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Robert Bristow-Johnson wrote (5 March 2010):<br>
<br>
<blockquote type="cite">i like Ranked Pairs best, too. and if the Smith
Set are three candidates, it and Shulze pick the same winner.<br>
<br>
><i> Bringing Plurality in would be a distraction, since we have no
need <br>
</i>><i> to go near this method and risk a worse answer.<br>
<br>
</i>it's a "worse answer" in a weird circumstance where an argument
could be made that any in the Smith set have <br>
some reasonable claim or legitimacy to be elected. why not the guy with
the most votes?
</blockquote>
<br>
Interpreting "most votes" as 'top-ranked on the greatest number of
ballots', the answer is that the resulting method<br>
fails the Clone-Winner and Minimal Defense criteria.<br>
<br>
49: A<br>
24: B<br>
27: C>B<br>
<br>
A>C 49-27, C>B 27-24, B>A 51-49<br>
<br>
More than half the voters have ranked B above A and A no higher than
equal bottom, and yet Smith,FPP elects A.<br>
<br>
The Ranked Pairs and River and Smith//MinMax and Schulze algorithms,
using Margins as the measure of defeat<br>
strength (referred to collectively as "Margins") and IRV also elect
A.<br>
<br>
Say we replace A with a set of clones, A1 and A2.<br>
<br>
26: A1>A2<br>
23: A2>A1<br>
24: B<br>
27: C>B<br>
<br>
(A2 > C > B > A1 > A2)<br>
<br>
Now Smith,FPP elects C violating Clone-Winner. Those other methods I
mentioned meet Clone-Winner and so<br>
elect one of the clones (A1). <br>
<br>
The number of people (ballots) that voted for (ranked above
equal-bottom) the clones and not C exceeds the number<br>
that voted for C, and yet C wins violating my suggested "Strong
Minimal Defense" criterion.<br>
<br>
Chris Benham<br>
<br>
<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/Minimal_Defense_criterion">http://wiki.electorama.com/wiki/Minimal_Defense_criterion</a><br>
<br>
<a class="moz-txt-link-freetext" href="http://nodesiege.tripod.com/elections/#critmd">http://nodesiege.tripod.com/elections/#critmd</a><br>
<br>
<a class="moz-txt-link-freetext" href="http://nodesiege.tripod.com/elections/#critclone">http://nodesiege.tripod.com/elections/#critclone</a><br>
<br>
Douglas Woodall splits Clone Independence into "Clone-Winner" and
"Clone-Loser".<br>
Clone-Winner says that if winning candidate X is replaced by a set of
clones than the winner must come from that<br>
set. Clone-Loser says that the winner shouldn't change if one (or
more) losers are replaced by a set (or sets) of clones.<br>
<br>
<br>
<br>
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