Eliezer advocates the "rationality is about winning" position, as timtyler note sin his reply to you.

And this is actually a Humean point. The idea is that passion is about what you want i.e. want qualifies as winning and rationality is about getting what you want i.e. how to go about winning.

As for Mr Bagehot's preference set, it's true that transitivity is a necessary condition for rationality because an agent with intransitive preferences has no coherent utility function.

However, I don't think that's an issue here. Bagehot's preferences are dependant on others, but that doesn't make them intransitive. I fact there's no way to test for intransitivity with fewer than three alternatives to choose from.