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<div dir="ltr" data-setdir="false">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.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Toby</div><div><br></div>
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On Saturday, 30 May 2026 at 16:32:07 BST, Kristofer Munsterhjelm via Election-Methods <election-methods@lists.electorama.com> wrote:
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<div><div dir="ltr">The Guardian 100 Best Novels thread got me thinking about a possible <br></div><div dir="ltr">additional benefit of LIIA (which may seem arbitrary otherwise).<br></div><div dir="ltr"><br></div><div dir="ltr">Suppose you have an election with 100 candidates. You want to analyze <br></div><div dir="ltr">some properties of the top five in more detail, which is hard to do with <br></div><div dir="ltr">the full 100. Then if the election method in use passes LIIA, you know <br></div><div dir="ltr">that you can just batch-eliminate the 95 losers and the method's <br></div><div dir="ltr">behavior among those top five will be the same.<br></div><div dir="ltr"><br></div><div dir="ltr">Most likely, the Smith set won't be five large, so you can do that with <br></div><div dir="ltr">any ISDA method. But LIIA may be useful in saying that there's never <br></div><div dir="ltr">going to be a situation where this goes wrong: where truncating at the <br></div><div dir="ltr">five best produces a different outcome.<br></div><div dir="ltr"><br></div><div dir="ltr">Granted, since Smith sets usually are small and you can get the same <br></div><div dir="ltr">benefit by using an elimination method, it's not a strong case for <br></div><div dir="ltr">wanting LIIA. But even though it's not a strong case for LIIA, it has <br></div><div dir="ltr">some justification. Elimination methods also often have monotonicity <br></div><div dir="ltr">problems or chaotic behavior that LIIA methods don't, which I suppose is <br></div><div dir="ltr">due to LIIA being a more demanding global criterion, so that designing <br></div><div dir="ltr">something to pass it makes it unlikely that you fail monotonicity just <br></div><div dir="ltr">because "the pieces don't fit together", so to speak.<br></div><div dir="ltr"><br></div><div dir="ltr">-km<br></div><div dir="ltr">----<br></div><div dir="ltr">Election-Methods mailing list - see <a href="https://electorama.com/em" rel="nofollow" target="_blank">https://electorama.com/em</a> for list info<br></div></div>
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