<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 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">
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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>