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<p><br>
49 A (sincere might be A>B)<br>
24 B<br>
27 C>B<br>
<br>
This is the classic example used by fans of the Minimal Defense
criterion to attack any method that elects A here, like IRV and
Margins.<br>
<br>
More than half the voters rank B above A and A no higher than
equal-bottom, and yet (failing MD) A wins. <br>
<br>
A big point for it is that the 27 C>B voters have reason to
regret not compromising and voting B>C.<br>
<br>
With this method, if their main concern is to defeat A they can
mark B as approved and achieve that goal without having to
insincerely<br>
order-reverse.<br>
<br>
A is the IRV winner. B will be the candidate with the most
approval opposition to A. B pairwise beats A. All the ballots
that rank B already<br>
truncate just below B, so B wins.<br>
<br>
The MD criterion has gone a bit out of fashion because it directly
contradicts the Chicken Dilemma criterion.<br>
<br>
49 A <br>
24 B (sincere is B>C)<br>
27 C>B<br>
</p>
<p>That says that the B faction should not be able to steal the
election from B by this defection (insincere truncation against a
faction that is giving<br>
yours its second-preference votes). Normal IRV meets CD.<br>
<br>
Here if the C>B voters have maybe not such a strong B>A
preference and want to guard against being stung by Defection,
then they can not<br>
mark B as approved. Then C will be the candidate with the most
approval opposition to the IRV winner A. A wins that pairwise
comparison and<br>
so is elected.<br>
<br>
The reason for the last part of the method in the full version is
that without it I fear that some voters might be able to rank one
or more extra <br>
candidates that changes the IRV winner from one that wins the
pairwise comparison against a candidate they prefer to one that
loses it,<br>
thereby breaking LNHelp.<br>
<br>
Chris B.<br>
<br>
<br>
<br>
</p>
<div class="moz-cite-prefix">On 6/08/2023 1:37 pm, Forest Simmons
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CANUDvfqq-TwhVHy4__pL9Ssc2YE-bhosDTw4TYtG4zC7f9s4ng@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="auto">For us old lazy guys who sometimes need help
seeing the obvious ... how about a couple of pertinent examples
with their most pertinent features high lighted?</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sat, Aug 5, 2023, 8:29 PM
C.Benham <<a href="mailto:cbenham@adam.com.au"
moz-do-not-send="true" class="moz-txt-link-freetext">cbenham@adam.com.au</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">This idea is
inspired by our recent and ongoing "war on Burial".<br>
<br>
Approval-enhanced IRV<br>
<br>
*Voters strictly rank from the top however many candidates
they choose <br>
and have the option of<br>
marking their highest-ranked approved candidate. Default
approval is to <br>
only the candidate ranked<br>
above all others.<br>
<br>
Find the winner of the pairwise comparison between the IRV
winner and <br>
the candidate X with the most<br>
approval opposition to the IRV winner.<br>
<br>
The IRV winner is elected if it wins (or say if ties) that
pairwise <br>
comparison.<br>
<br>
If X wins it, then do the whole thing again as if all ballots
truncate <br>
just below X.<br>
<br>
If that doesn't produce a new winner, then elect X.<br>
<br>
If it does, then elect the original IRV winner.*<br>
<br>
This should hang on to LNHelp while meeting modified versions
of LNHarm <br>
and Minimal Defense.<br>
<br>
Here is a maybe-good-enough-most-of-the-time shorter prettier
variation:<br>
<br>
*Voters strictly rank from the top however many candidates
they choose <br>
and have the option of<br>
marking their highest-ranked approved candidate. Default
approval is to <br>
only the candidate ranked<br>
above all others.<br>
<br>
If the IRV winner is also the most approved candidate then it
is elected.<br>
<br>
Otherwise elect the winner of the pairwise comparison between
the IRV <br>
winner and the candidate<br>
with the most approval opposition to the IRV winner.*<br>
<br>
Not a Condorcet method and probably nothing like a practical
proposal.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
<br>
</blockquote>
</div>
</blockquote>
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