[EM] Holy grail: PAR with FBC?

[C.Benham]

> 1. Voters can Prefer, Accept, or Reject each candidate. Default is Accept.

This seems to assume that all the voters are interested in all the 
candidates and like checking boxes, whereas
I should think that a lot of voters would be only interested in their 
favourite and content to keep voting the
way they did under plurality (and would presumably continue to do so 
under Approval).

They should be allowed to continue giving the most effective vote 
possible by simply giving a "Prefer" rating to their
favourite.  In-effect penalising such voters for forgetting to also give 
"Rejects"  to all their non-favourites is unfair
and dumb.

It will give voters who aren't fans of the new method extra reason to 
resent it.  Suppose that a strong candidate
from an established party very narrowly loses just because some of 
his/her supporters forgot to give out "Rejects".
Don't you think that might fuel a movement to dump the method?

> 2.Candidates with a majority of Reject, or with under 25% Prefer, are 
> eliminated, unless that would eliminate all candidates.

I don't like arbitrary thresholds.  Obviously this causes failure of 
Irrelevant Ballots Independence. But also there is the problem
that the final exact number of valid ballots can be disputed and/or take 
quite a while to establish.

Postal votes can take a while to come in, or may be mislaid and later 
found. The validity of certain ballots can be disputed and
the subject of legal proceedings.  Some people might have initially been 
denied the right to vote, but then succeed in having that
over-turned and are then allowed to vote.

It is much better if the algorithm just (more-or-less directly) compares 
the candidates with each other rather than measure them against
arbitrary percentage-of-the-votes thresholds.

> 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.

As Kevin pointed out and you now concede, this fails FBC.    Kevin 
Venzke's post  included:
>
> I believe under your method, the only time a voter doesn't eventually 
> upgrade his "accepts" into "prefers" is if he prefers every tally 
> leader that ever comes up. I guess most of the time, accepts and 
> prefers end up counting the same. But the concern would be that there 
> are ballots out there that prefer all the tally leaders (including my 
> compromise choice, but excluding my favorite) and accept some 
> candidates worse than my compromise. In that case I could regret 
> voting for my favorite because of how it affects the influence 
> contributed by other voters.

It sounds to me from this that the method would also fail Mono-raise.


> I think it even meets the voted majority Condorcet criterion, in an 
> election with 3 candidates and where all ballots use the full range

49: A>C>>B
03: C>A>>B
48: B>C>>A

100 ballots.  C>A 51-49,   C>B 52-48,    A>B 52-48.

C is the "majority CW", but this method eliminates C and B.

Chris Benham


On 11/8/2016 12:57 AM, Jameson Quinn wrote:
> 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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