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<div class="moz-cite-prefix">Kevin,<br>
<br>
On reflection I'm sure you're right about FBC, but I think it
would be much<br>
harder to make an example of the method failing mono-raise.<br>
<br>
Given the criterion (such as Plurality) compliances of the
MiinGS(etrw) method <br>
that selects the seed, I would think it very rare for a candidate
that can't win being <br>
the seed to be able to win otherwise.<br>
<br>
In the classic 49 A, 24 B, 27 C>B example, A wins if C is
the seed but loses if A is<br>
the seed. But of course MinGS(etrw) could never select as the seed
such a weak<br>
candidate as C .<br>
<br>
If I'm wrong I'd be interested in seeing an example.<br>
<br>
Chris Benham<br>
<br>
<br>
On 5/28/2015 9:47 AM, Kevin Venzke wrote:<br>
</div>
<blockquote
cite="mid:601820708.16858.1432772254721.JavaMail.yahoo@mail.yahoo.com"
type="cite">
<div style="color:#000; background-color:#fff;
font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial,
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<div id="yui_3_16_0_1_1432764762629_15088"><span
id="yui_3_16_0_1_1432764762629_15424">Hi Chris,</span></div>
<div id="yui_3_16_0_1_1432764762629_15088"><span><br>
</span></div>
<div id="yui_3_16_0_1_1432764762629_15088"><span
id="yui_3_16_0_1_1432764762629_15425">I like this kind of
method where you pick a pivotal candidate and check if the
other </span></div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><span
id="yui_3_16_0_1_1432764762629_15426">candidates can defeat
him, but typically these methods don't satisfy FBC or
mono-raise.</span></div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><span><br>
</span></div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><span
id="yui_3_16_0_1_1432764762629_15201">Off the top of my
head, what if some voters rank
Favorite=Compromise>...>Worst, </span></div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><span
id="yui_3_16_0_1_1432764762629_15441">resulting in </span>Favorite
being the seeded candidate and the winner being Worst. Isn't
it</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">possible
that if the voters lower Favorite in their rankings that
Favorite will no longer</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">be the
seed, and instead someone else will be the seed? If so, I
don't think there's</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">a way to
promise that Compromise would not go on to win the election.</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><br>
</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">Regarding
mono-raise, while it's obvious that getting raised can't stop
you from being</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">the seed if
you were the seed, what if you weren't the seed but you won
via approval in</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">the second
phase? Getting raised/lowered could change who the seed is,
and it may</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">be that you
can only win in phase 2 when certain candidates are the seed.
In fact,</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">becoming
the seed when you hadn't been the seed could even make you
lose.</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><br>
</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">Kevin</div>
<div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><br>
</div>
<br>
<div style="font-family: HelveticaNeue, Helvetica Neue,
Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12px;"
id="yui_3_16_0_1_1432764762629_15086">
<div style="font-family: HelveticaNeue, Helvetica Neue,
Helvetica, Arial, Lucida Grande, sans-serif; font-size:
16px;" id="yui_3_16_0_1_1432764762629_15085">
<div dir="ltr" id="yui_3_16_0_1_1432764762629_15084">
<hr id="yui_3_16_0_1_1432764762629_15159" size="1"> <font
id="yui_3_16_0_1_1432764762629_15083" face="Arial"
size="2"> <b><span style="font-weight:bold;">De :</span></b>
C.Benham <a class="moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au"><cbenham@adam.com.au></a><br>
<b><span style="font-weight: bold;">À :</span></b>
<a class="moz-txt-link-rfc2396E" href="mailto:election-methods@lists.electorama.com">"election-methods@lists.electorama.com"</a>
<a class="moz-txt-link-rfc2396E" href="mailto:election-methods@lists.electorama.com"><election-methods@lists.electorama.com></a> <br>
<b><span style="font-weight: bold;">Envoyé le :</span></b>
Mardi 26 mai 2015 1h57<br>
<b><span style="font-weight: bold;">Objet :</span></b>
Approval seeded by MinGS (etrw)<br>
</font> </div>
<div class="y_msg_container"
id="yui_3_16_0_1_1432764762629_15087"><br>
I've been trying to come up with a better method with
Bucklin-like <br>
virtues including Later-no-Help, even though<br>
there seems to be no call for any such thing and it
results in a method <br>
with a stronger truncation incentive than<br>
I like.<br>
<br>
The closest I came fills the bill with 3 candidates, but
can probably <br>
fail Majority for Solid Coalitions (aka Mutual Majority)<br>
with more.<br>
<br>
Approval seeded by Minimum Gross Score (equal-top rating
whole):<br>
<br>
*Voters fill out a multi-slot ratings ballot (I suggest as
many slots as <br>
there are candidates, up to say 4).<br>
Default rating (truncation) is bottom.<br>
<br>
Construct a pairwise matrix in which any ballot that
rates/ranks <br>
candidate X and Y equal-top gives a whole vote to both<br>
in the X v Y pairwise comparison. Those that rate at least
one of them <br>
in a lower position give a whole vote to one if they<br>
rate that one above the other, otherwise give no vote to
either.<br>
<br>
We are only concerned with pairwise scores, not defeats or
victories or <br>
ties. Select the candidate S whose lowest pairwise<br>
score is higher than any other candidate's lowest pairwise
score.<br>
<br>
Then interpret all the ballots that rate S above bottom
as approving S <br>
and all other candidates they rate no lower than S,<br>
and all the other ballots as approving all the candidates
they rate <br>
above bottom.<br>
<br>
Based on that interpretation, elect the most approved
candidate.*<br>
<br>
I claim that this meets the Favorite Betrayal Criterion,
Plurality, <br>
Irrelevant Ballots, Later-no-Help (maybe barring some
fantastic<br>
scenario with many candidates), Condorcet(Gross), Minimal
Defense, <br>
mono-raise, mono-add-top, mono-switch-plump,
mono-add-plump,<br>
mono-append, and 3-candidate Majority for Solid
Coalitions.<br>
<br>
Because I'm sure that it doesn't properly meet Majority
for Solid <br>
Coalitions, I don't count this as a complete success.<br>
<br>
Without the approval stage and the rule about equal-top
rating/ranking, <br>
it is Douglas Woodall's "MinGS" method (one of many<br>
he devised for test purposes).<br>
<br>
46 A<br>
44 B>C<br>
10 C<br>
<br>
C> A 54-46, A>B 46-44, B>C 44-10. The method
"seeds" A and then <br>
elects C.<br>
<br>
Electing A would be a failure of Minimal Defense and
electing B would <br>
show a failure of Later-no-Help. Unfortunately the
election of C<br>
is a failure of Chicken Dilemma (not compatible with the
method's <br>
compliance with Plurality and Minimal Defense).<br>
<br>
46 A<br>
44 B>C (sincere might be B or B>A)<br>
05 C>A<br>
05 C>B<br>
<br>
C> A 54-46, A>B 51-49, B>C 44-10. The method
"seeds" A and elects C.<br>
<br>
Here it resists Burial strategy better than the MinMax
(Margins) and <br>
(Losing Votes) Condorcet methods, which both elect B.<br>
<br>
46 A>C<br>
10 B>A<br>
10 B>C<br>
34 B=C<br>
<br>
C>B 80-54, B>A 54-46. A>C 56-44. The method
seeds B and elects C.<br>
<br>
Not electing the only candidate that is top-rated on more
than half the <br>
ballots may be an odd look by comparison with Bucklin, but
I'm not bothered.<br>
All the candidates are pairwise beaten and the winner is
rated above <br>
bottom on 90% of the ballots.<br>
<br>
<br>
40 A>C<br>
15 B>A<br>
20 B<br>
15 C>A<br>
10 C<br>
<br>
A>B 55-35, A>C 55-25, C>B 65-35. The method
seeds A and elects A.<br>
<br>
There are 100 ballots and A is the Condorcet(Gross) winner
(meaning that <br>
in each and all of A's pairwise contests A is<br>
strictly preferred to the other candidate by more than
half the voters). <br>
Bucklin elects C.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
<br>
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