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<div class="moz-cite-prefix">Forest,<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>
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<br>
<br>
<br>
On 6/5/2015 8:15 AM, Forest Simmons wrote:<br>
</div>
<blockquote
cite="mid:CAP29oneUc76a6EO1NTRA3wY-2M=N_Uku9v84JZU_aTJzNFBztg@mail.gmail.com"
type="cite">
<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 class=""><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
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF" text="#000000">
<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>
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