[EM] CRCLE ( Resolving Cycles- Margins Doesn't Do Very Well )

[Kevin Venzke]

David,

You have stumbled upon the margins vs. winning votes issue.

 --- Dgamble997 at aol.com a écrit : 
> A versus B      45 v 55   margin 10 winner B
> A versus C      51 v 49   margin  2  winner A
> B versus C      11 v 44   margin  33 winner C
> 
> C's defeat of B is locked first followed by B's defeat of A. This gives C>B>
> A. Under Ranked Pairs C the least supported candidate is the winner. Under 
> CRCLE ( using RP as an elimination method) assuming utilities for all candidates 
> close to 1.00  A is eliminated as Condorcet loser and C wins against B ( 44 v 
> 11).
> 
> Am I doing Ranked Pairs right ?

It looks like you are doing RP(margins) correctly.

> Assuming I am doing it right I don't think it's very good.

Yeah, not really.

> I came up with a different method of resolving cycles that seems better but 
> which I can't find described anywhere.
> 
> In instances of a cycle for Condorcet loser eliminate the candidate with the 
> lowest maximum level of support in pairwise comparisons.

This won't be cloneproof, because a cycle participant can benefit by running
along with a weak clone that he can trounce.

Instead, try RP(wv).  Instead of locking defeats in order of the greatest
margins, lock them in order of greatest absolute votes received by the winner.

> For the example:
> 
> 45 A
> 6 B>A
> 5 B>C
> 44 C>B
> 
> A versus B      45 v 55   margin 10 winner B
> A versus C      51 v 49   margin  2  winner A
> B versus C      11 v 44   margin  33 winner C

RP(wv) locks B>A (strength 55), then A>C (strength 51), and overrules
C>B (strength 44).  The ranking is B>A>C, the same thing you achieved with your 
rule.

I don't know if anyone here prefers margins to WV.  Markus posted something
relevant immediately before your message.

Kevin Venzke
stepjak at yahoo.fr


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