Re: Another reason for LIIA
Toby Pereira via Election-Methods <[email protected]> Sat, 30 May 2026 15:47:13 +0000 (UTC)
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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 <[email protected]> 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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<html><head></head><body><div class=3D"ydpfb2c7ffeyahoo-style-wrap" style=
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;"><div></div>
<div dir=3D"ltr" data-setdir=3D"false">Yes, this does make sense. A=
lso, regardless of the Smith set, candidates in any position can be involve=
d in a cycle, so presumably having LIIA would still be useful in this regar=
d.</div><div dir=3D"ltr" data-setdir=3D"false"><br></div><div dir=3D"ltr" d=
ata-setdir=3D"false">Toby</div><div><br></div>
=20
</div><div id=3D"ydpd8d0a5c0yahoo_quoted_0414273692" class=3D"ydpd8=
d0a5c0yahoo_quoted">
<div style=3D"font-family:'Helvetica Neue', Helvetica, Arial, s=
ans-serif;font-size:13px;color:#26282a;">
=20
<div>
On Saturday, 30 May 2026 at 16:32:07 BST, Kristofer=
Munsterhjelm via Election-Methods <[email protected]=
m> wrote:
</div>
<div><br></div>
<div><br></div>
=20
=20
<div><div dir=3D"ltr">The Guardian 100 Best Novels thread g=
ot me thinking about a possible <br></div><div dir=3D"ltr">additional benef=
it of LIIA (which may seem arbitrary otherwise).<br></div><div dir=3D"ltr">=
<br></div><div dir=3D"ltr">Suppose you have an election with 100 candidates=
. You want to analyze <br></div><div dir=3D"ltr">some properties of the top=
five in more detail, which is hard to do with <br></div><div dir=3D"ltr">t=
he full 100. Then if the election method in use passes LIIA, you know <br><=
/div><div dir=3D"ltr">that you can just batch-eliminate the 95 losers and t=
he method's <br></div><div dir=3D"ltr">behavior among those top five will b=
e the same.<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">Most likel=
y, the Smith set won't be five large, so you can do that with <br></div><di=
v dir=3D"ltr">any ISDA method. But LIIA may be useful in saying that there'=
s never <br></div><div dir=3D"ltr">going to be a situation where this goes =
wrong: where truncating at the <br></div><div dir=3D"ltr">five best produce=
s a different outcome.<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr"=
>Granted, since Smith sets usually are small and you can get the same <br><=
/div><div dir=3D"ltr">benefit by using an elimination method, it's not a st=
rong case for <br></div><div dir=3D"ltr">wanting LIIA. But even though it's=
not a strong case for LIIA, it has <br></div><div dir=3D"ltr">some justifi=
cation. Elimination methods also often have monotonicity <br></div><div dir=
=3D"ltr">problems or chaotic behavior that LIIA methods don't, which I supp=
ose is <br></div><div dir=3D"ltr">due to LIIA being a more demanding global=
criterion, so that designing <br></div><div dir=3D"ltr">something to pass =
it makes it unlikely that you fail monotonicity just <br></div><div dir=3D"=
ltr">because "the pieces don't fit together", so to speak.<br></div><div di=
r=3D"ltr"><br></div><div dir=3D"ltr">-km<br></div><div dir=3D"ltr">----<br>=
</div><div dir=3D"ltr">Election-Methods mailing list - see <a href=3D"https=
://electorama.com/em" rel=3D"nofollow" target=3D"_blank">https://electorama=
.com/em</a> for list info<br></div></div>
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