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<div class="moz-cite-prefix">Forest,<br>
<br>
Why do you want to give any points at all for middle ratings?<br>
<br>
What is wrong with simply 3-slot Smith//Top Ratings? <br>
<br>
Or 3-slot TTR, Top Ratings (aka ICT)?<br>
<br>
Chris Benham<br>
<br>
<br>
On 10/11/2016 9:22 AM, Forest Simmons wrote:<br>
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cite="mid:CAP29onf+qZCXtq=EFg5GHRs8yvYaFvJ4LiMiKucKNNdYK-Je0w@mail.gmail.com"
type="cite">
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<div>AS Chris Benham and Michael Ossipoff pointed
out this Smith//3Score doesn't disappoint the
defecting faction (B) unless the plumping faction
(C) is fairly close to half of the electorate. It
only works when C is plumped on at least 43
percent of the ballots.<br>
<br>
</div>
To make it work for Mike's example below where C is
plumped on only 100 out of 297 ballots, the middle
ranks have to count much les than half of the equal
top ranks. About 2 percent of the equal top value
would do.<br>
<br>
</div>
So with sincere ballots the point totals are ...<br>
<br>
</div>
99+.02(98) = 100.96 for A,<br>
</div>
98+ .02(99)= 99.98 for B, and <br>
</div>
100 for C. In this case A is both the CW and the points
winner.<br>
<br>
</div>
The B faction's defection simultaneously promotes C to the
Smith set and reduces A's point total to 99, making C (still
with 100 points) the method winner.<br>
<br>
</div>
<div>What makes this example hard is that the C faction is just
over one third of the electorate, and that the A and B
subfactions are very close in size.<br>
<br>
</div>
<div>For a defection attempt to succeed under these conditions
the B faction would have to possess very precise information.
If the A faction had the same information it would be easy for
them to make a defensive move in the form of truncating B on a
few ballots.<br>
</div>
<div><br>
</div>
<div>In practice, a point value substantially larger than .02
for the middle ranks would be adequate.<br>
</div>
<div><br>
</div>
<div>What would be a reasonable compromise? <br>
<br>
</div>
<div>How about 1/4 or 25% ?<br>
<br>
</div>
<div>In that case the A faction could say to the B faction, "You
rank me on two ballots and I will rank you on seven."<br>
<br>
</div>
<div>The resulting equilibrium would be<br>
<br>
</div>
<div>92 A<br>
</div>
<div> 7 A>B<br>
</div>
<div>96 B<br>
</div>
<div> 2 B>A<br>
</div>
<div>100 C<br>
<br>
</div>
<div>Candidate A is elected as the CW.<br>
<br>
</div>
<div>If B defects from this equilibrium proposal ...<br>
<br>
</div>
<div>92 A<br>
</div>
<div> 7 A>B<br>
</div>
<div>98 B<br>
</div>
<div>100 C<br>
<br>
</div>
<div>then {A, B, C} forms Smith, and C wins with 100 points,
while B gets only<br>
<br>
</div>
<div>98+7/4 = 99.75 points.<br>
<br>
<br>
</div>
<div>If grade style ballots were in use, the A faction could say
I will give you two B grades in exchange for two D's.<br>
<br>
</div>
<div>Two B grade points add up to 1.5 which would bring the B
candidate up to 99.5, still short of the 100 needed to tie the
C candidate.<br>
<br>
</div>
<div>On the other hand, the two D grades for the A candidate
would make her the Condorcet Winner.<br>
<br>
</div>
<div>When the plumping faction forms greater than 39 percent of
the electorate, then no strategy would be needed other than
for the larger subfaction to give D grades to the potential
defection candidate.<br>
<br>
</div>
<div>32 A(4), B(1)<br>
</div>
<div>31 B(4) (Sincere B>0)<br>
</div>
<div>39 C(4)<br>
</div>
<div><br>
</div>
<div>If eight or more of the B faction give A a positive rating,
then A wins as the only member of the Smith set.<br>
<br>
</div>
<div>If fewer than eight vote sincerely, then C and B are tied
with 156 grade points each.<br>
<br>
</div>
<div>So the method I am now proposing is <br>
<br>
</div>
<div>Smith//GPA<br>
<br>
</div>
<div>Elect the member of the Smith set with the largest Grade
Point Average.<br>
</div>
<div><br>
<br>
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<div><br>
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<div class="gmail_extra"><br>
<div class="gmail_quote"><br>
<blockquote class="gmail_quote"
style="margin:0 0 0
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From: Michael Ossipoff <br>
Yes, the method still allows chicken
dilemma defection to succeed.<br>
<br>
I tried an example in which the B
faction is about as large as possible
in<br>
comparison to the C faction.<br>
<br>
99: A>B<br>
98: B (sincere is B>A)<br>
100: C<br>
<br>
This results in a cycle, so everyone
is in the Smith-set.<br>
<br>
B has more Borda points than anyone
else.<br>
<br>
It looks as if it isn't possible to
have CD in a strategically good,<br>
reliable, uncriticizable. rank
method.<br>
<br>
ICT isn't good as a ranking method.
Only as a 3-slot method in which the<br>
middle rating is used only in
Chicken-Dilemma situations.<br>
<br>
In ICT, a candidate you rank middle
doesn't get much protection from you.<br>
<br>
But, in a chicken dilemma situation
you don't expect B to be a CWs anyway.<br>
<br>
3-Slot ICT is still my favorite, to be
used as an Approval version rather<br>
than a ranking method, with the middle
rating only for chicken dilemma.<br>
<br>
Plain MMPO meets Weak CD, FBC, LNHa,
and has wv-like strategy.<br>
<br>
Though it fails CD's strong original
version, if the defection is a<br>
burial--The method's wv burial
defensive advice would warn the A
voters to<br>
not rank B, if A is likely to be CWs.<br>
<br>
That's a unique, impressive &
amazing set of advantages.<br>
<br>
But there are some strongly-felt
criticisms to it. I've answered them,
and<br>
it seems to me that only one of them
is a genuine problem:<br>
<br>
...the possibility of the perpetual
burial fiasco.<br>
<br>
But I've told here why there's
something a bit mutually contradictory
about<br>
that fiasco's requirements.<br>
<br>
So I suggest that it doesn't rule out
MMPO or MAM, though it makes them<br>
just a little questionable &
unreliable.<br>
<br>
...but still worth a try because of
big advantages.<br>
<br>
I'd hoped that Bucklin with
conditional votes would be a good CD
method.<br>
But it's not as good as I'd hoped,
because the conditional votes option
can<br>
be strategically taken advantage of,
resulting in another chicken dilemma,<br>
differently-caused.<br>
<br>
I don't know if that rules out the
conditional option, but it supports
the<br>
conclusion that a CD rank method
always costs.<br>
<br>
Michael Ossipoff<br>
<br>
<br>
On Oct 9, 2016 3:19 PM, "Forest
Simmons" <<a moz-do-not-send="true"
href="mailto:fsimmons@pcc.edu"
target="_blank">fsimmons@pcc.edu</a>>
wrote:<br>
<br>
><br>
><br>
> (Continued below)<br>
><br>
><br>
>> Now, how do we adapt this to
general rankings? We assume that equal
top<br>
>> rankings and equal bottom or
multiple truncations are allowed.<br>
>><br>
>> For each ballot on which a
candidate is ranked above bottom but
below top<br>
>> that candidate receives one
point. For each ballot on which the
candidate<br>
>> is ranked top or equal top
that candidate receives two points.<br>
>><br>
>> The Smith candidate with the
greatest number of points wins.<br>
>><br>
>> [End of definition]<br>
>><br>
>> Note that the method does
satisfy CD unlike
Smith//ImplicitApproval.<br>
>> Jameson's idea of three slot
scores makes it work.<br>
>><br>
>> How does it do on burial?<br>
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