<div dir="ltr"><br><div class="gmail_extra"><br><br><div class="gmail_quote"><br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
Date: Wed, 23 Apr 2014 16:47:01 -0400<br>
From: Jameson Quinn <<a href="mailto:jameson.quinn@gmail.com">jameson.quinn@gmail.com</a>><br>
To: election-methods <<a href="mailto:election-methods@electorama.com">election-methods@electorama.com</a>><br>
Subject: [EM] Fwd: TACC (total approval chain climbing) example<br>
Message-ID:<br>
<<a href="mailto:CAO82iZwN-bEURnbYUzz6qZuswNucYkUr2vYdJnqWoaSv_bOThQ@mail.gmail.com">CAO82iZwN-bEURnbYUzz6qZuswNucYkUr2vYdJnqWoaSv_bOThQ@mail.gmail.com</a>><br>
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<br>
Oops; I mis-replied individually, instead of to the list. Here's what I<br>
said:<br>
----<br>
This thread is interesting. However, it's also very heavy on the acronyms.<br>
Can I ask that when you use an acronym, you make sure it's explained<br>
adequately on the electorama wiki? At a quick check,<br>
<a href="http://wiki.electorama.com/wiki/TACC" target="_blank">http://wiki.electorama.com/wiki/TACC</a> is inadequate and<br>
<a href="http://wiki.electorama.com/wiki/MAM" target="_blank">http://wiki.electorama.com/wiki/MAM</a> is nonexistent.<br>
<br>
As to the discussion: this is really the heart of the chicken dilemma. I<br>
don't think there's any way to look at a set of ballots like<br>
<br>
40 C<br>
35 A>B<br>
25 B<br>
<br>
... and get an answer that's not going to be wrong some of the time. If<br>
these ballots are honest, then B should win. If the B voters are truncating<br>
an honest A second preference, than A would be the ideal winner, but<br>
perhaps the system should choose C in order to discourage that strategy.<br>
And if enough of the B voters are truncating C, you could make an argument<br>
that C is the best winner.<br></blockquote><div><br>
<p class="MsoNormal">Jameson,</p><p class="MsoNormal"><br></p>
<p class="MsoNormal">You are absolutely right about the heart of the Chicken
Dilemma; there is no way to tell from the above ballot set alone who the real winner
should be, because different sincere scenarios <span style> </span>lead to the same set of ballots.<span style> </span>As you mentioned it could well be that A is
the sincere Condorcet candidate, and that the ballots reflect a chicken
challenge by the B faction.<span style> </span>Also it is
entirely possible that B is the sincere Condorcet candidate corresponding to
sincere preferences <br></p><p class="MsoNormal"><br></p>
<p class="MsoNormal">40 C>B, 35 A>B,<span style>
</span>25 B>C,</p><p class="MsoNormal"><br></p>
<p class="MsoNormal">and the voted ballot set represents a defense by the B
faction against a potential attack by the A faction.</p><p class="MsoNormal"><br></p>
<p class="MsoNormal">One way out of this predicament is an interactive method
like SODA.<span style> </span>But until the electorate is
educated and familiar with proxy methods like SODA, what can we do?</p><p class="MsoNormal"><br></p>
<p class="MsoNormal">Another way to solve this dilemma is to make sure that
raising B to equal top by the A faction makes a difference in the winner.<span style> </span>This raising of B makes B the ballot CW, so all
of the methods seriously considered by this EM list elect B in this case.<span style> </span>So if we want this move to make a difference,
A or C should be the winner for the original ballot set, repeated here for convenience:<span style></span></p><p class="MsoNormal"><br>40 C<br>
35 A>B<br>
25 B<br>
</p><p class="MsoNormal"><span style> </span></p>
<p class="MsoNormal">Condorcet(margins) elects A, and so fails the Plurality
Criterion, while the rest of the methods taken seriously on this EM list elect
B or C.<span style> </span>The ones that elect B, including
Condorcet(wv), do not distinguish adequately between the two cases. <br></p><p class="MsoNormal"><br></p>
<p class="MsoNormal">But Woodall, Benham, Implicit Approval Chain Climbing, and
Chris’s new method MaxLV(equal rank whole)Margins all elect C from the original
ballot set.</p><p class="MsoNormal"><br></p>
<p class="MsoNormal">Another way out of this dilemma is to give the voters an
explicit approval cutoff option.<span style> </span>Then the
method should elect respectively B or C according to the strength of the
preference expressed on the A faction ballots: 35 A>B, or 35 A>>B, respectively .</p><p class="MsoNormal"><br></p>
<p class="MsoNormal">Some methods that work this way are Condorcet(approval
margins), Condorcet(winning approval), Smith//Approval, and Majority Enhanced
Approval.<span style> <br></span></p><p class="MsoNormal"><br><span style></span></p><p class="MsoNormal"><span style></span>Another name for
Condorcet(winning approval) is Democratic Majority Choice.<span style> </span>Among all candidates that are not pairwise
beaten by any candidate with greater approval, it elects the one that beats all
of the others.</p><p class="MsoNormal"><br></p>
<p class="MsoNormal">In this example with the A>>B ballots instead of the
A>B ballots, the approval order is C>A>B, which is in line with the
pairwise beat cycle of C>A>B>C, so C is the only candidate not beaten
by an higher approval candidate.<span style> </span>So candidate
C is the DMC winner.<span style> <br></span></p><p class="MsoNormal"><span style><br> </span></p>
<p class="MsoNormal">From the Condorcet(winning approval) point of view, the
defeat where the approval of the winner is smallest is the one in which B
defeats C, since B has the smallest approval of any of the three candidates.<span style> </span>So this is the defeat that is the weak link
in the cycle.</p><p class="MsoNormal"><br></p>
<p class="MsoNormal">In general, a defeat of a candidate by an higher approval
candidate will never be the weakest link in a cycle, whether defeat strength is
measured by winning approval or by approval margins.</p>
<p class="MsoNormal">If there are two defeats directed toward higher approval,
winning approval gives more strength to the one with the higher source, while
approval margins gives more strength to the one with the smallest increase in
approval from source to target.</p><p class="MsoNormal"><br></p>
<p class="MsoNormal">In summary, explicit approval cutoffs and measurement of defeat
strength by winning approval or by approval margins, turns River, Beatpath (Schulze),
and Ranked Pairs into Chicken Proof methods.</p><p class="MsoNormal"><br></p>
<p class="MsoNormal">The winning approval strength versions are familiar to some
of us as DMC.<span style> </span>The methods Smith//Approval
and DMC are analogous to Benham and Woodall, except you replace IRV with
Approval and you replace the IRV elimination order with the approval order
(from lowest to highest).<span style> </span>If you eliminate
candidates from the bottom of the approval list until there is a candidate that
beats all of the rest pairwise, that candidate is the DMC winner.</p><p class="MsoNormal"><br></p>
<p class="MsoNormal">Majority Enhanced Approval (MEA) is practically the same as
Smith//Approval, but is a more seamless way of arriving at the winner.<span style> </span>In the rare cases where they differ, the MEA
winner will be an uncovered candidate that covers the Smith//Approval winner.</p><p class="MsoNormal"><br></p><p class="MsoNormal">Here's the definition of MEA: initialize a list with (the name of) the candidate at the top of the approval list. Then while all of the listed candidates are covered add to the list the name of the highest approval candidate that covers all of the other candidates on the list. Elect the candidate whose name was added to the list last.</p>
<p class="MsoNormal"><br></p><p class="MsoNormal">This MEA winner is a member of Landau, hence Smith. In addition (like Smith//Approval) the method MEA satisfies Independence from Pareto Dominated Alternatives, along with monotonicity, and clone independence (whenever clones are adjacent in the approval order).</p>
<p class="MsoNormal"><br></p><p class="MsoNormal">Because of these nice properties I prefer the use of explicit approval cutoffs. If any voters do not specify an explicit approval cutoff, then their truncations should by default be taken as disapproval,</p>
<p class="MsoNormal"><br></p><p class="MsoNormal">The approval cutoffs allow voters greater ability to make their will known. In some cases they help to discern strong preferences among ranked clones that would otherwise be impossible to express on mere ordinal ballots. Which is a stronger refutation of putative clone status? A new candidate D being ranked between C and C' on a few ballots. or an approval cutoff being placed between them on the same ballots?</p>
<p class="MsoNormal"><br></p><p class="MsoNormal">Where do we go from here?</p><p class="MsoNormal"><br></p><p class="MsoNormal">Forest<br></p><p class="MsoNormal"><br></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
</div></div><br></div></div>