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<blockquote type="cite">In the example profiles below 100 = P+Q+R,
and 50>P>Q>R>0. One consequence of these
constraints is that in all three profiles below the cycle
A>B>C>A will obtain.</blockquote>
<blockquote type="cite">
<div>(3) elect candidate B given</div>
<div>P: A</div>
<div>Q: B>>C (or B>C)<br>
</div>
R: C>>B. (or C>B)</blockquote>
<br>
Forest,<br>
In your profile (3), isn't B simply the Condorcet winner? (And
so there is no "cycle A>B>C>A")<br>
<br>
You presumably have in mind that the ballot will allow voters
indicate an approval threshold in their rankings. In that case one
method fills the bill is good old<br>
Approval Sorted Margins:<br>
<br>
<a href="https://wiki.electorama.com/wiki/Approval_Sorted_Margins">https://wiki.electorama.com/wiki/Approval_Sorted_Margins</a><br>
</p>
<div class="moz-cite-prefix">I think that method is somewhat better
at resisting Burial than Smith//Approval(explicit), which in this
April 2002 EM post by Adam Tarr is called<br>
"Approval-Completed Condorcet":<br>
<a class="moz-txt-link-freetext" href="http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html">http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html</a><br>
<blockquote type="cite"><span style="display: inline !important; float: none; background-color: transparent; color: rgb(0, 0, 0); font-family: Consolas; font-size: 13.33px; font-style: normal; font-variant: normal; letter-spacing: normal; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: pre-wrap; word-spacing: 0px;"><font size="+1">The following are the sincere preferences of my example electorate:
49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush</font></span><b><span style="display: inline !important; float: none; background-color: transparent; color: rgb(0, 0, 0); font-family: Consolas; font-size: 13.33px; font-style: normal; font-variant: normal; letter-spacing: normal; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: pre-wrap; word-spacing: 0px;">
</span></b></blockquote>
<blockquote type="cite"><span style="display: inline !important; float: none; background-color: transparent; color: rgb(0, 0, 0); font-family: Consolas; font-size: 13.33px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: pre-wrap; word-spacing: 0px;"><font size="+1">Say that some of the Gore>Bush>Nader voters were extremely non-strategic and decided to approve
both Bush and Gore. So the votes now look like:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush</font>
<font size="+1">
Now, Bush wins the approval runoff 55-51-33. This is where ACC's favorite
betrayal scenario comes in. Since Bush wins the approval vote, the only
way the majority can guarantee a Gore win is to make Gore the initial
Condorcet winner, which requires that the Nader camp vote Gore in first place.</font></span></blockquote>
<br>
Where Smith//explicit Approval fails, Approval Sorted Margins
easily elects the sincere Condorcet winner. <br>
</div>
<div class="moz-cite-prefix"><br>
Gore's approval score is 51 and Nader's is 33. Both adjacent pairs
(B-N and N-B) are pairwise out of order. The gap between 55 and
51<br>
is (much) smaller than that between 51 and 33, so we flip the
order of that pair to give the final order N>B>G which has
no adjacent <br>
pair out of order pairwise.<br>
</div>
<div class="moz-cite-prefix"><br>
Also giving the same result would be to use Approval(explicit)
Margins as the measure of defeat strength in a traditional
Condorcet method<br>
like Schulze or Ranked Pairs or Smith//MinMax.<br>
<br>
Chris Benham<br>
<br>
On 31/05/2019 8:03 am, Forest Simmons wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAP29onet+O9hCZJ6hvNnnpUWNyrDkKa9xFXrX5P-RPoF6ndtfw@mail.gmail.com">
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<div dir="ltr">
<div>In the example profiles below 100 = P+Q+R, and
50>P>Q>R>0. One consequence of these constraints
is that in all three profiles below the cycle A>B>C>A
will obtain.<br>
</div>
<div><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>(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>(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>
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