*Post by Greg Dennis*The 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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