There seems to be some confusion about what is meant by “independence of irrelevant alternatives” (IIA). For example, the Wikipedia article says “Most ranked ballot methods and Plurality voting satisfy the Majority Criterion, and therefore fail IIA automatically by the example above.” But Bordes and Tideman, in a 1991 paper, say that all “real-world” voting systems satisfy IIA.

They state that “IIA means that if the voters’ preferences over the potential-but-not-actual candidates change while their preferences over the actual candidates stay the same, then the choice among the actual candidates stays the same.” They say it is NOT a consistency criterion, as it has commonly been understood.

They go on to write:

"Obviously, no voting rule can make any use of information it does not have, and what transformation occurs in the information a rule does not have, whether that information shrinks (regularity) or changes (IIA), does not matter as long as the information the rule has and makes use of does not change.

“So to ask a voting rule to be a regular or an SCF to satisfy IIA means exactly that we want it to represent a possible real-world voting rule and not some fairy-world voting rule. In fact, in the Arrow Theorem we can do without the conditions of Universal Domain, Choice Consistency, and Unanimity and still have a recognizable voting rule, but we cannot do without IIA. For it is IIA (along with Nondictatorship) that ensures that the Arrow Theorem is a theorem about real-world voting rules. Without IIA it would be a theorem about a fairy-world, and hence quite uninteresting.”

What do y’all make of this? It looks to me like the Wikipedia claim quoted above refers to a version of IIA that differs from Arrow’s.