Yeah, that's the point. The initial preference function will guide the whole process; unless you change after each step the preference function used to compare,

Yeah, that's the point. The initial preference function will guide the whole process; unless you change after each step the preference function used to compare, in which case it may never converge to a stable point. And even if it converges, different initial functions could guide to totally different final results. That would make it hard to call any chosen function as "strictly better than any other".