[EM] Benham's Method looks best among Smith + CD methods

[C.Benham]

Forest,

Which method are you referring to in your example?  It appears to be 
simply MinMax (Losing Votes), and not anything
that we've been discussing lately.

The MMLV(erw)M method I've suggested elects A.

> The losing vote scores (for strongest defeats) are  D42>A35>B33>C32 

The Margins Sort algorithm flips D>A, then D>B, then D>C and then is 
happy with the order A>B>C>D.

River (and Ranked Pairs) locks A>B 2,  B>C 1,    (skips C>A -3),    
locks A>D -7,   B>D -9,   C>D -10

Chris Benham


On 5/1/2014 4:38 AM, Forest Simmons wrote:
> Yes, your description of the method is correct.  However, as much as I 
> like the idea it seems to have a fatal flaw:
>
> 21 ABCD
> 19 BCAD
> 18 CABD
> 14 DABC
> 14 DBCA
> 14 DCAB
>
> The losing vote scores (for strongest defeats) are D42>A35>B33>C32 .
>
> The Condorcet Loser D is elected.
>
> This example also shows failure of Clone Winner.
>
> By the way, I prefer Benham over Woodall for reasons similar to 
> yours:  Benham is more "seamless;" you don't have to compute the Smith 
> set; in fact, you don't have to even mention it in the method 
> description, unless you cannot resist the temptation to brag about it..
>
> Forest
>
>
> On Tue, Apr 29, 2014 at 6:29 PM, Michael Ossipoff 
> <email9648742 at gmail.com <mailto:email9648742 at gmail.com>> wrote:
>
>     Forest--
>     Oops! I forgot the A voters' transfer to C.
>     So Woodall does as well as Benham in that example. So my example
>     doesn't mean that Benham is better than Woodall.   ...But Benham
>     is a lot easier to propose to organizations that use or offer IRV.
>      You mentioned Chris's other method. Is that the one that does
>     Condorcet, measuring defeat-strengh by the defeater's Score minus
>     the defeated's score...where a candidate's Score is her pairwse
>     support in her strongest defeat?
>     That method elects C when B is middle CW, and the most favorite,
>     and A is least favorite, and A voters + C voters outnumer B
>     voters, and the A voters bury B?
>     Specific numeical instance of that example:
>     2: A>C>B (burying B)
>     4. B>A>C
>     3: C>B>A
>     Michael Ossipoff
>
>
>
>
> ----
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