[EM] New 3-slot FBC method

[Chris Benham]

I have an idea for a new 3-slot method, and if people like it I'm open 
to suggestions for a name.
(It  is similar to and partly inspired by Douglas Woodall's  "ApAV" method.)

> 1. Voters give each candidate a top rating , a middle rating or no 
> rating.
>
> 2. Fix the winning threshold T at 50% of the total valid ballots. Give 
> each candidate a score equal to
> the number of ballots on which it is top-rated. If the candidate X 
> with the highest score has a score
> equal or greater than  T, elect  X.
>
> 3. If not, eliminate the (remaining) candidate which is given a top or 
> middle rating on the fewest ballots, and
> on ballots that now top-rate none of the remaining candidates promote 
> all the middle-rated candidates to "top-rated"
> and accordingly amend the scores.
>
> 4. Again, if the now highest scoring candidate X has a score of at 
> least T then elect X. (T does not shrink
> as ballots 'exhaust').
>
> 5. Repeat steps 3 and 4 until there is a winner. If  no candidate ever 
> reaches a score of T, elect the candidate
> that is top or middle rated on the most ballots (i.e. the Approval 
> winner).


Note that in the course of the count no candidates are ever "demoted" on 
any ballots from middle-rated to
unrated. Both the winning threshold and the elimination order is fixed 
at the start and don't change.

I think this is now my favourite method that meets FBC/SF. I have it 
meeting this and Mono-raise and 3-slot Majority
for Solid Coalitions, and Plurality and  Minimal Defense.

Comparing it with MCA and ER-Bucklin(Whole)  it seems to have a less 
severe LNHarm problem and no disadvantages
that I can see except that is slightly more complicated than MCA.

Also it has several advantages over "Majoritarian Top Ratings"(MTR).  It 
doesn't have as bad a Clone-Winner problem.

25: A>B
23: B>A
45: C
07: D

MTR elects C here while my suggested method ("majoritarian disapproval 
elimination"? MDE) elects A.  B is a clone of
A, and if  B is dropped from the ballots then both methods elect A.

MDE  probably fails Condorcet(Gross), but doesn't as easily fail  
Condorcet Loser.

5:A>B
5:B>C
5:C>A
3:D>A
3:D>B
3:D>C

Here MTR elects the Condorcet Loser and  Approval Loser D. I think MDE 
can only elect a Condorcet loser who
is the Approval winner.

Also in MTR zero-info. voters  with one big sincere ratings gap (so they 
are chiefly concerned that any one of the acceptable/good
candidates defeats all the unacceptable/bad candidates) have the weird 
incentive to randomly middle-rate half the unacceptable
candidates in the hope of artificially handing out some 
majority-strength defeats. In MDE those voters should simply not middle-rate
any of the candidates (certainly none of the Unacceptables).

MTR has a saleability problem in that it uses a pairwise mechanism as 
part of its algorithm (MDD), but then fails both Condorcet and
Condorcet Loser . I think MDE's algorithm is more natural and more 
appealing to say "IRV supporters".

I'm interested in any comments or corrections.

Chris Benham





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