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<div class="moz-cite-prefix">Forest,<br>
<br>
Sorry you're right, I somehow miscounted.<br>
<br>
However the method certainly fails "Pairwise Plurality", and I
can't see what the justification (in terms of criterion
compliances) is for<br>
the bad failure of Condorcet Loser.<br>
<br>
Chris Benham<br>
<br>
On 6/6/2015 4:06 AM, Forest Simmons wrote:<br>
</div>
<blockquote
cite="mid:CAP29one832eAigjsDP_JcrMtPyujLotjw_4KRfeq-mG_Xs9kJw@mail.gmail.com"
type="cite">
<div dir="ltr">
<div>
<div>
<div>Chris,<br>
<br>
</div>
in the second example the symmetrically completed ballots
are<br>
<br>
<div>27 A<br>
</div>
<div>11 A>C<br>
</div>
<div>11 C>A<br>
</div>
<div>02 C<br>
</div>
<div>11 C>B<br>
</div>
<div>11 B>C<br>
</div>
27 B<br>
<br>
</div>
Candidate C, the IA-MPO winner, is ranked on 46 ballots.
Neither A nor B is top ranked on more than 38 ballots. So it
seems to me that Plurality is not violated.<br>
<br>
</div>
<div>In summary, IA-MPO does not violate the strong version of
Plurality on the symmetrically completed ballots, and does not
violate the (original) weaker version of Plurality (what I
called Plurality') when applied to the original ballots. I
think it is too early to throw it out.<br>
<br>
</div>
<div>Forest<br>
</div>
<div><br>
</div>
Forest<br>
</div>
<div class="gmail_extra"><br>
<div class="gmail_quote">On Fri, Jun 5, 2015 at 9:46 AM,
C.Benham <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div bgcolor="#FFFFFF" text="#000000">
<div>Forest,<span class=""><br>
<br>
<blockquote type="cite">"Symmetrical completion
normally would replace 16 A=C with 8 A>C and 8
C>A . I understand why you didn't do it that
way: you didn't want to go outside the category of
two slot ballots. But just because the voters have
to vote two slot ballots doesn't mean that we are
prohibited from using a counting method that creates
auxiliary data structures like matrices or three
slot rankings."</blockquote>
<br>
</span> Your presumption about my motive is wrong. I did
it that way because (perhaps because of lack of sleep)
that was the only way that occurred to me.<br>
I don't like 2-slot ballots and if they are used I can't
take seriously the idea that anything other than
Approval should be used to determine the winner.<br>
<br>
Also I wasn't suggesting or contemplating using the
symmetric completion at the top to modify IA-MPO, rather
I was just suggesting using it to test<br>
whether or not the result is in compliance with the
Plurality criterion.<br>
<br>
Unfortunately your second example shows that even the
newly modified version of IA-MPO (that works on the
ballots symmetrically completed at<br>
the top) miserably fails Plurality.<br>
<br>
Chris Benham
<div>
<div class="h5"><br>
<br>
<br>
On 6/5/2015 8:15 AM, Forest Simmons wrote:<br>
</div>
</div>
</div>
<blockquote type="cite">
<div>
<div class="h5">
<div dir="ltr"><br>
<div class="gmail_extra"><br>
<div class="gmail_quote">On Wed, Jun 3, 2015 at
7:43 PM, C.Benham <span dir="ltr"><<a
moz-do-not-send="true"
href="mailto:cbenham@adam.com.au"
target="_blank">cbenham@adam.com.au</a>></span>
wrote:<br>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF" text="#000000">
<div>...<br>
<span><br>
</span> Forest, I'm not sure that this
isn't the same as the normal Plurality
criterion. The reference to "first
preference" in the Plurality criterion
definition I think refers to exclusive
first preference.<br>
<br>
(I gather that Woodall's criteria are
only about strict rankings from the top,
which may or may not be truncated,) I
suppose it could and should be extended
to applying to ballots<br>
that are symmetrically "completed" only
at the top. Doing that to your example
gives:<br>
<br>
41 A<br>
18 C<br>
41 B<br>
<br>
Electing C on these ballots is insane
and I don't see how electing C on the
original ballots (where some of the
votes are given half to one candidate
and half to another) is<br>
really any more justified.<br>
<br>
Yes, this convinces me that the
Plurality criterion should definitely be
applied to to the ballots symmetrically
completed at the top and that we can
without regret<br>
kiss IA-MPO goodbye.<br>
</div>
</div>
</blockquote>
<div><br>
Symmetrical completion normally would
replace 16 A=C with 8 A>C and 8 C>A
. I understand why you didn't do it that
way: you didn't want to go outside the
category of two slot ballots. But just
because the voters have to vote two slot
ballots doesn't mean that we are prohibited
from using a counting method that creates
auxiliary data structures like matrices or
three slot rankings.<br>
<br>
</div>
<div>If we did this (I think more appropriate)
kind of symmetric completion, the working
ballots would become<br>
<br>
33 A<br>
</div>
<div>08 A>C<br>
</div>
<div>08 C>A<br>
<div>02 C<br>
</div>
08 C>B<br>
</div>
<div>08 B>C<br>
</div>
<div> 33 B<br>
</div>
<div>The resulting respective IA-MPO scores
for A, B, and C would become 49-49, 49-49,
and 34-41, so this version of IA-MPO with a
front end of symmetric completion at the top
would give a tie to A and B, the only
candidates with a non-negative score.<br>
</div>
<div><br>
</div>
<div>Let's try it on<br>
<br>
</div>
<div>27 A<br>
</div>
<div>22 A=C<br>
</div>
<div>02 C<br>
</div>
<div>22 B=C<br>
</div>
<div>27 B<br>
<br>
</div>
<div>Candidates A and B are tied for Approval
Winner with 49 approvals each against 46 for
C, making C the ballot Condorcet Loser.<br>
<br>
</div>
<div>Let's do the natural symmetric completion
to see the likely sincere ballots that would
be voted if equal ranking at top were not
allowed (nor practically required,as in
Approval):<br>
<br>
<div>27 A<br>
</div>
<div>11 A>C<br>
</div>
<div>11 C>A<br>
</div>
<div>02 C<br>
</div>
<div>11 C>B<br>
</div>
<div>11 B>C<br>
</div>
27 B<br>
</div>
<div><br>
</div>
<div>The respective IA-MPO scores for A, B,
and C are 49-49, 49-49, and 46-38, the only
positive difference. So C wins. Note that C
is still the ballot Condorcet Loser.<br>
<br>
</div>
<div>Whether or not we like this result
probably reflects how much we prefer a
centrist over an extremist, all else being
equal.<br>
</div>
<div> </div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px
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rgb(204,204,204);padding-left:1ex">
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<div> <br>
Another version of the criterion is
"Pairwise Plurality" (suggested a while
ago by Kevin or me): If candidate X's
lowest pairwise score is higher than
candidate Y's highest<br>
pairwise score, then Y must not be
elected".<br>
<br>
I like this. Both IA-MPO and SMD,TR
fail it, as in the two examples. <br>
</div>
</div>
</blockquote>
<div><br>
</div>
<div>Nice idea! <br>
</div>
</div>
<br>
</div>
</div>
</div>
</div>
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