[EM] Benham's method looks best ...

Forest Simmons fsimmons at pcc.edu
Tue Apr 29 16:55:27 PDT 2014


Michael,

Benham's other method MinLV(eq rank whole)Margins also elects C:

25 A>C
40 B>A
35 C>B

minLV's: B40>C35>A25

pairwise cyclic order B>A>C>B

The B>A defeat has a positive margin so it holds.
The C>B defeat has the least negative approval margin (-5 versus -10) so it
holds.
So the strongest beatpath (measured by approval margins) is C>B>A, and C
wins.

So Benham's two methods are the best contenders in the case of implicit
approvals.

If we allow explicit approvals, then it is reasonable for the sincere CW to
disapprove the other candidates, which changes the B ballots from 40 B>A to
40 B>>A.

The approval order is B75>C60>A25  The smallest (most negative) approval
margin is the -35 for the A>C defeat, so that is dropped, and the resulting
beatpath C>B>A is cemented in place.

Forest



From: Michael Ossipoff <email9648742 at gmail.com>
> To: "election-methods at electorama.com"
>         <election-methods at electorama.com>
> Subject: [EM] Benham's method looks best, among the Smith + CD methods
> Message-ID:
>         <CAOKDY5ANsUOE_r1BL8B_f6nHmJ=
> XFXLDbQDU0Gw5tOurjf8dTw at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> Benham's method can be vulnerable to burial when the CW has the smallest
> facton (lowest 1st choice vote). But what's the most important CW to
> protect from burial? What's the most likly size-comparison for the CW'
> faction?
>
> In every poll we ever conducted on EM, the CW was the Pluraliy winner.
>
> Which is more worth protecing? A CW of the smallest faction,or of the
> largest?
>
> Say there are 3 candidates A, B, and C.
>
> B is the middle CW. Sincere middle CW.
>
> The A voters bury B.
>
> How do the various Smith + CD methods do.
>
> At least one of them elects A, rewarding the brial.
>
> Some elect B  That's bette than electing A, but it doesn't deter burial.
>
> Of the Smith + CD methods I looked at, only Benham elects C in that
> scenario when A is the smallest faction.
>
>
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