[EM] Holy grail: PAR with FBC?

[Jameson Quinn]

Here's a new system. It's like PAR, but meets FBC, and deals with center
squeeze correctly in the few tricky cases where PAR doesn't. I'm
considering using the PAR name for this system, and renaming the current
PAR to something like "Old Par
<http://sr3.wine-searcher.net/images/labels/29/06/grand-old-parr-12-year-old-blended-scotch-whisky-scotland-10152906t.jpg>".
Meanwhile, the system below is temporarily called PARFBC
<http://wiki.electorama.com/wiki/PARFBC_voting>.


   1. Voters can Prefer, Accept, or Reject each candidate. Default is
   Accept.
   2. Candidates with a majority of Reject, or with under 25% Prefer, are
   eliminated, unless that would eliminate all candidates.
   3. Tally "prefer" ratings for all non-eliminated candidates.
   4. Find the leader in this tally, and add in "accept" ratings on ballots
   that don't prefer the leader (if they haven't already been tallied).
   5. Repeat step 4 until the leader doesn't change. The winner is the
   final leader.


...

This is pretty much a holy grail system from my perspective. It meets FBC
(I think; I don't have a proof, but it seems to me it should). It deals
with a simple chicken dilemma without a slippery slope. It deals with
center squeeze with naive ballots. I think it even meets the voted majority
Condorcet criterion, in an election with 3 candidates and where all ballots
use the full range (and you can add irrelevant "also-rans" to such an
election without breaking any compliances).

It has a sequential counting process like IRV, and so it fails summability;
but in most cases, step 4 will not change the outcome, so will happen only
once. (The main exception is if there's a voted Condorcet cycle.)

It even meets weakened versions of both Later No Help and Later No Harm;
weak enough so that they are compatible with the above passed criteria, but
strong enough so that I think most voters would be honest. Later No Help
holds if there's no possible Condorcet cycle; and Later No Harm holds if
the "later" candidate isn't on the edge of being eliminated.

I think that the explanation is clear and intuitive enough to be reasonably
acceptable to most voters. It involves only simple adding to tallies, not
anything couched in terms of sets or multiplication or the like.

Does anybody have any reason why this system should not be considered a
leading contender for "next step after approval"?
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