[EM] Bucklin-like method meeting Favorite Betrayal and Irrelevant Ballots

[Chris Benham]

 My so-far nameless  attempt at fixing Bucklin:

*Voters fill out 4-slot ratings ballots, rating each candidate as either Top, Middle1, Middle2
or Bottom. Default rating is Bottom, signifying least preferred and unapproved.

Any rating above Bottom is interpreted as Approval.

If any candidate/s X has a Top-Ratings score that is higher than any other candidate's approval
score on ballots that don't top-rate X, elect the X with the highest TR score.

Otherwise, if any candidate/s X has a Top+Middle1 score that is higher than any other candidate's
approval score on ballots that don't give X a Top or Middle1 rating, elect the X with the highest
Top+Middle1 score.

Otherwise, elect the candidate with the highest Approval score.*

 35: A
 10: A=B
 30: B>C
 25: C

 Here (like SMD,TR) it elects B.  Bucklin elects C

Forrest Simmons wrote (28 May 2010):


It seems to me that this new method would elect A, since A has the most TR (45
>versus 40 for B) and the greatest total of approvals below top is only 30 (by C).

Forest,

The pertinent phrase in the definition is "any other candidate's approval score on ballots that don't
top-rate X".   A does have the highest TR score (45) but can't win in the first round because on ballots
that don't  top-rate A  (30B>C, 25C)  C has an approval score of 55.

B's TR score is 40 and is allowed to win in the first round because on ballots that don't top-rate B
(35A, 25C) the highest approval score is only 35.

C's TR score is only 25  so of the candidates allowed to win in the first round B has the highest TR
score and so wins. And in any case on ballots that don't top-rate C  (35A, 10A=B, B>C)  A has
an approval score of  45 so B is the only candidate that is allowed to win in the first round.

Thanks for taking an interest 

Chris Benham