In an A versus B comparison, since A's "winning votes" are the ones for A, A's "losing votes" would be the ones for B.
A's ("winning" or "losing") votes are only votes for A. In an A versus
B comparison, the votes for A are "losing" if A loses that pairwise
contest and "winning" if A wins it.
The votes for B in that contest are not "A's losing votes". It might be
ok English to call them "A's opposing votes", but no-one mentioned
anything like that.
If B did worse against C (B beats C by less than 4), B becomes the winner under this method.
That would be an example of the failure of Mono-raise that I mentioned.
The methods that all behave like MinMax when there are just 3 candidates
all meet it.
BTW, Gross Loser Elimination (or any Winning Votes method) can't
function with only a "margin matrix". The gross scores are needed.
Chris
//>/Joshua, />//>/The wording is correct and the English seems plain to me. />//>/You just keep eliminating the candidate that has (among remaining
candidates) the worst (as measured by losing votes) pairwise loss. />//>/49 A />/24 B />/27 C>B />//>/A>C 49-27, C>B 27-24, B>A 51>49/
Joshua,
> In an A versus B comparison, since A's "winning votes" are the ones for A, A's "losing votes" would be the ones for B.
A's ("winning" or "losing") votes are only votes for A. In an A versus
B comparison, the votes for A are "losing" if A loses that pairwise
contest and "winning" if A wins it.
The votes for B in that contest are not "A's losing votes". It might be
ok English to call them "A's *opposing* votes", but no-one mentioned
anything like that.
> If B did *worse* against C (B beats C by less than 4), B becomes the winner under this method.
That would be an example of the failure of Mono-raise that I mentioned.
The methods that all behave like MinMax when there are just 3 candidates
all meet it.
BTW, Gross Loser Elimination (or any Winning Votes method) can't
function with only a "margin matrix". The gross scores are needed.
Chris
> *Joshua Boehme*joshua.p.boehme at gmail.com
> <mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20Poll%20on%20voting-systems%2C%0A%20to%20inform%20voters%20in%20upcoming%20enactment-elections&In-Reply-To=%3C8516d62a-9f4a-4390-a5b8-8673bb1a9fbb%40gmail.com%3E>
> /Sat Apr 20 04:15:16 PDT 2024/
>
>
> ------------------------------------------------------------------------
> In an A versus B comparison, since A's "winning votes" are the ones for A, A's "losing votes" would be the ones for B. Eliminating the candidate with the worst pairwise defeat is completely unambiguous, though.
>
>
> Interestingly this doesn't always resolve a three-way cycle in the typical way (margin matrix is row candidate over column candidate)...
>
> A B C
> A 0 2 -4
> B -2 0 6
> C 4 -6 0
>
> C gets eliminated, leaving A as the winner over B. Most methods would break A's weak win over B and make B the winner.
>
> If B did *worse* against C (B beats C by less than 4), B becomes the winner under this method.
>
>
> On 4/20/24 04:05, Chris Benham wrote:
> >//>/Joshua, />//>/The wording is correct and the English seems plain to me. />//>/You just keep eliminating the candidate that has (among remaining
> candidates) the worst (as measured by losing votes) pairwise loss. />//>/49 A />/24 B />/27 C>B />//>/A>C 49-27, C>B 27-24, B>A 51>49/
