Responding mostly to your first bit rather than the circular preferences.
But note, now, that the course of action I just said was “obviously” correct involves going “the wrong way” across the arrow connecting A to B.
This isn’t a failure of greedy maximization, but rather a failure of following your proposal in the first “diagrams” section about including everything you care about into the graph.
That is, having a reachable path from A → B and B → C but not A → C implicitly means that you care about the ordering, like as a sense of time or the effects of being in state B. You’ve failed to encode your preferences into the graph, because that is a valid set of preferences by itself.
A common way of “fixing” this is to just say the graph must be transitive. If there’s a path from A → B and B → C there must be on from A → C, likely defined by composition like your proposed plan.
Of course, here I’m taking the position of an arrow meaning the agents prefer going down an arrow and prefers that as a route. If you don’t have a route from A → C, then there must be some fact of the world that makes moving through B a problem.
I think your first sections confusion is just not actually putting all the relevant information into the graph.
Responding mostly to your first bit rather than the circular preferences.
This isn’t a failure of greedy maximization, but rather a failure of following your proposal in the first “diagrams” section about including everything you care about into the graph.
That is, having a reachable path from A → B and B → C but not A → C implicitly means that you care about the ordering, like as a sense of time or the effects of being in state B. You’ve failed to encode your preferences into the graph, because that is a valid set of preferences by itself.
A common way of “fixing” this is to just say the graph must be transitive. If there’s a path from A → B and B → C there must be on from A → C, likely defined by composition like your proposed plan.
Of course, here I’m taking the position of an arrow meaning the agents prefer going down an arrow and prefers that as a route. If you don’t have a route from A → C, then there must be some fact of the world that makes moving through B a problem. I think your first sections confusion is just not actually putting all the relevant information into the graph.