[EM] Re: IRV-Approval hybrid

[Chris Benham]

Kevin,
I  have a couple of new ideas concerning  "Approval Elimination Runoff". 
 The first concerns how to deal with multiple majorities.
I now think that if  at any stage there are rival majorities, then there 
should  a runoff between the biggest majority candidate and the most 
approved majority candidate.  My intuition tends to the view that 
 compliance with Participation can survive one elimination runoff, but 
not more.
My other idea is: if we can have IRV "without elimination"  (RWE), why 
not  AER  also without elimination?  BTW, I  think we need a better word 
for psuedo- eliminate  than just "eliminate".  I suggest the word 
"shunt", as in one or some of the candidates is
"shunted" on to a side-list where they may be processed in a different 
way from candidates which remain on the "main" list.
Maybe this method could simply be called "Approval Runoff":
1. Voters rank the candidates, equal preferences and truncation ok. Also 
voters may place an approval cutoff  (or give Yes or No
to each candidate). Default approval cutoff  is between 1 and 2 (or Yes 
to  candidates marked 1, and No to the rest).
2. If any candidates are marked as 1 on a majority of ballots, then 
eliminate the rest. If there is more than one, then eliminate those that 
are neither marked as 1 on the greatest number of  ballots nor  marked 
as approved on the greatest number of ballots. If  2 remain after this, 
then they runoff.
3. If step2 did not apply, then shunt the least approved candidate on to 
a side-list, and  those ballots which solely marked this shunted 
candidate as 1, shall now contribute a vote (each) to the candidate(s) 
on the next-from-the-top preference level.
Does any candidate now have a majority? If yes, go to step 2.
4.If not, then shunt the candidate on the main (original) list with the 
fewest approvals on to the side-list. Ballots which , just prior
to the shunting, were contributing to the tallies of no other candidates 
on the main list, shall after the shunting, contribute a vote
(or a vote each) to the candidate(s) left on the main list that is 
marked as most preferred, and also to any candidate(s) on the side-list 
(that the ballot does not already contribute to) that  is preferred more 
or equally. If any candidate, on either list, has
now a  tally  which is more than half the number of ballots, then go to 
step 2. If not, repeat step 4, and so on.

Sorry if any of that is clumsy or unclear.

Chris Benham