[EM] Automatic LIIA Independent of Locking Order

[Toby Pereira]

 I'm not sure if this relates to your question at all, but any method can easily be converted to an LIIA-passing method, without changing the winner. Instead of using the method's "natural" finishing order, declare just the winner initially and then for 2nd place, remove the winner from the process and find the new winner and declare them to be 2nd, and so on.
Going off on a tangent, I've always felt that LIIA has somehow found its way into the "standard list" of election method criteria without any proper scrutiny of its utility. It's not clear what purpose it serves. It sounds good because it has "IIA" in it, but it doesn't really have much, if anything, to do with the IIA criterion. It's certainly not a stepping stone towards it.
I think when I mentioned this before, Kristofer said that if the winner drops out for some reason, then you can just elect 2nd place as the order wouldn't change if you ran the election again without the original winner. But the flipside of this is that after the election, 2nd place might be found to be ineligible for some reason, and there would be some elections where an LIIA-failing method would save you from the embarrassment of the original 3rd placed candidate becoming the new winner.
In any case, given how easy it is to make a method LIIA compliant, if your favourite method doesn't pass LIIA, it's no barrier to still using a method that elects the same winner (which is the most important thing in a single-winner election), further bringing its relevance into question.
Toby
    On Friday, 1 May 2026 at 14:57:20 BST, Gustav Thorzen via Election-Methods <election-methods at lists.electorama.com> wrote:  
 
 Ranked Pairs satisfy Local Independence of Irrelevant Alternatives criterion,
but I got curious if this property is obtained independently of locking order.

For context, ISDA comes independently of locking order,
but ISDA is implied by LIIA + Majority criterion,
so I got curious if LIIA is what actually is obtained
and ISDA simply followed from it.

I tried to create a proof for a positive result,
but quickly discovered I could not figure out how
to cover scenarios containing multiple matchups
to be locked in at the same time.

Any help would be much appreciated.
Gustav

P.S: I have started to suspect I need to fail LIIA
for a MMPO locking order to satisfy all of
AFB+Mono+LN-Harm+MB-ISDA
unless LIIA satisfaction is automatic independently of locking order,
and then figured it was interesting enough of a question on its own.

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