Having been born and raised in the big city of Los Angeles, I think I'm more conscious of whether or not to make eye contact, and the possible good or bad outcome of eye contact, or really, of whether or not to acknowledge something or someone at all -- whether to pretend nothing's happening and just mind my own business.
I've noticed that friends of mine from smaller towns don't have the same kind of eye contact rules as me. Similarly, I have heard musicians complain that L.A. audiences just stand and stare during a band's performance, instead of dancing and singing along.
I think I'm one of those.
Here are some of my rules that I follow but that I don't expect to necessarily make me sound like a great gal:
I pretend not to see people having embarrassing moments like tripping and falling or spilling their water everywhere. This may seem like a mean thing, as opposed to asking someone if they need help, but when I myself trip or spill something, I don't want to be noticed, and I don't need help. What help could be offered in minor accidents? I think it's more gracious not to draw attention to someone's mishap. Also, in most cases, there isn't much I can do to actually help that person. Like, if it was an elderly woman who tripped, of course I would help her up and see if she needed medical attention or whatever the situation called for, but if it's a co-worker who trips over her shoelace, what actual help could I give her?
I ignore mentally ill people who are yelling on the street, because I know there's nothing I can truly do to help, and any attempt to offer some assistance in such a situation would just be an empty gesture to look good. Also, I don't want to put myself in danger by engaging with someone who isn't in control of their actions.
I make eye contact with homeless people when they are asking for money, even/especially when I don't have money to give. I try not to stay and chit-chat though, because I don't overvalue my own company. When I've had lowly jobs --- security guard, front desk clerk, janitor --- and someone thinks "I'm gonna make this person's day by having a conversation with them" I just want them to shut the fuck up and leave me be. I usually assume that this is the same thing a homeless person feels about chit-chatting with someone they don't know and have nothing in common with, especially when it's not going to help them get food or a place to stay.
There is a homeless person near my office who is a dick and I go out of my way not to make eye contact with him, because I don't naively lump all homeless people together into being long-suffering saints. They're just people; some are cool, others are assholes. The homeless guy I don't like is definitely an asshole and a bit of a bully.
I ignore riots and police activity. I ignore drug deals. There is a guy on the corner of a street I pass in downtown every day who dresses like the stereotypical image of a pimp, in a huge real fur white jacket, and i don't make eye contact with him, and pretend to ignore interactions he has with other people, but when he's not looking, I soak up every moment of his presence, because the whole thing is so surreal and cinematic -- an actual pimp on an actual street corner, in an actual white fur coat.
I make aggressive eye contact with businessmen in the elevator in my office building who are doing that power-play thing of trying to take up too much space to crowd everyone else out, like to be the alpha dog or whatever thing they're thinking.
One thing I wish I didn't ignore is a constant, yet hard to prove, form of sexual harassment I have to put up with every day -- here's a case where I can't use my withholding of or use of eye contact to control a situation.
Anyway, like it or lump it, these are my rules. I'm a calculated ignorer of sensational stuff, and someone who uses eye contact to control situations as best as I can. After all, it's a jungle out there.