<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
</head>
<body>
<p>Ted,<br>
<br>
<blockquote type="cite">As a long time fan of Margin Sorted
Approval (AKA <a
href="https://electowiki.org/wiki/Approval_Sorted_Margins">Approval
Sorted Margins</a>), I've been thinking about various ways to
improve it.</blockquote>
<br>
To solve what "problem"?<br>
<br>
<blockquote type="cite">
<div><br>
</div>
<div>I started thinking about how one might implement an
automatic approval cutoff, designed to give each ballot its
own strategically optimal cutoff.</div>
</blockquote>
<br>
Not possible with just ranking information. To revisit the
classical example:<br>
<br>
49 A (presumably sincere, but maybe sincere is A>C)<br>
24 B (sincere may be B>C, that is what the C supporters
believe)<br>
27 C>B (sincere, but could be C>B>>>A or
C>>>B>A)<br>
<br>
If we claim that we are trying to elect the sincere CW and
therefore avoid giving the voters a strong truncation incentive
then the approval cutoffs need to be explicit and manual so as to
squash any post election complaints from losers.<br>
<br>
<blockquote type="cite">
<div><br>
</div>
<div>One reasonable strategy in Approval Voting generally is to
determine, for each ballot, the highest ranked candidate(s)
who are in the Smith Set, and then put the Approval Cutoff
below that rank.</div>
</blockquote>
<br>
In the above example that would mean we interpret the C>B
ballots as giving approval to both C and B, giving the win to B
(as the sole winner by Double Defeat). But then the C supporters
could have a semi-reasonable complaint: "We didn't mean to really
approve of B. We only expressed our weak B>A preference because
we assumed (or were led to believe) that the B supporters would
return the favour by voting B>C. We object to them being
rewarded for their treacherous defection."<br>
<br>
But if the approval cutoffs are explicit any complaint like that
gets a crushing rejoinder. If they voted C>B|>A giving the
win to B, it is "Your complaining about the election of a
candidate you explicitly approved of? You could have prevented B
from being elected by not approving B. You cannot reasonably
expect the voting method to read minds and call C the winner. C
was Doubly Defeated by A."<br>
<br>
Or if they voted C|>B causing A to win and their complaint is
"But we prefer B to A and B pairwise beat A" then the rejoinder is
"If you really wanted B to defeat A why didn't you approve of B?
If you had, then B would have won."<br>
<br>
With an explicit approval cutoff there is no clone issue because
when the method has a ratings element candidates have to have the
same ratings (here being on the same side of the approval cutoff)
to qualify as clones.<br>
<br>
So either we say to the voters "This is an Approval-ish high SU
method, so we are not interested in your rankings among unapproved
candidates" or we say "We are interested in whatever ranking you
care to express and if there is a top cycle then your approval
cutoffs will help determine the winner".<br>
<br>
I am open to both but prefer the second because it allows greater
voter expression. In the first case we need a method that meets
Double Defeat (Implicit) and in the second one that meets Double
Defeat(Explicit).<br>
<br>
My favourites are MSA(implicit) and MSA(explicit), but the two
versions of Smith//Approval also fill the bill and are not bad.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
</p>
<div class="moz-cite-prefix">On 22/10/2024 9:02 am, Ted Stern wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAHGFzOR1zg_GPiVyRnOib2nsH3pBaAs1jYQDuqkZj0vkju3shQ@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="ltr">As a long time fan of Margin Sorted Approval (AKA <a
href="https://electowiki.org/wiki/Approval_Sorted_Margins"
moz-do-not-send="true">Approval Sorted Margins</a>), I've been
thinking about various ways to improve it.
<div><br>
</div>
<div>I started thinking about how one might implement an
automatic approval cutoff, designed to give each ballot its
own strategically optimal cutoff.</div>
<div><br>
</div>
<div>One reasonable strategy in Approval Voting generally is to
determine, for each ballot, the highest ranked candidate(s)
who are in the Smith Set, and then put the Approval Cutoff
below that rank.</div>
<div><br>
</div>
<div>But what happens if there is a Condorcet cycle, and the
candidate who would ordinarily win in Approval voting ("A")
using that strategy is cloned ("A1, A2, A3"). and there is a
cycle in that clone set? With the strategy.above, the approval
cutoff will be placed just below the top clone on the ballot.
This would cause a split of approval for the A# candidates,
affecting not only Margin Sorted Approval but also Approval
Voting more generally.</div>
<div><br>
</div>
<div>This special case seems highly unlikely, but it points to a
cloning resistance issue with any Approval augmented Condorcet
method.</div>
<div><br>
</div>
<div>Thoughts?</div>
</div>
<br>
<fieldset class="moz-mime-attachment-header"></fieldset>
<pre wrap="" class="moz-quote-pre">----
Election-Methods mailing list - see <a class="moz-txt-link-freetext" href="https://electorama.com/em">https://electorama.com/em</a> for list info
</pre>
</blockquote>
</body>
</html>