<div dir="ltr">Forest,<div><br></div><div>I like the idea of an Approval-Sorted-Margins based method. I think it is simple enough to explain and handles cycles in an transparent fashion. You, Chris and I had some private conversations about this some years back.</div><div><br></div><div>I would prefer an explicit approval cutoff. I think the following version is easy to understand:</div><div><ul><li>Equal rating allowed, rating from 0 to 9 (10 slots)</li><li>Bottom 5 slots (0-4) are disapproved, top 5 slots (5-9) are approved.</li><li>Rank inferred from rating.</li></ul><div>What is Strong FBC, and why doesn't Approval meet it?</div><div><br></div><div>Chris's "tweaked IRV" seems to be a version of DMC/ASM with elimination. Does that elimination change approval cutoffs and other pairwise counts? If not, it could be summable. If it does, and is not summable and doesn't satisfy either FBC or CC, why do you like it?<br></div><div><br></div><div>Ted</div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Jun 27, 2019 at 2:55 PM Forest Simmons <<a href="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</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 dir="ltr">A simple, easy to understand solution!<br></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Jun 26, 2019 at 10:10 PM C.Benham <<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.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 bgcolor="#FFFFFF">
<p>Earlier in response to this I suggested some Condorcet methods.
Here is a non-Condorcet method<br>
that also fills the bill: a tweaked IRV:<br>
<br>
*Voters strictly rank candidates from the top and also give an
approval cutoff, default placement<br>
of which is just below top.<br>
Candidates that are pairwise beaten by a more approved candidate
are disqualified.<br>
If more than one candidate is undisqalified then eliminate the
candidate highest-ranked on the fewest<br>
ballots. Repeat until only one undisqualified candidate remains.
Elect that candidate.*<br>
<br>
As compensation for failing Condorcet, this should keep most of
IRV's resistance to Burial strategy and<br>
be more-or-less immune to the "DH3" pathology. The normal IRV
winner can only lose to a candidate<br>
that both pairwise beats it and is explicitly more approved.<br>
<br>
<a class="gmail-m_2905920860376175872gmail-m_-5528847402285978116moz-txt-link-freetext" href="https://rangevoting.org/DH3.html" target="_blank">https://rangevoting.org/DH3.html</a><br>
<br>
In all 3 of Forest's scenarios all but one candidate is
disqualified.<br>
<br>
Chris Benham<br>
<br>
</p>
<div class="gmail-m_2905920860376175872gmail-m_-5528847402285978116moz-cite-prefix">On 31/05/2019 8:03 am, Forest Simmons
wrote:<br>
</div>
<blockquote type="cite">
<div dir="ltr">
<div>In the example profiles below 100 = P+Q+R, and
50>P>Q>R>0. <br>
</div>
<div>I am interested in simple methods that always ...</div>
<div><br>
</div>
<div>(1) elect candidate A given the following profile:</div>
<div><br>
</div>
<div>P: A</div>
<div>Q: B>>C</div>
<div>R: C,</div>
<div>and <br>
</div>
<div><br>
(2) elect candidate C given</div>
<div>P: A</div>
<div>Q: B>C>></div>
<div>R: C,<br>
</div>
<div>and <br>
</div>
<div><br>
(3) elect candidate B given</div>
<div>
<div>P: A</div>
<div>Q: B>>C (or B>C)<br>
</div>
<div>R: C>>B. (or C>B)<br>
</div>
<div><br>
</div>
<div>I have two such methods in mind, and I'll tell you one of
them below, but I don't want to prejudice your creative
efforts with too many ideas.<br>
</div>
<div><br>
</div>
<div>Here's the rationale for the requirements:</div>
<div><br>
</div>
<div>Condition (1) is needed so that when the sincere
preferences are</div>
<div>
<div>P: A</div>
<div>Q: B>C</div>
<div>R: C>B,</div>
<div>the B faction (by merely disapproving C without
truncation) can defend itself against a "chicken" attack
(truncation of B) from the C faction.</div>
<div><br>
</div>
<div>Condition (3) is needed so that when the C faction
realizes that the game of Chicken is not going to work for
them, the sincere CW is elected.</div>
<div><br>
</div>
<div>Condition (2) is needed so that when sincere
preferences are</div>
<div>
<div>P: A>C</div>
<div>Q: B>C</div>
<div>R: C>A,</div>
<div>then the C faction (by proactively truncating A) can
defend the CW against the A faction's potential
truncation attack.</div>
<div><br>
</div>
<div>Like I said, I have a couple of fairly simple methods
in mind. The most obvious one is Smith\\Approval where
the voters have control over their own approval cutoffs
(as opposed to implicit approval) with default approval
as top rank only.The other method I have in mind is not
quite as simple, but it has the added advantage of
satisfying the FBC, while almost always electing from
Smith.<br>
</div>
</div>
</div>
</div>
</div>
<br>
<fieldset class="gmail-m_2905920860376175872gmail-m_-5528847402285978116mimeAttachmentHeader"></fieldset>
<pre class="gmail-m_2905920860376175872gmail-m_-5528847402285978116moz-quote-pre">----
Election-Methods mailing list - see <a class="gmail-m_2905920860376175872gmail-m_-5528847402285978116moz-txt-link-freetext" href="https://electorama.com/em" target="_blank">https://electorama.com/em</a> for list info
</pre>
</blockquote>
<div id="gmail-m_2905920860376175872gmail-m_-5528847402285978116DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2"><br>
<table style="border-top:1px solid rgb(211,212,222)">
<tbody><tr>
<td style="width:55px;padding-top:13px"><a href="http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient&utm_term=oa-4885-b" target="_blank"><img src="https://static2.avg.com/2000491/web/i/ipm/icon-envelope-tick-green-avg-v1.png" alt="" style="width: 46px; height: 29px;" width="46" height="29"></a></td>
<td style="width:470px;padding-top:12px;color:rgb(65,66,78);font-size:13px;font-family:Arial,Helvetica,sans-serif;line-height:18px">Virus-free. <a href="http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient&utm_term=oa-4885-b" style="color:rgb(68,83,234)" target="_blank">www.avg.com</a>
</td>
</tr>
</tbody></table>
<a href="#m_2905920860376175872_m_-5528847402285978116_DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2" width="1" height="1"> </a></div></div>
</blockquote></div>
----<br>
Election-Methods mailing list - see <a href="https://electorama.com/em" rel="noreferrer" target="_blank">https://electorama.com/em</a> for list info<br>
</blockquote></div>