Universality particularly seems to be unnecessary for electoral systems, and I'm unconvinced that IIA is an appropriate criteria though it has some intuitive appeal.
Hm, I think that narrowly IIA is important - changes low down the list shouldn't effect what's high up in the list, or people will be discouraged from voicing their true opinion about the options they perceive as less popular. In the full sense, which includes changes at the top affecting things lower, it may not be necessary.
I don't think I'm currently grokking universality with the depth I need to assess it. I remember it seeming reasonable when I did dig deep in all this, ages back.