[EM] Error on wiki IIA page?

[Kristofer Munsterhjelm]

On 01/14/2018 12:02 AM, Greg Dennis wrote:
> The IIA page
> <http://wiki.electorama.com/wiki/Independence_of_irrelevant_alternatives> of
> the wiki says:
>   "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).