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Peter Barath wrote:<br>
<blockquote type="cite">
<pre wrap="">And what about the method (I don't know the name) in which
the least approved candidate is eliminated until there is
a Condorcet-winner?</pre>
</blockquote>
That is called "Definite Majority Choice". It has some alternative
algorithms.<br>
<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/Definite_Majority_Choice">http://wiki.electorama.com/wiki/Definite_Majority_Choice</a><br>
<br>
<blockquote type="cite">
<pre wrap="">Does it also fail FBC?</pre>
</blockquote>
<br>
Yes. All methods that meet the Condorcet criterion fail FBC. Condorcet
is incompatible<br>
with FBC. Kevin's "adjustment" of Condorcet//Approval to meet FBC
causes it to no<br>
longer strictly meet the Condorcet criterion.<br>
<br>
<blockquote type="cite">
<pre wrap="">Did somebody
analyse the strategy incentives then?</pre>
</blockquote>
Yes, it has been discussed a lot at EM. It used to be my favourite.<br>
<br>
31: A>>B<br>
32: B>>C<br>
37: C>>A<br>
<br>
Leaving aside the approval cutoffs, methods that don't elect C here
must fail mono-raise.<br>
With these rankings and also C being the most approved candidate, for
me a method needs<br>
a good excuse for not electing C. <br>
<br>
DMC and also "Approval-Weighted Pairwise" both elect C. <br>
<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/Cardinal_pairwise">http://wiki.electorama.com/wiki/Cardinal_pairwise</a><br>
<br>
I like "Approval-Sorted Margins".<br>
<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/Approval_Sorted_Margins">http://wiki.electorama.com/wiki/Approval_Sorted_Margins</a><br>
<br>
I also like using that method to find the lowest-ordered candidate,
eliminate that candidate, and then<br>
repeat the process until one remains, each time interpreting ballots
that make no approval distinction<br>
among remaining candidates as approving all except those they rank
(among the remaining candidates)<br>
bottom or equal-bottom. (I think that is also good for plain ranked
ballots that allow truncation but not<br>
an explicit approval cutoff.)<br>
<br>
An algorithm that is equivalent or nearly equivalent to ASM is to use
one of Beatpath, River or Ranked Pairs<br>
measuring the 'defeat strength' by the difference between the two
candidates' approval scores. I proposed this<br>
a while ago as "Approval Margins".<br>
<br>
Chris Benham<br>
<br>
<br>
<blockquote cite="mid200708202239.14795.peb@freemail.hu" type="cite">
<blockquote type="cite">
<pre wrap="">By the way, electing from the Condorcet top tier using approval
would be called Smith//Approval or Schwartz//Approval depending on
which top tier is used. I don't typically consider these methods
because they are more complicated than Condorcet//Approval and
can't be adjusted to satisfy FBC.
</pre>
</blockquote>
<pre wrap=""><!---->
And what about the method (I don't know the name) in which
the least approved candidate is eliminated until there is
a Condorcet-winner? Does it also fail FBC? Did somebody
analyse the strategy incentives then?
(And here I don't think of a method in which all ranked
candidates are considered as approved, but a whole preference
order with a cutoff mark somewhere between.)
Peter Barath
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</pre>
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