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

[Chris Benham]

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.

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