It's unclear what is meant in the rules:
Determine Turn Order (page 21)
In a mental conflict, compare your Careful approach—attention to detail will warn you of danger.
What "danger" is it referring to?
The "danger" is the ensuing conflict where one or more opponents are going to try and take you out. For mental conflicts, using Careful to determine turn order rewards those who pay attention to what things that are being said, how they are being said, body language, and so forth.
This means that when a Roman Senator is about to try and make you look like a fool in the baths to undermine you with the rest of the Senate, you know what is about to happen and can react first.