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