It's exactly the same in the west. The difference is that it's generally more discreet and requirements for the directness with which one must "know someone" are more strict and "knowing someone" and "favors" are much harder to apply across departments/organizations. We're not talking Chicago or rural counties in the deep south here, this is how things work in your run of the mill state and local government.
I agree that there is more indirection involved but I disagree about the discreetness: it's not that corruption in the US is more discreet, it's just far more transparent and normalized within the culture. There is red tape and a bunch of rules to follow so it gives everyone involved a false sense of fairness. You don't give someone a bribe, you donate to their political campaign or charity - which then hires their family to be on the board or as some consultant with a plausibly deniable role. In return, you get Requests For Proposals and contracts with requirements disqualifying everyone except the company owned by one guy who "donated." Even in cases where people are breaking the law, there's simply no money for enforcement or even any established mechanisms for doing so (often on purpose), especially as the changing media landscape erodes local journalism.
From personal experience: I don't bribe policemen, I donate to the police union or contribute money towards some officer's or family member's health or college fund. I don't bribe school administration, I go to a few Booster Club events a year and throw money at whatever their latest stupid fund is. I don't bribe teachers, I show up on the first day of school with enough science lab kits and other school supplies for a whole class. I don't bribe my doctors, I contribute money to the nonprofit clinics they are partnered with, which then pays part of the doctor's annual salary directly so that they can focus more on the clinic.
There is far more indirection and the "return on investment" is certainly far less than what I saw when living in Russia, for example, but that's just lipstick on a pig because at the end of the day, it works. When my kid and his friends were caught with drugs (not cannabis), I got to the station less than 5 minutes after they did and was able to get them out by the next day without even seeing a judge (the evidence was "misplaced" on the way to lockup so the prosecutor felt it wasn't worth his time). When he got into a fight with a close friend, I managed to get both of them off with an in-school suspension instead of an expulsion that would go on their permanent records. Never once did I bring up the donations or threaten to cut them off - my rhetoric in each situation basically boiled down to "boys will be boys but I'll make sure they know what it means to be punished" but the deference I received was far more than the average person would, even when getting special treatment for someone else's kid.
"Donating" falls under the broader category of "community involvement". You pick a small thing that you can put a disproportionate amount of money toward and dominate it or you take lead on something that people will remember. Nobody remembers if you donate $100 to a bunch of things. People remember when you foot the entire bill for some thousand or two dollar expense that kids normally would hold bake sales for. You need to keep on top of it ("donate" to something every few years) but the point is that someone at whatever organization you have to deal with recognizes your last name and associates it with whatever good thing you did and you get favorable treatment similar to what you normally need to be extended family to get. The smaller the town/city the less you need to do to be known as "good"
For example, when some party gets shut down by the cops the kids of the grocery store owner who donates all the food for some annual police/fire/vfw bbq don't have to worry about getting misdemeanors. When it's time to determine who gets what contracts the company that generously sponsored the boy scout troop that the son of whoever is making the decision will get special consideration (all the blue collar small businesses don't sponsor local stuff because it has a negative ROI).
Exactly. You have to donate money or time in ways that maximize your exposure to the in-group you are targeting, which would be the police officers, teachers, school administrators, etc. If you want deference, you need to get involved in ways that make their lives easier or better because that warm fuzzy feeling they'll have when they see or hear your name is very powerful and subliminal.
For example, I live in LA and the 90s were very tough for police all across the state after the Rodney King riots. I was buddies with one of the guys heading up reform in the LAPD after the riots so I "donated" a thousand bucks to have him come out for a weekend and teach the basics of community policing to my underfunded local PD - something that I felt was important anyway because of the wealth inequality in my town. The department didn't have it in their budget to hire him themselves but they did have state money for overtime for police training so not only did every officer get training but they got paid extra to do it. Since my name was dropped multiple times as the sponsor of the training, all of the officers in the department knew who I was and associated my name with someone who supports the department in concrete ways (even if years later, they couldn't remember why!). It also didn't hurt that the training opened their eyes to new strategies at a time when tensions between police and civilians were boiling over.
Also, you can actually do this by donating a little bit to a lot of things but it has to be strategic. For example, a few members of the Booster Club and I have an ongoing scholarship at my local high school where we throw in $250 per donor per student for textbooks for anyone whose parents didn't go to college. Since my town is very wealthy, the number of students who qualify for this scholarship is minimal (a few thousand a year split between 4 people) but it is a guaranteed scholarship to anyone who qualifies so every teacher and administrator knows about the scholarship and who the donors are. Since we are explicit about the money going towards textbooks, it also sounds like a lot more than it really is because people think of the scholarship in the narrow context of textbook costs instead of overall graduation cost.
While your honesty is intriguing, suggesting people do this is pretty immoral. Why don't we spend our time online talking about ways to do things fairly, that'd probably do humanity a favor instead of instilling behaviors to the detriment of most of us.