Post by Greg DennisThe IIA page
<http://wiki.electorama.com/wiki/Independence_of_irrelevant_alternatives> of
"Neither the Borda count, Coombs' method nor Instant-runoff voting
satisfies the less strict criteria above."
But doesn't instant runoff satisfy IPDA? A Pareto-dominated candidate
will necessarily have no first preferences and be eliminated
immediately, as if they never existed, right?
IPDA compliance can be rather tricky to verify because it's one of those
things where it seems obvious that a method should satisfy it, yet it's
not always so.
But I think you're right. It is a consequence of Plurality passing IPDA
in the strong sense that all Pareto-dominated candidates end up tied for
last place with zero first preferences.
And since it's impossible for a candidate that has zero first
preferences to get any from the elimination of another candidate that
has zero first preferences (as long as there are a finite number of
candidates in total), they'll all be eliminated at the start of IRV.
The more general observation would be something like:
If X is a method that ranks every candidate in a particular sort of set
S last, and X is independent of candidates in set S, then the
loser-elimination method based on repeatedly eliminating the loser
according to X is also independent of candidates in set S.
In IRV's case, X is Plurality and S is the set of candidates with zero
first preferences.
A consequence of this is that if you're doing IRV, you can batch
eliminate every candidate with zero first preferences without having to
do a recount between each round.
If I were to guess, I'd guess that either the person who wrote that
statement on the wiki was just wrong, or he wrote it, and then only
later was IPDA added to the list of IIA-like criteria (by someone else).
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