# [EM] Question about the Plurality Criterion

Chris Benham cbenhamau at yahoo.com.au
Mon Jun 24 10:38:55 PDT 2013

```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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