[Election-Methods] independence of mutually irrelevant alternatives?

[Greg]

I'm attempting to classify different kinds of irrelevant alternatives.
In particular, I'm trying to partition irrelevant alternatives into
those that IRV eliminates and those it does not. It seems that IRV
eliminates failures of IIA if and only if it represents a failure of
the mutual majority criterion. That is, IRV is independent of the
addition of any candidate who, when added, belongs to a subset of
candidates S, such that more than half the voters strictly prefer
every candidate outside S to every candidate in S. Could we call this
Independence of Mutually Irrelevant Alternatives (IMIA) criterion? To
make an analogy: the Smith criterion is to Local IIA as as the Mutual
Majority criterion is to IMIA. Let me know if this is already a
well-defined notion.

Greg