"Say there are some alternatives to choose among. They could be policies, public projects, candidates in an election, distributions of income and labour requirements among the members of a society, or just about anything else. There are some people whose preferences will inform this choice, and the question is: which procedures are there for deriving, from what is known or can be found out about their preferences, a collective or “social” ordering of the alternatives from better to worse?"
Keep reading. This one is more than just math.
It just means that those "apparently quite reasonable assumptions" weren't reasonable after all and must be relaxed a bit according to a precise definition.
You just took a mathematical theorem and went into a completely unrelated tangent. It's as if someone says there's no point in keeping development schedule because temporal order is relative to the observer.
Please don't do that.