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Hello,<br>
My current favourite plain ranked-ballot method is "Approval-Sorted
Margins(Ranking) Elimination":<br>
<br>
1. Voters rank candidates, truncation and equal-ranking allowed.<br>
<br>
2. Interpreting ranking above bottom or equal-bottom as 'approval',
initially order the candidates <br>
according to their approval scores from the most approved (highest
ordered) to the least approved<br>
(lowest ordered).<br>
<br>
3. If any candidate Y pairwise beats the candidate next highest in the
order (X) , then modify the order<br>
by switching the order of the X>Y pair (to Y>X) that are
closest in approval score.<br>
Repeat until all the candidates not ordered top are pairwise beaten by
the next highest-ordered candidate.<br>
<br>
4. Eliminate and drop from the ballots the (now) lowest ordered
candidate.<br>
<br>
5. Repeat steps 2-4 until one candidate (the winner) remains.<br>
<br>
<br>
Simply electing the highest ordered candidate after step3 is
ASM(Ranking):<br>
<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/Approval_Sorted_Margins">http://wiki.electorama.com/wiki/Approval_Sorted_Margins</a><br>
<blockquote type="cite">First "seed" the list in approval order. Then
while any alternative X pairwise defeats the alternative Y<br>
immediately above it in the list, find the X and Y of this type that
have the least difference D in approval, <br>
and modify the list by swapping X and Y.</blockquote>
It is equivalent to ASM(R) in the situation where there are three
candidates in the top cycle with no voter<br>
ranking all three above bottom (and in any election with just three
candidates).<br>
<br>
The advantage of this over ASM(R) is that there is less truncation
incentive and voters who rank all the <br>
viable candidates plus one or more others will normally face little or
no disadvantage compared to informed<br>
strategists. At some point in the process all except the candidates in
the top-cycle will be eliminated, and <br>
assuming three remain then from that point it will proceed like an
ASM(R) election as though the "over-rankers"<br>
'approve' their two most preferred candidates (of the 3 in the top
cycle).<br>
<br>
An advantage it has over Winning Votes (BP, RP,River) is that it
doesn't have a 0-info. random-fill incentive.<br>
Also unlike both WV and Margins it meets the Possible Approval Winner
(PAW) criterion.<br>
<br>
35: A<br>
10: A=B<br>
30: B>C<br>
25: C<br>
<br>
C>A 55-45, A>B 35-30, B>C 40-25.<br>
<br>
In this Kevin Venzke example, if we assume that voters rank all
approved candidates strictly above all others<br>
then it isn't possible for B to be approved on more ballots than A. WV
and Margins elect B.<br>
<br>
ASM(R)E, like ASM(R) and DMC(R), elects C.<br>
<br>
It seems obvious that ASM(R)E meets Minimal Defense.<br>
<a class="moz-txt-link-freetext" href="http://nodesiege.tripod.com/elections/#critmd">http://nodesiege.tripod.com/elections/#critmd</a><br>
<i><a><i><br>
If more than half of the voters rank candidate A above candidate B, and
don't rank candidate B above <br>
anyone, then candidate B must be elected with 0% probability.</i></a></i><br>
<br>
Referring to this definition, while A and B remain uneliminated A will
always be considered to be more 'approved'<br>
than B and of course A pairwise beats B, so B will always be ordered
below A and so must at some point be <br>
eliminated.<br>
<br>
Chris Benham<br>
<br>
<a><i></i></a><br>
<br>
<br>
<br>
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