Here's a confusion I have about preference orderings in decision theory.

Caveat: the observations I make below feel weirdly trivial to me, to the point that I feel wary of making a post about them at all; the specter of readers rolling their eyes and thinking "oh he's just talking about X in a really weird way" looms large in my mind as I type. It feels like I'm probably just unaware of some standard term or concept in the literature, which would make everything "snap into place" if I knew about it. If so, let me know.

diagrams

Let's say I draw something like this:

Here, the letters represent something like "world states," and an arrow like <span>_mathrm{A} rightarrow mathrm{C}_</span> means "C is preferred to A (by the 'agent' whose preferences this graph describes)."