[EM] Majority Approval Filter (MAF) - Draft 3

[Rob Lanphier]

Hi everyone,

I've made some progress on the Majority Approval Filter proposal,
which (as of December 7) I've published as "Draft 3" on electowiki;
<https://electowiki.org/wiki/MAF>

The current draft is more verbose, but I hope that it's clearer and
more straightforward than the last two drafts.  I've also published a
blog post introducing latest draft on my personal blog[1] and on
Medium[2]
[1]: https://blog.robla.net/2018/12/09/replacing-the-jungle-primary-december-edition/
[2]: https://medium.com/@robla/replacing-the-jungle-primary-december-edition-cf971801402c

Here's my simplified version of the explanation:
1. Select the candidate who receives the highest approval rating
2. Also add all candidates who receive greater than 50% approval
3. Possibly add opposition candidates if doing so is necessary to
ensure that at least 75% of the electorate has someone they hope to
vote for in the general election.  Limit the number of candidates who
qualify with 40%-50% approval to be less than or equal to the number
of candidates who qualify with 50%-75% approval.

I realize there's some handwaving in this simplified version, so I'm
including the full text of the important bits below.

Thanks especially to Ted Stern, but also to everyone who replied on
the "[EM] Approval-based replacement for jungle primary" thread.  I
greatly appreciate the later replies from Kristofer Munsterhjelm and
Richard Fobes, and I owe you two more detailed and direct replies to
their emails now that I've published Draft 3.

Rob
--------------
Addendum - Full definition of Majority Approval Filter (Draft 3)
Copied from <https://electowiki.org/wiki/MAF>):

### Goal ###

A set of rules for holding a primary election with an Approval
Voting-style ballot, providing motivation for all candidates to achieve
the highest approval rating, and resulting in a general election Ballot
Satisfaction Score of at least 75%. The "Ballot Satisfaction Score" is
the percentage of the electorate which approves of at least one
candidate on a given ballot.

### Pools ###

Candidates advancing to the general election must qualify for one of the
following "Pools". Candidates that don't qualify for one of the Pools
below are "Non-advanced Candidates". By default, all candidates are
Non-advanced Candidates until they qualify for one of these Pools:

-   "Supermajority Candidate Pool" - all candidates who receive greater
    than 75% approval
-   "Plurality Candidate Pool" - all candidates who receive greater than
    50% approval, but do not qualify for the Supermajority Candidate
    Pool. If no candidate receives greater than 50% approval, this pool
    will contain the leading candidate, who may have less than 50%
    approval.
-   "Opposition Candidate Pool" - a subset of candidates who receive
    greater than 40% approval, but do not qualify for the Plurality
    Candidate Pool

### Rules ###

Sequential steps for filling the above Pools with qualified candidates:

1.  Select the candidate who receives the highest approval rating. This
    is the "Top Candidate" and automatically qualifies for the general
    election ballot by one of the following rules:
    -   1a. If the Top Candidate receives greater than 75% approval, add
        this candidate to the Supermajority Candidate Pool.
    -   1b. If the Top Candidate receives less than 75% approval, add
        this candidate to the Plurality Candidate Pool.
2.  Complete the Supermajority Candidate Pool and the Plurality
    Candidate Pool using the following rules:
    -   2a. Add any Non-advanced Candidates with greater than 75%
        approval to the Supermajority Candidate Pool
    -   2b. Add any Non-advanced Candidates with less than 75% approval,
        but greater than 50% approval to the Plurality Candidate Pool
3.  Evaluate the Ballot Satisfaction Score (defined above) using the
    following rules:
    -   3a. If the Ballot Satisfaction Score is greater than 75%,
        candidate selection is complete. Skip to step 5
    -   3b. If the Ballot Satisfaction Score is less than 75%, proceed
        to step 4.
4.  If there is one or more candidates in the Plurality Candidate Pool,
    attempt to add an equal number qualified candidates to the
    Opposition Candidate Pool, evaluating each Non-advanced Candidate
    using the following steps
    -   4a. Find the Non-advanced Candidate with the highest approval
        score.
        -   If this candidate has less than 40% approval, no further
            candidates qualify to be added to the Opposition Candidate
            Pool. Proceed to step 5.
        -   If this candidate has greater than 40% approval, add this
            candidate to the Opposition Candidate Pool, then proceed to
            step 4b.
    -   4b. Compare the size of the Plurality Candidate Pool and the
        Opposition Candidate Pool
        -   If the Plurality Candidate Pool has more candidates than the
            Opposition Candidate Pool, skip back to step 3.
        -   If the Opposition Candidate Pool contains an equal number of
            candidates to the Plurality Candidate Pool, proceed to
            step 5.
5.  Candidate selection is complete. Advance all candidates in the
    Supermajority Candidate Pool, the Plurality Candidate Pool, and the
    Opposition Candidate Pool to the general election.