Technically, you cannot rationally argue for anything.
I suppose you could use master rationalist skillz to answer the question "What will persuade person X?" but this relies on person X being persuadable by the best arguer rather than the best facts, which is not itself a characteristic of master rationalists.
The more the evidence itself leans, the more likely it is that a reasonably rational arbiter and a reasonably skillful evidence-collecter-and-presenter working on the side of truth, cannot be defeated by a much more skillful and highly-paid arguer on the side of falsity.
A master rationalist can still be persuaded by a good arguer because most arguments aren't about facts. Once everyone agrees about facts, you can still argue about goals and policy - what people should do, what the law should make them do, how a sandwich ought to taste to be called a sandwich, what's a good looking dress to wear tonight.
If everyone agreed about facts and goals, there wouldn't be much of an argument left. Most human arguments have no objective right party because they disagree about goals, about what should be or what is right.
This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. Feel free to rid yourself of cached thoughts by doing so in Old Church Slavonic. If a discussion gets unwieldy, celebrate by turning it into a top-level post.
If you're new to Less Wrong, check out this welcome post.