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-------- Original Message --------
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<th valign="baseline" align="right" nowrap="nowrap">Subject: </th>
<td>Re: Participation examples</td>
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<th valign="baseline" align="right" nowrap="nowrap">Date: </th>
<td>Wed, 17 Sep 2003 15:16:04 +0930</td>
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<th valign="baseline" align="right" nowrap="nowrap">From: </th>
<td>Chris Benham <a class="moz-txt-link-rfc2396E" href="mailto:chrisbenham@bigpond.com"><chrisbenham@bigpond.com></a></td>
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<th valign="baseline" align="right" nowrap="nowrap">To: </th>
<td>Kevin Venzke <a class="moz-txt-link-rfc2396E" href="mailto:stepjak@yahoo.fr"><stepjak@yahoo.fr></a></td>
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<th valign="baseline" align="right" nowrap="nowrap">References: </th>
<td><a class="moz-txt-link-rfc2396E" href="mailto:20030916221203.95947.qmail@web13807.mail.yahoo.com"><20030916221203.95947.qmail@web13807.mail.yahoo.com></a></td>
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Kevin,<br>
Thanks, very interesting. See comments below.<br>
<br>
Kevin Venzke wrote:<br>
<blockquote type="cite"
cite="mid20030916221203.95947.qmail@web13807.mail.yahoo.com">
<pre wrap="">Chris,
--- Chris Benham <a
class="moz-txt-link-rfc2396E" href="mailto:chrisbenham@bigpond.com"><chrisbenham@bigpond.com></a> a écrit :
</pre>
<blockquote type="cite">
<pre wrap="">Kevin,
Regarding the 3 methods I have recently posted: "Approval Runoff"
(AERWE), "Improved Generalised Bucklin" (featuring "forwards-backwards
runoff"), and Condorcet completed by reduced-rank Condorcet.
I would be very interested in seeing any examples of Participation failure.
</pre>
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<pre wrap=""><!---->
I've come up with one each. You may want to check my IGB work.
Condorcet completed by utility-based compression:
40 b 100, c 80, a 0
35 c 100, a 25, b 0
B is the CW and wins.
Add in:
25 a 100, b 25, c 0
Now there's a cycle. When the ballots are compressed to two-rank, C is the winner.</pre>
</blockquote>
CB: A pity, but is there a better Condorcet completion method? It is certainly
a better way to count high-resolution <br>
CR ballots than just adding them up (and yet, with sincere voting, likely
to get the same result.)<br>
<blockquote type="cite"
cite="mid20030916221203.95947.qmail@web13807.mail.yahoo.com">
<pre wrap="">"AERWE" (Approval Runoff):
6 A>D>C | B (The pipes are the approval cutoffs.)
5 B>D>C | A
A has a majority and wins.
Add in:
4 C>A | B>D
First B and then A are shunted, at which point D has a majority.</pre>
</blockquote>
CB: Agreed. My/our version of Condorcet-Approval hybrid gives the same
result.<br>
<blockquote type="cite"
cite="mid20030916221203.95947.qmail@web13807.mail.yahoo.com">
<pre wrap="">Improved Generalised Bucklin (IGB):
6 A>E>B>C>D
5 B>E>A>C>D
The final pairing is A vs. E, and A wins, clearly.
</pre>
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CB: I think it is safe to say that this method meets the Majority criterion.<br>
<blockquote type="cite"
cite="mid20030916221203.95947.qmail@web13807.mail.yahoo.com">
<pre wrap="">Add in:
4 C>D>A>B>E
Now the final pairing is E vs. himself, so E wins.
</pre>
</blockquote>
No, I get A as the second finalist. Then A>E 10-5, and so A (the
CW) wins.<br>
IGB second finalist.<br>
Elimination mini-election 1.<br>
Rnd.1: A:0 B:0 C:0 D:11 E:4 Eliminate D.<br>
Elim. m-e 2.<br>
Rnd.1: A:0 B:0 C:11 E:4 Eliminate C . Now the ballots
equate to:<br>
<br>
6:A>E>B<br>
5:B>E>A<br>
4:A>B>E<br>
<br>
Elm. m-e 3.<br>
Rnd.1: A:5 B:6 E:4<br>
Rnd.2: A:5 B:10 E:15 All ballots contribute to either or both of
E and B, so eliminate E.<br>
Then A>B 10-5 and so A is the second finalist.<br>
<br>
Chris Benham.<br>
<blockquote type="cite"
cite="mid20030916221203.95947.qmail@web13807.mail.yahoo.com">
<pre wrap="">
Please tell me if your results differ.
Kevin Venzke
<a class="moz-txt-link-abbreviated" href="mailto:stepjak@yahoo.fr">stepjak@yahoo.fr</a>
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