[EM] Majority winner set

LAYTON Craig Craig.LAYTON at add.nsw.gov.au
Sun Nov 19 16:46:08 PST 2000

Martin wrote:

>Isn't there another majority winner set consisting of A & B? And another
for B &
>Or do I misunderstand your 'absolute majority'?

Yes, I think so.  Absolute majority means majority of all votes cast (ie
over 50%).  B is not included in the majority winner set.  However, I should
clarify that the majority winner set is those candidates who are in the
Smith set, and pairwise beat another member of the Smith set by an absolute
majority.  This removes the contradiction in my original message.  If B
defeated C by 52 - 48, then the majority winner set would consist of all
three candidates A,B,C, and another method is needed to decide between them
- probably Minmax(wv) for want of a better alternative.

LAYTON Craig wrote:

> I'm proposing a majority winner set method.  It could go with a new
> (which would be failed by margin systems, and either passed or failed by
> winning votes systems depending on the specific wording).
> Definition of majority winner set:
> The set of candidates who pairwise beat all candidates outside the Smith
> set, and pairwise beat at least one candidate inside the Smith set by an
> absolute majority
> Where this set contains at least one candidate, and is smaller than the
> Smith set, all candidates not in the majority winner set are eliminated.
> The majority winner set becomes the new Smith set, and the test is
> reapplied.
> eg Smith Set
> A>B   55 - 45
> B>C   47 - 35
> C>A   51 - 35
> -Majority Winner Set consists of A & C

> -A is eliminated
> -Majority Winner Set consists of C
> Also handy for resolving draws.  Consider the same as above, but with C>A
> 50-50.  Majority winner set consists of A.
> Comments?

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