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Jameson Quinn wrote (18 Oct 2010):<br>
<blockquote type="cite">
<pre>I edited Electowiki to essentially replace the Bucklin-ER article with a
new, expanded MCA article. In this article, I define 6 MCA variants. I find
that as a class, they do surprisingly well on criteria compliance. Please
check my work:
<a
href="http://wiki.electorama.com/wiki/Majority_Choice_Approval#Criteria_compliance">http://wiki.electorama.com/wiki/Majority_Choice_Approval#Criteria_compliance</a>
</pre>
</blockquote>
<br>
<blockquote type="cite">
<h2><span class="mw-headline" id="Criteria_compliances">Criteria
compliances </span></h2>
<p>All MCA variants satisfy the <a
href="http://wiki.electorama.com/wiki/Plurality_criterion"
title="Plurality criterion">Plurality criterion</a>, the <a
href="http://wiki.electorama.com/wiki/Majority_criterion_for_solid_coalitions"
title="Majority criterion for solid coalitions" class="mw-redirect">Majority
criterion for solid coalitions</a>, <a
href="http://wiki.electorama.com/wiki/Monotonicity_criterion"
title="Monotonicity criterion">Monotonicity</a> (for MCA-AR, assuming
first- and second- round votes are consistent), and <a
href="http://wiki.electorama.com/wiki/Minimal_Defense_criterion"
title="Minimal Defense criterion">Minimal Defense</a> (which implies
satisfaction of the <a
href="http://wiki.electorama.com/wiki/Strong_Defensive_Strategy_criterion"
title="Strong Defensive Strategy criterion">Strong Defensive Strategy
criterion</a>). </p>
</blockquote>
<br>
It is well known that in general run-off methods fail mono-raise (aka
Monotonicity), and these methods <br>
are no exception.<br>
<br>
22: A<br>
23: A>C<br>
24: B<br>
27: C>B<br>
02: D>C<br>
06: E<br>
(104 ballots)<br>
<br>
TR scores: A45, B24, C27, D2, E6.<br>
Approval scores: A45, B51, C52, D2, E6.<br>
<br>
I am assuming that 3-slot ballots are used, and since no candidate has
either a Top Ratings or Approval<br>
score that reaches the majority threshold the runoff will be between
the TR winner A and the Approval<br>
winner C. <br>
<br>
A wins that runoff 45-29, but if the 2 D>C ballots change to D>A
the Approval winner changes to B and<br>
now A loses that runoff 47-49.<br>
<br>
22: A<br>
23: A>C<br>
24: B<br>
27: C>B<br>
02: D>A (was D>C)<br>
06: E<br>
(104 ballots)<br>
<br>
TR scores: A45, B24, C27, D2, E6.<br>
Approval scores: A47, B51, C50, D2, E6.<br>
<br>
Also I would quibble that methods that use ballots that don't allow
voters to express a full ranking of the <br>
candidates really properly meet Majority for Soild Coalitions, but
instead just meet a restricted form of<br>
it (which is nonetheless very valuable).<br>
<br>
And I'm surprised that a MCA advocate doesn't mention the Favourite
Betrayal criterion. Of course the<br>
suggested runoff "variants of MCA" also fail that.<br>
<br>
Chris Benham<br>
<br>
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