Ben,
MinMax(Margins) fails the Plurality criterion. It elects the candidate with the
weakest pairwise loss as measured by the difference between the two
candidates' vote tallies.
An alternative definition is that it elects the candidate who needs the fewest
number of extra bullet-votes to be able to pairwise-beat all the other
candidates.
3:A
5:B>A
6:C
C>B 6-5, B>A 5-3, A>C 8-6.
That method elects B, but the Plurality criterion says that B can't win because
of C.
Given that if the B voters had truncated the winner would have been C, this is
also a failure of the Later-no-Help criterion.
The method meets the Condorcet criterion and Mono-add-Top. It has been promoted
here by Juho Laatu.
Chris Benham
Ben grant wrote (24 June 2013):
As I have had it explained to me, the Plurality Criterion is: "If there are two
candidates X and Y so that X has more first place votes than Y has any place
votes, then Y shouldn't win".
Which I think means that if X has, for example, 100 votes, then B would have to
appear on less than 100 ballots and still *win* for this criterion to be
failed, yes?
I cannot imagine a (halfway desirable) voting system that would fail the
Plurality Criterion - can anyone tell me the simplest one that would? Apart
from a lame one like "least votes win", I mean?
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