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

[Forest Simmons]

Date: Wed, 30 Apr 2014 19:17:39 +0930
> From: "C.Benham" <cbenham at adam.com.au>
> To: election-methods at lists.electorama.com
> Subject: Re: [EM] Benham's Method looks best among Smith + CD methods
> Message-ID: <5360C6BB.4050903 at adam.com.au>
> Content-Type: text/plain; charset="iso-8859-1"; Format="flowed"
>
>
> >  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
>
> I have this as indecisive between B and C.
>
> B>A>C>B.   MinMax Losing Votes scores:  B4 > C3 > A2.  Margins Sort is
> indecisive as to which pair to flip: B>C or C>A?
>
> B>A  (4-2 = 2),     A>C  (2-3 = -1),   C>B (3-4 = -1).
>
> I haven't put much thought on how best to break such ties, but I'm
> inclined to say it should be in favour of the candidate with the higher
> score.
>

I agree; when margins are indecisive, go by the gross score of the pairwise
winner, in this case C>B should get locked in according to this rule rather
than A>C because 3>2.

In other words the defeats with strongest LV strengths are

 C>B (3), B>A (4) ,

so C is elected.

Here that is B,  the sincere CW.
>
> Chris Benham
>
> On 4/30/2014 10:59 AM, Michael Ossipoff 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
> >
> >
> > ----
>
> -----------------------------
>

And please disregard the following message!

Forest


> Message: 2
> Date: Wed, 30 Apr 2014 12:08:15 -0700
> From: Forest Simmons <fsimmons at pcc.edu>
> To: Michael Ossipoff <email9648742 at gmail.com>
> Cc: "election-methods at electorama.com"
>         <election-methods at electorama.com>
> Subject: Re: [EM] Benham's Method looks best among Smith + CD methods
> Message-ID:
>         <CAP29ondHpaF5tf+OFqLH7t0FBmP2O=U=
> Z+57aSwiiCXH8k8XYw at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> 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
>
>
>
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