[EM] Another reason for LIIA

[Toby Pereira]

 Yes, this does make sense. Also, regardless of the Smith set, candidates in any position can be involved in a cycle, so presumably having LIIA would still be useful in this regard.
Toby
    On Saturday, 30 May 2026 at 16:32:07 BST, Kristofer Munsterhjelm via Election-Methods <election-methods at lists.electorama.com> wrote:  
 
 The Guardian 100 Best Novels thread got me thinking about a possible 
additional benefit of LIIA (which may seem arbitrary otherwise).

Suppose you have an election with 100 candidates. You want to analyze 
some properties of the top five in more detail, which is hard to do with 
the full 100. Then if the election method in use passes LIIA, you know 
that you can just batch-eliminate the 95 losers and the method's 
behavior among those top five will be the same.

Most likely, the Smith set won't be five large, so you can do that with 
any ISDA method. But LIIA may be useful in saying that there's never 
going to be a situation where this goes wrong: where truncating at the 
five best produces a different outcome.

Granted, since Smith sets usually are small and you can get the same 
benefit by using an elimination method, it's not a strong case for 
wanting LIIA. But even though it's not a strong case for LIIA, it has 
some justification. Elimination methods also often have monotonicity 
problems or chaotic behavior that LIIA methods don't, which I suppose is 
due to LIIA being a more demanding global criterion, so that designing 
something to pass it makes it unlikely that you fail monotonicity just 
because "the pieces don't fit together", so to speak.

-km
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