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<p>Etjon,<br>
<br>
Your Iterated Bucklin method appeals to me more than normal
Bucklin. You have gotten rid of at least some of the Irrelevant
Ballots problem. In my first example below, deleting the 2X
ballots changes the Bucklin winner from B to A.<br>
<br>
But among methods that interpret not-truncated as approval, I
don't see it as a serious contender. I much prefer
Margins-Sorted Approval and Smith//Approval and
Condorcet//Approval. Also close to being in that category is
Smith//Descending Acquiescing Coalitions.<br>
<br>
Chris B.<br>
<br>
</p>
<div class="moz-cite-prefix">On 18/10/2024 3:36 pm, Etjon Basha
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CA+EJN6SaVAt4Yapk4=h8OR8bKTp+TmfrKTwt6jYgna-XCKxs7Q@mail.gmail.com">
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<p class="MsoNormal"><span lang="EN-US">Hi Chris,<span></span></span></p>
<p class="MsoNormal"><span lang="EN-US"> </span></p>
<p class="MsoNormal"><span lang="EN-US">Thank you
for your feedback.<span></span></span></p>
<p class="MsoNormal"><span lang="EN-US"> </span></p>
<p class="MsoNormal"><span lang="EN-US">On the LNHa
failure on the margin scenario (absolute margins was what
I was thinking indeed),
A should win. <span></span></span></p>
<p class="MsoNormal"><span lang="EN-US"><br>
</span></p>
<p class="MsoNormal"><span lang="EN-US">Now, I put somewhat
less weight on LHNa since we’re operating in the
“truncation allowed” paradigm,
and all candidates explicitly ranked are candidates
explicitly endorsed. I would
be halfway OK with my favorite losing to my second
favorite in this case. In
this case, those A voters who gave B the win are hopefully
seeing B as the one
most likely to win, and although they prefer A, they would
think A has far fewer
chances to win. If they had a proper indication of the
relative support of the
two, they would hopefully not have ranked B. <span></span></span></p>
<p class="MsoNormal"><span lang="EN-US"><br>
</span></p>
<p class="MsoNormal"><span lang="EN-US">Of course,
this means that the method is on par with Approval in this
case, defeating the
point of ranking in the first place. But in practice, I
hope it wouldn’t fail
LNHa as often as approval (and require less strategising
of the voter), though it may well fail it more often the
Iterated
Bucklin or the other versions electing from the SCS. I
think it elects Condorcet more often than all
of them though. <span></span></span></p>
<p class="MsoNormal"><span lang="EN-US"><br>
</span></p>
<p class="MsoNormal"><span lang="EN-US">Point taken
on clones too, about whom I didn’t even think about. These
defeat the whole
point of the universal cutoff underpinning the whole set,
a pretty serious
failure indeed.<span></span></span></p>
<p class="MsoNormal"><span lang="EN-US"><br>
</span></p>
<p class="MsoNormal"><span lang="EN-US">Somewhat
interestingly,
my original favorite – electing the candidate who wins by
the least votes – produces A or
Y in both cases, but the method elects the Condorcet loser
(B) in 3A, 6BC, 4C,
5ACB, a very serious failure as well. I suppose then
between clones and the CL,
none of these appear to be much better than Iterated
Bucklin at least. <span></span></span></p>
<p class="MsoNormal"><span lang="EN-US"> </span></p>
<p class="MsoNormal"><span lang="EN-US">Regards, <span></span></span></p>
<p class="MsoNormal"><span lang="EN-US"> </span></p>
<p class="MsoNormal"><span lang="EN-US">Etjon<span></span></span></p>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Fri, Oct 18, 2024 at
2:48 PM Chris Benham <<a
href="mailto:cbenhamau@yahoo.com.au" moz-do-not-send="true"
class="moz-txt-link-freetext">cbenhamau@yahoo.com.au</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<p>Etjon,<br>
<br>
</p>
<blockquote type="cite">
<pre
style="white-space:pre-wrap;color:rgb(0,0,0);font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial">3. Electing the Serious Candidate that wins their cutoff count by
the most approvals *compared to the runner up*. May fail Condorcet the
least. Likely the most sensible of the bunch.</pre>
</blockquote>
Does "compared to the runner up" refer to the absolute
margin or the relative margin? In other words, are we
talking about the margin by the greatest number or the
greatest percentage or ratio? <br>
<br>
Here is my example (from my 2 November 2024 EM post)
designed to highlight the disadvantages of Bucklin compared
with Hare:<br>
<br>
<pre
style="white-space:pre-wrap;color:rgb(0,0,0);font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial">40 A>B
30 B
09 C
02 X
81 ballots
Here your "Serious Candidate" set is A,B and your "likely most sensible" method 3 elects B (70-40 versus 40-30), but I find it absurd and unacceptable to not elect A.
A is a "Dominant Candidate", the number of ballots on which A is voted above all other candidates is greater than A's maximum pairwise opposition.
It seems that your Iterated Bucklin method elects A here.
<a href="https://electowiki.org/wiki/Iterated_Bucklin" target="_blank"
moz-do-not-send="true" class="moz-txt-link-freetext">https://electowiki.org/wiki/Iterated_Bucklin</a>
<blockquote type="cite"><pre
style="white-space:pre-wrap;color:rgb(0,0,0);font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial">5. Electing the Serious Candidate that wins the election if the
cutoff is set at the FPP winner.</pre>
</blockquote>
This would elect A here but (like FPP) fails Clone-Winner.
29 A>Y>B
11 Y>A>B
30 B
09 C
02 X
Y is clone of A. Adding this candidate changes the winner from A to B. (Iterated Bucklin still elects A.)
Chris B.
</pre>
<p><br>
<b
style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial">Etjon
Basha</b><span
style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline"><span> </span></span><a
href="mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20A%20few%20more%20Bucklin%20variants%2C%20because%20why%20not%3F&In-Reply-To=%3CCA%2BEJN6Qj5tsq3%2BR6B_5YLDRA%3DzfRu0DOgMwBXJy7N0RA0Z0RYQ%40mail.gmail.com%3E"
title="[EM] A few more Bucklin variants, because why not?"
style="font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal"
target="_blank" moz-do-not-send="true">etjonbasha at
gmail.com</a></p>
<i
style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial">Sat
Sep 21 04:53:21 PDT 2024</i><span
style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline"></span>
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<li><br>
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<hr
style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial">
<pre
style="white-space:pre-wrap;color:rgb(0,0,0);font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial">Dear gentlemen,
A while ago I did write here about the Iterated Bucklin
<<a href="https://electowiki.org/wiki/Iterated_Bucklin"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://electowiki.org/wiki/Iterated_Bucklin</a>> method on which I’ve
recently had a chance to think and generalize about a bit more. Maybe some
of the below could be novel or otherwise of interest.
First, and for our purposes today, let's define the *Serious Candidates Set*
in the context of a ranked ballot, to include those candidates who would
win an approval count if they served as the approval cutoff across all
ballots.
In the [2:A>B, 3:C>A, 4:A>B] election as an example, the Set would include
A and B only, as applying the cutoff at C would still elect B.
I’ve been checking some random simulations from Kevin Venzke’s
<a href="http://votingmethods.net" target="_blank"
moz-do-not-send="true">votingmethods.net</a>, and here are some properties of this Set that I
*suspect*:
1. If there is a Condorcet Winner, this Set should always include
them.
2. Otherwise, this Set should always partially overlap with the
Smith Set.
Now, quite a few methods emerge once the Serious Candidate Set is isolated
(by actually checking the approval winner once every candidate is used as a
cutoff). The five below allow truncation and equal ranking, and have been
checked (again courtesy of <a href="http://votingmethods.net"
target="_blank" moz-do-not-send="true">votingmethods.net</a>) to ensure that they are
different from one-another and the 40-odd other methods Kevin has
aggregated over there.
So, which member of the Serious Candidate Set should be elected?
1. Electing the Serious Candidate that wins their cutoff count by
the most approvals. Rather obvious but not too much of an improvement over
Approval (if any at all). Terrible Later No Harm failures, though this is
in the context where truncation is allowed. Fails Condorcet.
2. Electing the Serious Candidate that wins their cutoff count by
the *least* approvals. A bit counterintuitive, but winning by the least
means that the winner had to “dip” the least into each approver’s rankings.
If this is not compliant with Later No Harm, it should at least fail
rarely. It would fail Later No Help spectacularly though, indeed having a
huge incentive to always rank your least favorite candidate that is still
likely to win last, instead of leaving them unranked. Unfortunately, I’ve
seen it elect the Condorcet Loser at least once.
3. Electing the Serious Candidate that wins their cutoff count by
the most approvals *compared to the runner up*. May fail Condorcet the
least. Likely the most sensible of the bunch.
4. Iterated Bucklin (now fitting into this generalised family) will
always elect a member of the Set, but it seems to be neither of the three
above with consistency. I cannot seem to find the pattern the method lands
on.
5. Electing the Serious Candidate that wins the election if the
cutoff is set at the FPP winner. If the FPP winner is in the Set to begin
with, they will be elected. Otherwise, again a method that elects a winner
from the set through no obvious pattern. Of particular interest to me since
it’s the only method in here that can be hand-counted with relative ease
(it’s just an FPP count and an approval count after that).
For reference, standard Bucklin may not always elect members of the Set so
cannot be retconned into this tree. I've tested quite a few other methods,
and there are some for which I'm still to find a failure to elect from the
Serious Candidates Set, including Borda and, unsurprisingly, many approval
variations and Approval-Condorcet hybrids.
Just some preliminary thoughts above, hopefully of some interest.
Best regards,
Etjon Basha</pre>
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</blockquote>
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<br>
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