# [EM] Question about the Plurality Criterion

Benjamin Grant panjakrejn at gmail.com
Mon Jun 24 11:17:54 PDT 2013

```Thanks for the note - squirreling this away for future study. :)

-Benn

On Mon, Jun 24, 2013 at 1:38 PM, Chris Benham <cbenhamau at yahoo.com.au>wrote:

> 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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>
>
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