quite fascinating that Facebook hasn't patched this potential abuse yet, it's been available for almost a year.
Bottom line: the list of friends in your EdgeRank and the list of friends on your profile are almost, but not quite, entirely unlike each other.
Comparing my closest friends to those that are showing up on my Facebook profile
Why bother?
Facebook needs to constantly drive your engagement, and they have infinite data about you. They are trying to seamlessly integrate their experience into every pore of your life and make you even more connected. They are saying they can predict when hookups and breakups will happen. Who do you think they would put on your profile?
It would work
Adding "people who look at you" to your Facebook profile would act as the poke that never got clicked. The most basic (inter)action, something that wants to lead to something bigger. The invisible act of someone longing for engagement. Potential connection, potential partnership, potential relationship. The beyond EdgeRank scary social experiment, which holds infinite possibilities, positive and negative. An almost godly algorithm. Why would anyone even think of doing it differently? It simply doesn't get much better than this.
I would do it, I believe Facebook would do it as well, but even if they did, it's pretty clear why they can't tell us. This feature would work only as long as we wouldn't really believe it's being used. That's why you need to forget about all of this and simply enjoy your virtual life.
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