I was trying to assume maximum ignorance - maximum uncertainty as to who you might meet, and their abilities and values.

If you have a better idea as to what you face, then you can start shopping around bargaining solutions to get the one you want. And in your example, Alice would certainly prefer KSBS and NBS over PMWBS, which she would prefer over MWBS.

But if, for instance, Dave had slightly less resources that Alice, then it's no longer true. And if any of them depart from (equal) linear utility in every single resource, then it's likely no longer true either.