How can I follow up if a polite request to follow the rules has been declined?

Question

How should I follow up if a polite request to adhere to the rules is ignored or declined?

An Example

Dutch trains have special silent compartments (Dutch: stiltecoupé), where people are supposed to keep quiet — no conversations, no music, no conversations on the phone.

Sometimes, while sitting in such a compartment, people who don't know or don't care, start talking. I can approach them and politely ask them to be quiet, please, since they're in the silent compartment.
While most people will comply, some won't and will either ignore me or give a rude reply.

The Question

How do I follow up? It's not just in the situation described above, it could be neighbourhood kids trying to cut large branches (they brought a saw) off the tree in front of my house (not my tree but a municipal tree), for instance.

What do I do when a polite request to adhere to the rules has been ignored or declined?

My preferred outcome would be for the people to cease their unwanted behaviour, but at a minimum I'd like to save face.
("Please stop that." "No." "Oh, okay.")

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I'd like to note I'm not a stickler for rules — at least, I don't think I am — but I would like people to follow them if they align with my personal preferences — a quiet train journey; not having a barren stump in front of my house.

Answer 1

You don't engage with them any further than necessary. It's clear if they don't want to listen to the rules that you aren't going to be able to persuade them. If you're not a person in a position for power or authority (and if you are you can just remove them) then they're probably not going to listen to you without causing a huge fuss or even argument, and even then that might not go in your favour.

Go and get someone who should be dealing with rule breaking, an officer, conductor or anyone else who has at least some authority and let them deal with it. They probably even have training on how to deal with this type of person, and you could observe and learn from what they do.

I personally feel as though there is no point trying to save face in front of that sort of person, they aren't worth your time or effort. If you've explained what they're doing is wrong and they still do it just leave them to, go and get someone more official, and let them deal with them and take the relevant action. Just as a personal preference I would even reply if they refuse, I would just go and seek the relevant authority/personal.