[EM] Automatic LIIA Independent of Locking Order

[Kristofer Munsterhjelm]

On 2026-05-01 16:42, Kevin Venzke via Election-Methods wrote:
>   Hi Gustav,
> 
> Le vendredi 1 mai 2026 à 08:52:30 UTC−5, Gustav Thorzen via Election-Methods <election-methods at lists.electorama.com> a écrit :
>> 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
> 
> I've never implemented Ranked Pairs as locking multiple defeats at the same time,
> since there could be cyclic incompatibilities introduced by this. Instead I try to
> traverse all possible orderings (or agree on a random tiebreaker for pairs ahead of
> time). That's not very convenient for proofs, I guess.

This seems related to something I suspect: that the process itself needs 
some kind of tiebreaker, and that you can't propagate ties up to the 
final ranking.

I wrote a post about it here: 
http://lists.electorama.com/pipermail/election-methods-electorama.com/2025-January/006813.html

For new combinations of criteria, I think it would be useful to look at 
three-candidate elections first and see if any patterns stand out. 
That's how I figured out the whole resistant set concept, at least. But 
even that's hard: does there exist a three-candidate method that passes 
all of MMPO's criteria without its extreme Plurality failures? Who knows.

-km