I think people try pretty hard to come to accurate answers given the information available, and have inherited or come up with various tools for this (e.g. probabilistic forecasting). Whether that counts as "rationality" or not depends a lot on your definitions of what it means to be rational, and how low your bar is. 

I don't think we're perfectly rational, and there's an argument that we aren't investing as much resources as optimal for rationality or epistemics-enhancing interventions. But it's pretty hard to answer a broad question like "How Is EA Rational?", and I don't think the crux is a specific form of argument mapping that we use or don't use.

At face value, the answer is something like we're reasonably good at coming to accurate enough answers to hard-ish questions. Whether this is "good enough" depends on whether "accurate enough" is good enough, how hard the questions we ultimately want to solve are, and whether/how much we can do better given the resources available.

But I don't think this is exactly what you're asking. In sum, I don't think "is X rational" has a binary answer.

List of reasons I think EA takes better actions than most movements, in no particular order:

• taking weird ideas seriously; being willing to think carefully about them and dedicate careers to them
• being unusually goal-directed
• being unusually truth-seeking
  • this makes debates non-adversarial, which is easy mode
• openness to criticism, plus a decent method of filtering it
• high average intelligence. Doesn't imply rationality but doesn't hurt.
• numeracy and scope-sensitivity
  • willingness to use math in decisions when appropriate (e.g. EV calculations) is only part of this
• less human misalignment: EAs have similar goals and so EA doesn't waste tons of energy on corruption, preventing corruption, negotiation, etc.
• relative lack of bureaucracy
• various epistemic technologies taken from other communities: double-crux, forecasting
• ideas from EA and its predecessors: crucial considerations, the ITN framework, etc.
• taste: for some reason, EAs are able to (hopefully correctly) allocate more resources to AI alignment than overpopulation or the energy decline, for reasons not explained by the above.

Structured debate mechanisms are not on this list, and I doubt they would make a huge difference because the debates are non-adversarial, but if one could be found it would be a good addition to the list, and therefore a source of lots of positive impact.

I think, based on the way you're phrasing your question, you're perhaps not fully grasping the key ideas of Less Wrong style rationality, which is what EA rationality is mostly about. It might help to read something like this post about what rationality is and isn't as a starting point, and from there explore the Less Wrong sequences.

TLDR: We don't have some easy to summarise methodology and being rational is pretty hard. Generally we try our best and hold ourselves and each other accountable and try to set up the community in a way that encourages rationality. If what you're looking for is a list of techniques to be more rational yourself you could read this book of rationality advice or talk to people about why they prioritise what they do in a discussion group

Some meta stuff on why I think you got unsatisfactory answers to the other questions

I wouldn't try to answer either of the previous questions because the answers seem big and definitely incomplete. I don't have a quick summary for how I would resolve a disagreement with another EA because there are a bunch of overlapping techniques that can't be described in a quick answer. 

To put it into perspective I'd say the foundation to how I personally try to rationally approach EA is in the Rationality A-Z book but that probably doesn't cover everything in my head and I definitely wouldn't put it forward as a complete methodology for finding the truth. For a specific EA spin just talking to people about why they prioritise what they prioritise is what I've found most helpful and an easy way to do that is in EA discussion groups (in person is better than online).

It is pretty unfortunate that there isn't some easy to summarise methodology or curriculum for applying rationality for charity current EA curricula are pretty focussed on just laying out our current best guess and using those examples along with discussion to demonstrate our methodology.

How is EA rational then?

I think the main thing happening in EA is that there is a strong personal, social, and financial incentive for people to approach their work "rationally". E.g people in the community will expect you to have some reasoning which led you to do what you're doing, and they'll feedback on that reasoning if they think it's missing an important consideration. From that spawns a bunch of people thinking about how to reason about this stuff more rationally, and we end up with a big set of techniques or concepts which seem to guide us better.