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Andrew,<br>
Oops! In my last message a reference to "other IRV methods" should
have read "other Condorcet methods".<br>
<blockquote type="cite">In common with IRV and Schulze it meets the
Plurality criterion and Clone Independence. In common <br>
with other IRV methods, we lose IRV's Later-no-Harm and Mono-add-Top.</blockquote>
should read:<br>
<blockquote type="cite">In common with IRV and Schulze it meets the
Plurality criterion and Clone Independence. In common <br>
with other Condorcet methods, we lose IRV's Later-no-Harm and
Mono-add-Top. <br>
</blockquote>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
The entire corrected message:<br>
<br>
<br>
Andrew Myers wrote:
<br>
<br>
<blockquote type="cite">Here's an obvious idea that must have been
considered before. How about using the basic Condorcet method, but
running IRV on the Schwartz set, if any? Are there any known results on
how well this works/vulnerabilities/etc.? <br>
<br>
<br>
<br>
<br>
</blockquote>
<br>
Andrew,
<br>
Yes. Douglas Woodall has demonstrated that dropping the non-members of
the Schwartz/Smith set
<br>
from the ballots and then applying IRV causes the resulting method to
fail both mono-add-plump
<br>
and mono-append, two very weak (normally easy to meet) criteria that I
rate a essential.
<br>
<br>
He refers to IRV as "AV" (Alternative Vote) and the Smith set as "CNTT"
(Condorcet(Net) Top Tier):
<br>
<br>
<blockquote type="cite">abcd 10 <br>
bcda 6 <br>
c 2 <br>
dcab 5 <br>
<br>
All the candidates are in the top tier, and the AV winner is a. But <br>
if you add two extra ballots that plump for a, or append a to the two <br>
c ballots, then the CNTT becomes {a,b,c}, and if you delete d from all <br>
the ballots before applying AV then c wins. <br>
<br>
</blockquote>
<br>
<br>
But instead we don't need to even mention the Schwartz or any other set
in the algorithm:
<br>
<br>
"Before the first and each subsequent IRV elimination, check to see if
the there is a single candidate X
<br>
with no (among remaining candidates) pairwise losses. As soon as an X
appears, elect X."
<br>
<br>
That <b class="moz-txt-star"><span class="moz-txt-tag">*</span>does<span
class="moz-txt-tag">*</span></b> meet mono-append and mono-add-plump,
with no disadvantage compared to the other
<br>
method. Like IRV, it still fails mono-raise.
<br>
<br>
In common with IRV and Schulze it meets the Plurality criterion and
Clone Independence. In common
<br>
with other Condorcet methods, we lose IRV's Later-no-Harm and
Mono-add-Top.
<br>
<br>
I like it, with above-bottom equal preferences not allowed so as to
make Pushover ("turkey raising")
<br>
strategy more difficult.
<br>
<br>
It has the property that when there are three candidates XYZ, and X
wins with more than a third of the
<br>
first preferences, then changing some ballots from Y>X>Z to
Y>Z>X can't change the winner to Y.
<br>
<br>
The other property that it has in common with IRV but not Schulze etc.
is that in the zero-information case
<br>
regardless of how the voter rates the candidates the voter has no
"strategy" that is better than sincere ranking.
<br>
<br>
Some dislike the fact that it fails Minimal Defense.
<br>
<br>
49: A
<br>
24: B
<br>
27: C>B
<br>
<br>
Here it elects A.
<br>
<br>
46: A>B
<br>
44: B>C (maybe "was" B>A or B)
<br>
10: C
<br>
<br>
Here I like the fact that it elects A. Meeting both MD and the
anti-burial property ("Dominant Mutual Third Burial Resistance"?)
<br>
would force the method to elect C.
<br>
<br>
Chris Benham
<br>
<br>
<br>
<br>
<blockquote cite="mid453324A7.3000403@cs.cornell.edu" type="cite">
<pre wrap=""> </pre>
</blockquote>
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