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

[fsimmons at pcc.edu]

----- Original Message -----
From: Chris Benham
Date: Thursday, May 27, 2010 12:10 pm
Subject: Bucklin-like method meeting Favorite Betrayal and Irrelevant Ballots
To: EM

>  
> This is my suggestion as a good Favorite Betrayal complying
> method, as an alternative
> to SMD,TR.
>
> It uses multi-slot ratings ballots. I suggest 4-slot ballots as
> adequately expressive, so
> I'll define that version:
>
> *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.*
>
> By comparison with Bucklin  I think it just swaps compliance
> with Later-no-Help for Irrelevant
> Ballots, a great gain in my view for a method that fails Later-
> no-Harm.
>
> The incentive for voters to truncate and compromise (in other
> words not use the middle ratings
> slots) is less strong.
>
> 40: A>B
> 35: B
> 25: C
>
> Here (like SMD,TR) it elects the Condorcet winner A.  Bucklin
> elects B.
>
> 35: A
> 10: A=B
> 30: B>C
> 25: C
>
> Here (like SMD,TR) it elects B.  Bucklin elects C

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).
.
>
> The example is from Kevin Venzke. Electing B demonstrates
> failure of a criterion I called "Possible
> Approval Winner" (and Forest Simmons something like "Futile
> Approval"). It says that if the voters all
> enter an approval threshold in their rankings (always making
> some approval distinction among the candidates
> but none among those voted equal) that is as favourable as
> possible for candidate X without making X the thus
> indicated approval winner, then X mustn't win.
>
> In the example above B can't be more approved than A.
>
> 21: A>C
> 08: B>A
> 23: B
> 11: C
>
> Like Bucklin it meets the Plurality criterion. In this example
> where SMD,TR fails that criterion by electing A, it
> and Bucklin both elect C.


> Any comments?
>
>
> Chris Benham
>
>
>
>
>