<div dir="ltr"><br><div class="gmail_extra"><br><br><div class="gmail_quote"><br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
Date: Wed, 30 Apr 2014 19:17:39 +0930<br>
From: "C.Benham" <<a href="mailto:cbenham@adam.com.au">cbenham@adam.com.au</a>><br>
To: <a href="mailto:election-methods@lists.electorama.com">election-methods@lists.electorama.com</a><br>
Subject: Re: [EM] Benham's Method looks best among Smith + CD methods<br>
Message-ID: <<a href="mailto:5360C6BB.4050903@adam.com.au">5360C6BB.4050903@adam.com.au</a>><br>
Content-Type: text/plain; charset="iso-8859-1"; Format="flowed"<br>
<br>
<br>
> You mentioned Chris's other method. Is that the one that does<br>
> Condorcet, measuring defeat-strengh by the defeater's Score minus the<br>
> defeated's score...where a candidate's Score is her pairwse support in<br>
> her strongest defeat?<br>
> That method elects C when B is middle CW, and the most favorite, and A<br>
> is least favorite, and A voters + C voters outnumer B voters, and the<br>
> A voters bury B?<br>
> Specific numeical instance of that example:<br>
> 2: A>C>B (burying B)<br>
> 4. B>A>C<br>
> 3: C>B>A<br>
<br>
I have this as indecisive between B and C.<br>
<br>
B>A>C>B. MinMax Losing Votes scores: B4 > C3 > A2. Margins Sort is<br>
indecisive as to which pair to flip: B>C or C>A?<br>
<br>
B>A (4-2 = 2), A>C (2-3 = -1), C>B (3-4 = -1).<br>
<br>
I haven't put much thought on how best to break such ties, but I'm<br>
inclined to say it should be in favour of the candidate with the higher<br>
score.<br></blockquote><div> </div><div>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.<br>
<br></div><div>In other words the defeats with strongest LV strengths are<br><br></div><div> C>B (3), B>A (4) ,<br><br></div><div>so C is elected.<br></div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
Here that is B, the sincere CW.<br>
<br>
Chris Benham<br>
<br>
On 4/30/2014 10:59 AM, Michael Ossipoff wrote:<br>
> Forest--<br>
> Oops! I forgot the A voters' transfer to C.<br>
> So Woodall does as well as Benham in that example. So my example<br>
> doesn't mean that Benham is better than Woodall. ...But Benham is a<br>
> lot easier to propose to organizations that use or offer IRV.<br>
> You mentioned Chris's other method. Is that the one that does<br>
> Condorcet, measuring defeat-strengh by the defeater's Score minus the<br>
> defeated's score...where a candidate's Score is her pairwse support in<br>
> her strongest defeat?<br>
> That method elects C when B is middle CW, and the most favorite, and A<br>
> is least favorite, and A voters + C voters outnumer B voters, and the<br>
> A voters bury B?<br>
> Specific numeical instance of that example:<br>
> 2: A>C>B (burying B)<br>
> 4. B>A>C<br>
> 3: C>B>A<br>
> Michael Ossipoff<br>
><br>
><br>
> ----<br>
<br>
-----------------------------<br></blockquote><div><br></div><div>And please disregard the following message!<br><br></div><div>Forest<br></div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
Message: 2<br>
Date: Wed, 30 Apr 2014 12:08:15 -0700<br>
From: Forest Simmons <<a href="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</a>><br>
To: Michael Ossipoff <<a href="mailto:email9648742@gmail.com">email9648742@gmail.com</a>><br>
Cc: "<a href="mailto:election-methods@electorama.com">election-methods@electorama.com</a>"<br>
<<a href="mailto:election-methods@electorama.com">election-methods@electorama.com</a>><br>
Subject: Re: [EM] Benham's Method looks best among Smith + CD methods<br>
Message-ID:<br>
<CAP29ondHpaF5tf+OFqLH7t0FBmP2O=U=<a href="mailto:Z%2B57aSwiiCXH8k8XYw@mail.gmail.com">Z+57aSwiiCXH8k8XYw@mail.gmail.com</a>><br>
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<br>
Yes, your description of the method is correct. However, as much as I like<br>
the idea it seems to have a fatal flaw:<br>
<br>
21 ABCD<br>
19 BCAD<br>
18 CABD<br>
14 DABC<br>
14 DBCA<br>
14 DCAB<br>
<br>
The losing vote scores (for strongest defeats) are D42>A35>B33>C32 .<br>
<br>
The Condorcet Loser D is elected.<br>
<br>
This example also shows failure of Clone Winner.<br>
<br>
By the way, I prefer Benham over Woodall for reasons similar to yours:<br>
Benham is more "seamless;" you don't have to compute the Smith set; in<br>
fact, you don't have to even mention it in the method description, unless<br>
you cannot resist the temptation to brag about it..<br>
<br>
Forest<br>
<br>
<br></blockquote></div><br></div></div>