<html><head></head><body><div class="ydp6c506a05yahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:13px;"><div></div>
<div dir="ltr" data-setdir="false">As Kristofer says, minimising IIA failure (at least with ranked ballots) just means using Condorcet, and I think they would all be equal in that respect. However, even if there is a Condorcet winner, one could still argue, <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">at least sometimes, </span></span>that there has been an IIA failure. Say there are three main candidates - A, B and C. Polls suggest that it's close and that there will be no Condorcet winner, but that A will likely win under the particular method used. C then drops out before the election causing B to win. One might call this an IIA failure.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">The other question is whether C dropping out was a good thing. We went from probably not having a Condorcet winner to having one as a result of C dropping out. Arguably C standing gives us more information overall about voter preferences. And as A would have won if C had stood, A is arguably the most likely "best" winner.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">So while it might be nicer to have a clear Condorcet winner, in situations where it's close enough for there to be a possible cycle if certain candidates stand, arguably it's better if they do stand, causing the cycle and giving us more information.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Toby</div><div><br></div>
</div><div id="ydp8b10e7ecyahoo_quoted_0244402846" class="ydp8b10e7ecyahoo_quoted">
<div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;">
<div>
On Monday, 13 November 2023 at 20:55:48 GMT, Kristofer Munsterhjelm <km_elmet@t-online.de> wrote:
</div>
<div><br></div>
<div><br></div>
<div><div dir="ltr">On 2023-11-13 19:35, Richard, the VoteFair guy wrote:<br clear="none">> Just because it's impossible to get zero IIA failure rates doesn't mean <br clear="none">> "we have to let go of" it, in the sense of not trying to reduce IIA <br clear="none">> failures.<br clear="none">> <br clear="none">> Although all methods fail IIA, measuring HOW OFTEN those failures occur <br clear="none">> is insightful. Some methods have much higher failure rates than others.<br clear="none">> <br clear="none">> As I've said before, I believe reducing failure rates is more important <br clear="none">> than regarding fairness criteria as pass/fail (yes/no) flags that are <br clear="none">> worth counting simplistically.<br clear="none"><br clear="none">Suppose that a majoritarian method fails Condorcet. Then there exist <br clear="none">elections where the CW is X, but the method elects Y. Then eliminating <br clear="none">every candidate but Y and X makes X beat Y, so these elections have IIA <br clear="none">failure.<br clear="none"><br clear="none">Suppose that there's a Condorcet cycle. Then every majoritarian ranked <br clear="none">election method fails IIA: suppose without loss of generality that the <br clear="none">method elects A, and that B beats A pairwise. Eliminating every <br clear="none">candidate but A and B leads B to win, hence an IIA failure.<br clear="none"><br clear="none">Suppose a majoritarian ranked method passes Condorcet and the election <br clear="none">has a Condorcet winner. Then the method passes IIA for that election, <br clear="none">because eliminating any set of non-winning candidates still leaves that <br clear="none">candidate a Condorcet winner.<br clear="none"><br clear="none">So if we want to minimize IIA failure, and IIA failure exists whenever <br clear="none">we can remove a set of candidates who did not win and thus change the <br clear="none">winner, we would want to pass Condorcet.<div class="ydp8b10e7ecyqt3442634398" id="ydp8b10e7ecyqtfd10768"><br clear="none"><br clear="none">-km<br clear="none">----<br clear="none">Election-Methods mailing list - see <a shape="rect" href="https://electorama.com/em" rel="nofollow" target="_blank">https://electorama.com/em</a> for list info<br clear="none"></div></div></div>
</div>
</div></body></html>