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

[Ted Stern]

Hi Rob,

Your proposal makes sense to me for elections with a certain amount of
consensus.  However, it would be prudent to ensure that your method can
still yield a reasonable solution in the absence of clear consensus.

For example, say candidate A1 is the approval winner with 40%.  There are
no candidates in the Plurality Approval or Opposition Candidate pool.

My preference in such a situation would be to include

A1, the approval winner,
A2, the approval runner-up,
B, the approval winner after excluding all ballots that approve A1, and
must have excluded approval strictly less than 40%.

If total approval for A1 and B is less than 75%, I would continue including
the approval winner on ballots that exclude A1, B, and previous
complementary opposition candidates, until the 75% threshold is met.  In
the example above, A1's approval plus B's excluded approval could very
easily fall below 75%, so it would likely be necessary to include candidate
C, the candidate whose approval is highest on ballots that do not approve
of either A1 or B.

I think including A2 (even if A2 is different than B or C) is important
because with less than 50%, there isn't a strong consensus on A1.

Unfortunately this method does require a recount, but you can get A1, A2
and B with just a single summable count (accumulating the pairwise array of
votes for candidate i when candidate j is not approved), and in subsequent
counts, that pairwise array can help find both C and D if necessary.

On Sun, Dec 9, 2018 at 8:32 PM Rob Lanphier <robla at robla.net> wrote:

> 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.
> ----
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