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
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