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

C.Benham cbenham at adam.com.au
Wed May 14 10:19:48 PDT 2014

```> > 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.

Forest,

Here you "agree" with me, but somehow we have different winners.
Actually our tie-breaking proposals are different.

I suggest that of all the possible winners that could be produced by all
the possible (arbitrary) tie-breaks, elect the one with the
highest score.

In the example the two possible winners are B and C, and of those two B
has the higher score so I say elect B.  I think that procedure
is more likely to elect the positionally stronger candidate. In this
example B is  positionally dominant.

Chris Benham

On 5/1/2014 5:08 AM, Forest Simmons wrote:
>
>
>
>
>     Date: Wed, 30 Apr 2014 19:17:39 +0930
>     From: "C.Benham" <cbenham at adam.com.au <mailto:cbenham at adam.com.au>>
>     To: election-methods at lists.electorama.com
>     <mailto: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
>     <mailto: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 <mailto:fsimmons at pcc.edu>>
>     To: Michael Ossipoff <email9648742 at gmail.com
>     <mailto:email9648742 at gmail.com>>
>     Cc: "election-methods at electorama.com
>     <mailto:election-methods at electorama.com>"
>             <election-methods at electorama.com
>     <mailto: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 <mailto:Z%2B57aSwiiCXH8k8XYw 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
>
>
>
>
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info

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