Another reason for LIIA
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
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@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
Election-Methods mailing list - see https://electorama.com/em for list info
All's I know is that Ranked Pairs appears to get LIIA and Schulze does not. And the two methods appear to be equally good in all other respects (and better than everything else): https://en.wikipedia.org/wiki/Ranked_pairs#Comparison_table
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
On 05/29/2026 5:48 PM EDT Kristofer Munsterhjelm via Election-Methods election-methods@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
Election-Methods mailing list - see https://electorama.com/em for list info
On 2026-05-30 22:10, robert bristow-johnson via Election-Methods wrote:
All's I know is that Ranked Pairs appears to get LIIA and Schulze
does not. And the two methods appear to be equally good in all other
respects (and better than everything else) ...
One disadvantage of RP (and I suspect of all Condorcet methods that pass
LIIA) is that you can't have tied outcomes (e.g. A and B tied for first
place); you need to use your tiebreaker inside the method itself.
I don't think that's a problem for large political elections since
pairwise ties are unlikely, just saying that there's some property
where Schulze beats RP.
-km