Mike,
You wrote (Mon.Jun.6):
Now, about the Plurality Criterion:
Doesn't it say: X must not win if the number of people voting Y in 1st
place is greater than the number of peope voting X over Y?
No. The "pairwise version" says that X must not win if there are more
voters that rank X above all the other candidates than there are voters
that rank Y over *any* candidate.
But will failure of the Plurality Criterion cause a strategy problem
for voters?
Possibly only the relatively mild one of giving them a random-fill
incentive, but not all voting method problems are strategy problems. (IMHO).
No one has made a case that the Plurality Criterion is essential, or
that failing it is a grave problem.
I thought I did that here:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/014958.html
"Plurality: if some candidate x has more first-preference votes than
some other candidate y has votes in total, then x's probability
of election must be greater than y's."
In his papers, Woodall likes to economise on axioms; so doesn't
include the common-sense axiom that a ballot that leaves one candidate
unranked should be treated/regarded the same as a ballot that ranks
this candidate last and all the other candidates the same.
His "votes in total" refers to explicit rankings in any position.
Incorporating this axiom, a "version" of the Plurality criterion I
like is
"If some candidate x is ranked in first-place on more ballots than
candidate y is ranked above equal-last, then y can't win".
A Woodall example:
11 ab
07 b
12 c
C has more first-preference votes than A has above-last-place votes,
so A is barred by C's "plurality" over A.
A>B 11-7 (m3)
B>C 18-12 (m6)
C>A 12-11 (m1)
Margins elects A, while WV elects B.
It took me a long time before I could see any particular point to this
criterion, but now I rate it very highly.
Obviously if candidate x has a "plurality" over candidate y, then x
pairwise beats y. If y is elected, then those voters that prefer x to y
will have a virtually *unanswerable* complaint: "How can you justify
x losing to y? Maybe x losing to some z can be justified, but not to y!"
If some pairwise method that fails Plurality has just replaced FPP,
and x's supporters are not great fans of the new method and x comes
FP-first,
then it is easy to imagine that a riot could be fomented.
That said, my current favourite single-winner rankings method is
CDTT,IRV, which also fails the Plurality criterion. When the method
meets Later-no-Harm while failing
Later-no-Help all the voters have an incentive (normally, and in the
zero-info. case) to fully rank, thus making a failure of Plurality in
practice very unlikely.
A possible "real-world" horror scenario is that a lot of voters truncate
anyway, acting on the advice of parties whose agenda is to bring the
method into disrepute so that they are in a better position to move to
have it scrapped.
In the 49A, 24B, 27C>B scenario both CDTT,IRV and MMPO,FPP elect C,
which is a serious violation of the Plurality criterion.
Chris Benham
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