[EM] 3-slot method

[Chris Benham]

Participants,
I  am not really a fan of  these toy-like limited-slot ratings-ballot 
methods, but nonetheless I've recently been inspired to compose
one.  For want of  a prettier new name, it could be called  "Majority 
 Approval Runoff".

(1) Voters put the candidates into one  three slots,  Preferred, 
Approved, or Disapproved.  (Default is Disapproved).

(2) If not all the candidates are rated as Disapproved by a majority, 
then eliminate those that are.

(3) After the eliminations, candidates who are rated as Approved on 
ballots that rate no (remaining) candidate as Preferred
are promoted on those ballots to Preferred.

(4) Elect the winner of the pairwise comparison between the candidate 
who is (after steps 2 and 3) most Preferred and the
candidate who is least Disapproved.

Expanded  to more than three slots  (say, with an extra Disapproval 
slot) this has clone problems. Without the step 3 promotions,
there could in some situations be (more) incentive to not use the middle 
slot.
This gets right away from  Condorcet cycles, and Winning Votes  versus 
Margins. The individual steps are are all quite intuitive, and
so probably saleable (except perhaps for the 3-slot ballot).

I am sure it is better than the Bucklin-like 3-slot MCA and  3-slot CR 
 (the 1,0,-1 point count method). There is far less
disincentive to ignore the middle slot, and it meets a kind  of   Mutual 
Majority (aka Majority for  solid coalitions).

I  assume that the right strategy in this method, assuming the voters 
know who the three leading candidates are, is  give each of  these
candidates a different rating and then also rate as Preferred any 
candidate the voter prefers to the preferred leading candidate and
rate as Approved any candidate the voter likes less than the preferred 
leading candidate and (at least) as much as the Approved leading
candidate.

Here is a Burying example from James Green-Armytage:

40: A>C>B  (sincere is A>B>C)
46: B>A>C
07: C>A>B
07: C>B>A
100 ballots, B>A>C>B, B is sincere CW.

MAR  Disapprovals:                  A7,    B47,  C46.  (None are 
Disapproved by a majority, so none are eliminated.)
Approvals (including Preferreds): A93,  B53,  C54.  (A is most Approved)
Preferreds:                                  A40,  B46,  C14    (B is 
most Preferred)

A and B runoff,  B>A 53-47  so  B wins.

As I understand the latest  Kevin Venzke 3-slot Condorcet,  the least 
Approved candidate that pairwise beats all the candidates
with greater  Approval  wins.  In  this case that is  A, rewarding the 
Buriers.
I  have a contrary example, but in that example the Buriers' candidate 
is the most Preferred candidate with 49% of  the first-preferences,
and so that failure is far less serious (IMHO) than this one.

Comments are welcome.

Chris Benham